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 Graded lessons in harmon' 
 
 3 1924 021 751 163 
 
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GRADED LESSONS 
 
 IN HARMONY 
 
 BY 
 
 F. H. SHEPARD 
 
 (Revised and Prepared by 
 A. Agnes Shepard and Florian A. Shepard) 
 
 Mr, Shepard is the Author of "Harmony Simplified," "Children's 
 Harmony," "How to Modulate," "Piano-Touch and 
 Scales," "Church Music and Choir-Train- 
 ing;," "Keyboard Diagram," Etc, 
 
 NEW YORK 
 
 G. SCHIRMER, INC, 
 
 3 East 43d Street 
 
 1914 
 
Ax^k'^^s 
 
 Copyright, 1914, by G. Schirmer, Inc. 
 
 All Rights Reserved 
 Entered at Stationers' Hall, London 
 
 Blanchard Press 
 
 Isaac H. Blanchard Company 
 
 New York 
 
FRANK H. SHEPARD 
 
BIOGRAPHICAL SKETCH 
 
 OF 
 
 FRANK H. SHEPARD 
 
 Frank H. Shepard was born in Bethel, Conn., in 1863. 
 At the age of fourteen he invented a machine by which he 
 was enabled to earn the money for a musical education. This 
 invention, simplifying the process of cloth production, was 
 prophetic of his later discoveries in Music. 
 
 From 18S0 to 1884 he studied organ with Eugene Thayer 
 and others in Boston and New York; did concert organ work 
 at the Great Hopkins (Roosevelt) Organ in Great Barringtoh, 
 Mass.; organized Boy Choir at Trinity Cathedral, Cleveland. 
 
 As a foundation for his original researches, Mr. Shepard 
 enjoyed the instruction of leading American and European 
 teachers, including nearly four years (1885-1889) at the Leip- 
 zig Conservatory, under Bruno Zwintscher and Dr. Paul for 
 piano; Homeyer, the Gewandhaus organist; Dr. Jadassohn for 
 harmony, counterpoint, canon and fugue; Herr Gustav 
 Schreck for free composition and form; and Torrsleff for 
 voice. 
 
 In 1889 he published Hozv to Modulate in which is pre- 
 sented the principle of "Attendant Chords," which gives a 
 deeper insight into the mysteries of Musical Structure, and a 
 working knowledge in more different directions than any other 
 single detail of Musical Theory. Not only does it supply a 
 simple, comprehensive plan for modulation, but it is equally 
 essential in analysis, improvisation, transposition and the 
 understanding of many foreign chords, like those at the begin- 
 ning of Mendelssohn's "Wedding March," or throughout his 
 "Spring Song." The book also contains the "Principle of 
 Artistic Modulation." 
 
 In 1890 appeared Piano Touch and Scales, containing prob- 
 ably the first presentation of the principle of relaxation. In 
 the same year came Church Music and Choir Training, giving 
 him a standing as an authority upon the training of the boy 
 voice and management of boy choirs. 
 
iv Graded Lessons in IJarmnny 
 
 In 1891 The Shepard School of Music was established at 
 Orange, N.J. The large three manual concert pipe organ 
 (Hutchings), now in the Recital Hall, was erected chiefly by 
 Mr. Shepard's own hands and completed in December, 1912. 
 
 In 1896 Harmony Simplified was published. Presenting so 
 much that was new, both in principle and practice, this book 
 was a most daring venture; the positions taken in the book 
 proved unassailable, no word of opposition ever reaching its 
 author; and its unprecedented sale among modern works of 
 its class is significant of popular approval. Mr. Shepard has 
 made several valuable contributions to the science and peda- 
 gogy of musical theory, contributions in the line of simplifica- 
 tion and systematic grouping. One, of the highest importance 
 to students, is his grouping of the seven most difficult chords 
 of music in one class, showing how they are all forms of one 
 and the same chord principle. By this method even the chords 
 of the Augmented Sixth, which have always been a bone of 
 contention among authorities on composition, become abso- 
 lutely simple both to form and to recognize. To understand 
 the inner meaning and qualities of the chord of the Dominant 
 Seventh, which Mr. Shepard shows as a foundation principle, 
 leads directly to the understanding of the structure and use 
 of the more complicated forms, such as the Diminished Sev- 
 enth, Dominant Ninth and the three forms of the Augmented 
 Sixth chord. The principle involved^ though simple, is prac- 
 tically universal in its application. 
 
 In 1899 appeared the Keyboard Diagram. 
 
 In 1901 Mr. Shepard began teaching Harmony by Corre- 
 spondence. 
 
 1906 saw the formal launching of the Shepard Piano Sys- 
 tem by Mail. The finding of the power of mental vitaliza- 
 tion, the rapid unfoldment of other principles from this, and 
 the crystallization into a distinctive system, make it worthy of 
 a distinctive name. As evidenced by the spontaneous expres- 
 sions of students from all parts of the world, the Shepard 
 Piano System is a new force in music study and teaching. 
 
 Many of the advances made in the piano work are of the 
 deepest significance, and when collected and applied in a logi- 
 cal, comprehensive system they form an epoch-making event 
 in the development of the science of piano teaching and study. 
 To Mr. Shepard's mind the work he accomplished in Harmony 
 had not one-tenth of the value possessed by his piano work, 
 which was the result of twenty years of search and study, of 
 experiment and discovery; and this, together with his promul- 
 
Graded Lessons in Harmoni/ v 
 
 gation of so many distinctive, diverse and important advances, 
 made him many grateful and warm friends all over the 
 world. 
 
 The years 1907-9 were partly devoted to the planning and 
 partial writing of books on Ear-training, Sight Singing and 
 Transposition. 
 
 In 1908 A Key to Harmony Simplified and a Classroom 
 Manual was published. This was the result of long years of 
 experience in the teaching of classes and individuals, and is 
 in large measure a systematic compilation of personal notes 
 to pupils, together with the best solutions (and explanations) 
 of the exercises assigned in Harmony Simplified. 
 
 During the last years of his life, and especially after the 
 publication of the Key, until his death in February, 1913, Mr. 
 Shepard devoted his best time and attention to the comple- 
 tion of the Shepard Piano System. This work, considered by 
 its author as by far his greatest achievement, was given 
 permanent form in the shape of a Correspondence Normal 
 Course — a form such that it may be easily imparted and 
 spread among all earnest musicians. By an almost superhuman 
 effort just before his death, Mr. Shepard gave to this Piano 
 Normal Course its finishing touches; and the nearly simul- 
 taneous completion of this system and of the home organ, 
 the one a symbol of his work, the other of his play — for 
 mechanics fascinated him as intensely as music inspired him — 
 formed the culmination of a life devoted to simplifying and 
 broadening musical principles and to stimulating musical 
 ideals. 
 
PREFACE 
 
 Mr. Frank H. Shepard, as teacher and pedagogue, re- 
 ceived such enthusiastic commendations and spontaneous 
 expressions of help and delight from those pursuing his 
 Correspondence Harmony Course, that it seems imperative 
 to present these lessons, together with his personal notes 
 and suggestions, in book form. To those who know Har- 
 mony Simplified it is hardly necessary to say simplicity, 
 thoroughness and practical application characterize the 
 contents of the lessons contained in this volume. 
 
 The first lessons reveal the "Laws of Relationship," the 
 real foundation of musical structure and the source of the 
 "rules." Part-writing becomes absorbingly interesting, 
 because principles are used instead of rules. The Key- 
 board Drill is unique and of great help to piano teachers 
 and students, as is the Ear-training. 
 
 These lessons are designed to help teachers to teach 
 Harmony in a simple and practical manner, having fully 
 as much reference to the needs of the performer as to 
 those of the composer. It provides the teacher with de- 
 lightful material for class talks, lectures and scientific 
 presentation of the subject in a logical manner. 
 
 This work supplies a new and vital element in musical 
 culture. It is not Harmony study alone, as generally 
 understood, for it differs in many respects. Some of its 
 unique features are: 
 
 (1) Keyboard Work. In order to make the work 
 practical for teachers and performers, much attention is 
 given to the formation and use at the keyboard, of the va- 
 rious Intervals, Chords, Cadences and other progressions 
 including also Improvising, Modulating and Transposing. 
 With the aid of the Keyboard Diagram this also becomes 
 possible in Harmony class work. 
 
ii Graded Lessons in Harmony/ 
 
 (2) The Replacing of the Numberless Rules for Part- 
 writing by a few broad principles, which explain hath 
 rules and exceptions. 
 
 (3) The Classification of the Chords of the Dominant 
 Seventh, Major and Minor Ninth, Diminished Seventh and 
 the three forms of the Augmented Sixth, as only slightly 
 
 DIFFERING FORMS OF ONE AND THE SAME HARMONY, simpli- 
 fying wonderfully these more complicated chords. 
 
 (4) "The Principle of Tendencies," which explains 
 many of the perplexing things in Musical Theory, and 
 simplifies the subject wonderfully. 
 
 (5) The "Attendant Chords," which make many for- 
 eign harmonies clear. 
 
 (C) Modidation, presented in a very simple and prac- 
 tical form. 
 
 (7) Studies in Analysis and Ear-training, with hints 
 on Improvising. 
 
 (8) The Knowledge of the Underlying Principles of 
 Acoustics, Musical Structure and Tone Relations, which 
 explain most of the mysterious things about which many 
 trained musicians are unenlightened. 
 
 (9) The Use of the "Sharpest Note" as a means of 
 analyzing foreign chords, which is a revelation to most 
 musicians. 
 
 The earnest student will find that the faithful study of 
 these lessons will build a practical musicianship ; will give 
 the power to do things at the keyboard; to hear and to 
 think music; to analyze, to modulate and to improz'isc. 
 The study should not only teach him much that he wishes 
 to know, but should broaden him mentally and musically. 
 This work goes right to the heart of music. 
 
 I take pleasure in acknowledging my indebtedness in 
 this work to a number of friends : in particular, to Mr. 
 Isaac H. Blanchard, my constant counsellor, for courte- 
 sies, personal and professional, in aid of my labor now 
 ended; and to numerous correspondence pupils of Mr. 
 Shepard and myself, who by their deep interest and 
 thoughtful questions have stimulated further thought and 
 have pointed out opportunities for the clearer expression 
 of ideas already formulated. For much time and care 
 
Graded Lessons in Harmony ix 
 
 spent in revising manuscripts, verifying references and 
 footnotes, and correcting proof sheets of the present work, 
 as well as for valuable suggestions during its preparation, 
 I am grateful beyond my power of expression to Miss 
 Violet L. Jacquin, whose personal connection with Mr. 
 Shepard for more than eight years has rendered her 
 sympathetic cooperation invaluable. 
 
 A. Agnes Shepaed (Mrs. F. H.), 
 Director of Shepard School of Music, 
 
 Orange, N.J. 
 September, 1914. 
 
CONTENTS 
 
 Lessons 1-4, §§1-42*. Scales. Material for study— The Ma- 
 jor scale as a principle — The Minor scales — Signatures — 
 Related keys — The Chromatic scales — The office of the 
 half-step — Principle of Melodic Tendencies — The meaning 
 of Scale Relationships — Keyboard exercises — Written 
 exercises — Ear-training — Drills — Questions and answers — 
 Collateral reading and suggestive notes. 
 
 Lessons S-8, §§43-68. Intervals. Material for study — Gen- 
 eral names — Specific names — Measurement of intervals — ■ 
 Inversions — Consonant and dissonant intervals — Disso- 
 nant intervals that sound well — Difference between Major 
 and Perfect intervals — Keyboard exercises — Drills — 
 Written exercises — Ear-training — Questions and answers 
 — Collateral reading — Suggestive notes — Daily technique 
 drill in theory. 
 
 Lessons 9-13, §§69-99. Triads. Material for study— The 
 principle of chord building — The alternate letter principle 
 — Chord structure in general — The material of music, or 
 the scale as the basis of all music — The specific forms of 
 triads : Major, Minor, Diminished and Augmented — About 
 the terra position — Improvisation — Bounding and Rocking 
 chords — Inversions — Principal and secondary triads — 
 Doubling — Figuring — Keyboard and written exercises — 
 Special drills — Methods of practice — Recitations — Variety 
 of drill — Ear-training — Questions and answers — Collateral 
 reading — Important notes. 
 
 Lessons 14-18, §§100-116. Part-writing — Triads. Material 
 for study — Connection of triads in simplest form — To 
 connect triads when there is no common note — How to 
 discover Consecutive Fifths and Octaves in written work — 
 To avoid the Augmented Second from 6 to 7 of the Minor 
 scale — Concerning the rule which requires the common 
 note to remain in the same voice — How to choose be- 
 tween two possible progressions — Hidden Fifths and Oc- 
 taves — Broken chords — Chord individuality — Correlative 
 character of different chord forms — Transposition — Key- 
 board and written exercises — How to use the Key — Ques- 
 tions — Collateral reading — Observations and special notes. 
 
 * Numbers refer to paragraphs. 
 
Graded Lessons in Harmony xi 
 
 Lessons 19-23, §§117-150. Chords of the Seventh. Material 
 for study — Construction — Positions — Inversions — Com- 
 bining the various positions and inversions — Figuring — 
 Consonance and Dissonance as a principle — The principle 
 of Tendencies — The principle of Resolution — Practical 
 application — The closing formula — Keyboard and written 
 exercises — Drills — Observations and notes — Questions and 
 answers — -Ear-training — Important collateral reading and 
 observations. 
 
 Lessons 24-26, §§151-158. Part-writing — Dominant Seventh 
 Chord. Material for study — The principles of Part- 
 writing — The principle of Harmonic Tendencies — Special 
 directions, hints, etc. — Perception of music through hear- 
 ing — Keyboard and written exercises — Questions — Ear- 
 training — Notes on advanced part-writing — Collateral 
 reading. 
 
 Lesson 27, §159. Cadences, — Elaborated Melodically. Ma- 
 terial for study — Passing notes — Improvisation — Key- 
 board and written exercises. 
 
 Lesson 28, §160. Harmonizing the Scale. Material for study 
 — Written exercises. 
 
 Lessons 29-33, §§161-172. Part-writing — Secondary Seventh 
 Chords. Material for study — Resolutions — Exercises with 
 non-cadencing resolutions — Keyboard and written exer- 
 cises — Questions — Ear-training — Collateral reading — Har- 
 monizing the scale — Analytical and comparative reviews. 
 
 Lesson 34, §§173-176. Introduction to Modulation. Material 
 for study — Modulation to Sub-dominant — To relative 
 Minor — Relative sharpness of scale tones — Processes — 
 Formula — Keyboard and written exercises — Notes. 
 
 Lesson 35, §§177-180. Attendant Chords. Material for study 
 — Preparation for modulation and analysis — Keyboard 
 and written exercises — Questions — Notes. 
 
 Lesson 36, §§181-185. Modulation — Use o£ Attendant Chords. 
 
 Material for study — Treatment of bass in inverted chords 
 — Drill — Keyboard and written exercises — Remarks — Har- 
 monizing the scale. 
 
 Lessons 37-38, §§186-191. Chord Analysis. Material for 
 study — Analysis of hymn tunes — Detailed process — Analy- 
 sis of piano music — Passing-notes — Material for analysis. 
 
xii Graded Lessons in Harmony 
 
 Lesson 39, §§192-198. Chord of the Dominant Seventh and 
 Ninth. Material for- study — Inversions — Preparation of 
 dissonances — Keyboard and written exercises — Drills — 
 Questions — Ear-training. 
 
 Lessons 40-42, §§199-215. Chord of the Diminished Seventh. 
 Material for study — Inversions — Study of roots and nota- 
 tion — To discover the key in which a foreign fundamental 
 chord is written — To proceed from the chord of the 
 Diminished Seventh to any one of the twelve Major and 
 twelve Minor keys — Keyboard and written exercises — 
 Drills — Notes and observations — Questions — Harmonizing 
 the scale. 
 
 Lessons 43-44, §§216-225. Chords of the Augmented Sixth 
 Material for study — The Augmented Six-three chord — 
 the Augmented Six-four-three chord — The Augmented 
 Six-five-three chord — Attendant chords may appear in 
 the form of the Augmented Sixth chord — Keyboard and 
 written exercises — Questions — Harmonizing the scale. 
 
 Lessons 45-47, §§226-230. Modulation. Material for study- 
 New tonality is thoroughly estabhshed by addition of the 
 closing formula — Ways and means of modulating — Drills 
 — Keyboard and written exercises — Questions. 
 
 Lessons 48-49, §§231-237. Altered Chords. Material for 
 study — Keyboard and written exercises — Questions. 
 
 Lessons 50-54, §§238-253. Paseing-notes — Suspensions. Ma- 
 terial for study — Keyboard and written exercises — Ques- 
 tions. 
 
 Lessons 55-56, §§254-266. Chord Analysis (Cont.). Material 
 for study — Analysis — Drill in transposing hymn tunes into 
 the four clefs and in reading orchestral music — Keyboard 
 and written exercises — Questions. 
 
 Lessons 57-60, §§267-285. Harmonizing Melodies. Material 
 for study — Review — Exercises in transposition, in writing 
 and at the keyboard — Original harmonization— Original 
 examples of hymn tunes and phrases written in free form 
 for piano. 
 
 Lesson 61, §286. Analysis and Form. Material for study — 
 Exercises. 
 
Remarks and Suggestions 
 
 The plan of this work is to carry on simultaneously 
 several different lines of training, to secure not only a 
 knowledge of Harmony, but also of other related subjects, 
 insuring a broad and useful culture in Music. Included 
 in the course arc: (1) Constructive work at the key- 
 board, which is the most helpful training ever devised for 
 the practical musician; (2) Harmony study proper, but 
 with Principles substituted for Arbitrary Rules, and many 
 new practical features; (3) Analysis; (4) Ear-training; 
 (5) Part-writing and Composition. 
 
 In the preparation of each lesson the student should 
 thoughtfully study the matter assigned, writing down 
 every question or observation that may occur. He will 
 then do the exercises, many of which may be done at 
 keyboard. In some lessons will be found a series of test 
 questions to be answered in writing. These answers, 
 with the written exercises and the record of the keyboard 
 exercises, together with incidental questions, might con- 
 stitute a recitation. This lesson should be corrected, 
 further test questions given to cover any vveak points 
 revealed by the recitation, and the advance lesson as- 
 signed. 
 
 Each lesson is designed to take from three to five 
 hours in preparation, including the Keyboard Drill and 
 Ear-training. Do not consider a lesson complete when 
 you have answered the questions and studied the subject 
 matter. Fully one-half of the time should be spent on 
 keyboard and other drill. 
 
 Systematic work is essential to real success. 
 
 Remember that in all this work the underlying thought 
 and the principles involved are of the first importance. 
 Many students think they have the whole matter when 
 they have written the exercises (without thought), or 
 have answered the questions without realizing the rela- 
 tionship to the foundation principles. 
 
 Facility in doing is just as necessary as knowledge. 
 The exercises are designed to give this facility and to 
 teach you to think musically either at the keyboard or 
 away from it. 
 
 Courage! Always approach your study with the 
 thought, / will, not I wish I could. 
 
"Untwisting all the chains that tie 
 The hidden soul of Harmony." 
 
 — Milton. 
 
THE SHEPARD 
 
 GRADED LESSONS 
 
 IN HARMONY 
 
 Note; Those using this volume* in teaching or for self- 
 instruction will find it necessary to have a copy of Har- 
 mony Simplified** and one of A Key to Harmony Simpli- 
 fied and a Classroom Manual*** by F. H. Shepard. 
 
 LESSON I 
 
 Motto — Not only Knowledge, but also Facility is to he 
 
 attained. 
 
 Let these Two Points control your study. 
 
 SCALES 
 The Major Scale As a Principle. 
 
 , 1. STUDY. 
 
 Read daily for one week Harmony Simplified, §§1-35, 
 45. Also, Collateral Reading and Suggestive Notes §12. 
 
 2. KEYBOARD EXERCISES. 
 
 (1) Form Half-steps and Whole-steps from any and 
 every note, as described in H. S., §1. N.B. — In teaching 
 
 * Paragraphs in The Shepard Graded Lessons In Harmony are referred 
 to as § — , 
 
 ** Paragraphs in Harmony Simplified are referred to as H.S., ^ — . 
 
 ***Key — , refers to sections in A Key to Harmony Simplified and a ClasS' 
 room Manual. 
 
2 Graded Lessons hi Harmony 
 
 children, this point should receive ample drill before con- 
 structing the scales. 
 
 (2) Learn to number the degrees of any scale. (H. S., 
 §§ 2-6.) 
 
 (3) Form the scales G, D, A, E, B, F-sharp and 
 C-sharp, numbering the degrees as you touch the cor- 
 responding keys, and observing the steps and half-steps. 
 Xote any difficulties. If you are not sure of the note^ 
 you may write the scales before playing them. 
 
 (4) Form similarly the double-sharp scales. (See 
 H. S., §7.) 
 
 (5) Form similarly the scales in flats. (See //. .S"., §8.) 
 
 (6) Form similarly the double-flat scales. (See H. S., 
 §9.) 
 
 3. SPECIAL NOTE. 
 
 For this first lesson it is more important to find the 
 principles involved — to discover the inner meaning of the 
 scale relations — than to have a recitation that is perfect. 
 Sometimes pupils think that this lesson is so easy that it is 
 simply something to be "gotten over with" as soon as 
 possible, and they are surprised enough to discover the 
 true beauty and the deep principles involved. The chief 
 point of the lesson is, then, not the correct writing of the 
 scales, but the discovery of the underlying thought. 
 
 4. WRITTEN EXERCISES. 
 
 (1) Following the pattern shown in Fig. 5 of H. S., 
 drawing the line from 5 down to 1 of the next scale, 
 write the above named Major scales. N.B. — At the end 
 of each scale, and on the same staff, draw a double bar 
 and then write the signature, taking it from the scale 
 as shown in H. S., §12. 
 
 5. RECITATION. 
 
 (Recite to yourself or to a friend.) 
 
 (1) Without seeing a keyboard, test as to the steps 
 and half-steps above and below any and every note. 
 
 (2) Recite the notes of the scale; that is, taking any 
 given scale, simply name the notes as they occur, not 
 forgetting the sharps or flats. If unfamiliar with the 
 
Graded Lessons in Harmony 3 
 
 scales you may follow the wording shown in H. S., 
 §4; but if able, you need simply mention the notes 
 alone. For example, the notes of the scale of B are 
 B, C-sharp, D-sharp, E, F-sharp, G-sharp, A-sharp, B. 
 If not too difficult for you, let this exercise include the 
 double-sharp and double-flat scales. Use the metronome 
 to test the speed you attain, naming one note to each beat. 
 
 6. EAR-TRAINING. 
 
 Read H. S., §§47-50. See also the special Ear-training 
 Exercises, §11. 
 
 (1) Try to sing (or hum or whistle) half and whole 
 steps above and below given notes upon the piano. Prove 
 by playing the note after singing it. 
 
 (2) Practice 1-5 of the Ear-training Exercises. 
 N.B. — Ear-training is not obligatory, but of extreme value, 
 and is recommended. 
 
 7. QUESTIONS.* 
 
 Commence to write the answers after a day or two 
 of study. 
 
 Note. Advanced students, if they feel quite sure they 
 have nothing to learn about scale-writing or key-relation- 
 ships, need write only two scales each, in sharps, flats, 
 double-sharps and double-flats. Even if they understand 
 the matter themselves, they may gain a point about how 
 to teach others. 
 
 (1) Where are the half-steps in the Major scale? 
 
 (2) State two or three foundation principles covering 
 its construction. 
 
 (3) For what are sharps used?f Also double-sharps? 
 
 (4) How many kinds of Major scales are there, and 
 why? 
 
 (5) For what are flats and double-flats used?f 
 
 (6) What is a signature?! Give its origin. f 
 
 (7) State the order of sharps in the signature ; of flats. 
 
 * For best results write original answers to these questions before reading 
 those given below. 
 
 t But few reach the underlying thought in these questions. 
 
4 Graded Lessons in Harmony 
 
 (8) Describe Tetrachords and their office in the order 
 of keys.* 
 
 (9) Give the order of scales with sharps; also with 
 flats. 
 
 (10) What is the difference between a scale and a 
 key ?f 
 
 8. ANSWERS. 
 
 (1) The half-steps in the Major scale are from 3 to 4 
 and from 7 to 8. This is a law, because it represents a fixed 
 relationship. A short formula for scale-construction is : 
 "The half-steps are from 3 to 4 and from 7 to 8. All other 
 steps are whole-steps." Let your pupils memorize this. 
 
 (2) (I) Do not write two notes upon the same degree of 
 the staff. (IT) Do not skip any letter. In other words, the 
 letters must be used consecutively, else it is not a scale. See 
 H. S.. §5. 
 
 (3) When we look deeply for the real principles, we see 
 that sharps and flats (also double-sharps and double-flats) 
 are used primarily and originally to make the scales alike or 
 to represent THE scale, i.e., the scale principle, at any and 
 all pitches. 
 
 (4) There is ONLY ONE KIND of Major scale, since the 
 different so-called scales are merely duplicates of the one 
 scale principle at different pitches, that is, in different keys. 
 Many people think that the scale of Ab is a different kind of 
 scale from the scale of D, for example; but a melody, or 
 musical thought, can be represented just as well in on-e as in 
 the other. 
 
 (5) For the same reason as with sharps — to make the 
 scales ahke; or to represent the one Major scale principle. 
 
 (6) This question is more frequently missed than almost 
 any other, for but few see the connection betzveen the scale 
 and th^ signature. The answer is : "A signature is the col- 
 lected sharps or flats used in forming the scale. Its source 
 is in the scale or in its uniform construction." Signatures 
 come from the scale — not vice versa. See how the scale 
 and its relationships are the true foundation, not only of 
 music, but of its notation as well. Also see this point later 
 in the notation of chords. 
 
 (7) The order of sharps is: F|, C», Gt, DJ, AJt, E«, 
 Bit. 
 
 * But few reach the underlyinR thought in these questions, 
 t These questions are designed to stimulate orifiinal thought. 
 
Graded Lessons in Harmony 5 
 
 The order of flats is : Bb', Eb, Ab, Db, Gb Cb, Fb. 
 Observe that one is the exact reverse of the other, and 
 tell why, if you can. 
 
 (8) Tetrachords are scales of four tones which come 
 from an old Greek form. They might be described in our 
 notation as half-scales, since we find in each Major scale two 
 Tetrachords, one placed above the other. Their office in the 
 order of keys is most important, as they explain some of 
 the most important matters in related keys and in musical 
 form. As each key or scale is related through its two Tetra- 
 chords to the scale having one more sharp, on the one hand, 
 and to the scale having one less sharp, on the other hand, we 
 have at once the familiar group of the three keys called the 
 Tonic, Dominant and Sub-dominant. 
 
 (9) The order of scales with sharps is G, D, A, E, B, 
 
 F#, at. 
 
 The order of scales with flats is F, Bb, Eb, Ab, Db, Gb, Cb. 
 Can you repeat the above quickly, and state the number of 
 sharps or flats in each key? 
 
 (10) The "scale" implies the regular succession of the 
 7 (or 8) tones; while ''key" implies the same relationships, 
 but with no particular order required. In both scale and 
 key notice that relationship of tones is implied, or the choice 
 of tones having fixed relations to each other. Remember 
 that relationship is the great foundation of music and the 
 original source of all its laws. (Think ^eeply on this last 
 statement.) 
 
 9. NOTE ABOUT DOUBLE-SHARPS AND DOUBLE- 
 FLATS IN THE SIGNATURE. 
 
 It is not customary to use double-flats or double-sharps 
 in the signature, although I do not recognize any reason 
 why they could not be used. At present it seems to be 
 the idea to express the key in the most simple manner; 
 other than this, I see no reason why the double-sharps or 
 double-flats should not be used in the signature. 
 
 When a key expressed by double-sharps or double-flats 
 is required in a composition, it is expressed by means of 
 accidentals; and some composers, after writing a few 
 measures with the accidentals- required, make an enhar- 
 monic change into the simpler form. For example, if the 
 required key is that of D(, which will contain two double- 
 sharps, the composer will probably (after modulating to 
 that key) write two or three measures in that key of DJ, 
 using the proper accidentals ; after which he will draw a 
 
6 Graded Lessons in Harmony 
 
 double bar and write the signature of Eb, which is the 
 simpler form, and continue in the key of Eb. By first 
 writing a few measures in the key of Dlt he recognizes the 
 true relationships of the keys, and having done this, he 
 continues in the notation which is easier for the performer. 
 
 10. HOW TO WRITE THE SCALES. 
 
 The scale should show: first, the skeleton, that is, the 
 figures ; second, the half-steps, by the curved line between 
 3 and 4, and 7 and 8 (also by the curved line between the 
 notes indicated by these figures) ; third, the tetrachords, 
 by means of the larger curved line as shown below; 
 fourth, the logical growth of the signature, by writing it 
 after the scale instead of at the beginning of the line ; 
 fifth, the relationship between the successive scales, by a 
 line drawn from the fifth down to the Tonic of the next 
 scale. 
 
 To show all these points, but one scale should be writ- 
 ten on a line. You will find this much better for refer- 
 ence, and it will be of great help to you in teaching the 
 scales. 
 
 Fig. 1. 
 
 A 
 
 Q 
 
 3^4- 
 
 Ear-Training. 
 
 11. (Read carefully H. S., §§47-52.) This work is a mat- 
 ter of Growth — not of rote learning. If you are deficient 
 in musical hearing, or have never given attention to the 
 subject, it will open a new world of pleasure, and will 
 become a new avenue of acquisition as well. 
 
 First establish the feeling for tonality or tone relations, 
 through the ability to sing (and recognize) the tones of 
 the scale and chord. These two elements — the scale and 
 the chord — are the foundation of all music. They are 
 given in the lines a) and b) of the Ear-training Exercises. 
 
 Next, take up a few of the simpler exercises — not more 
 than six — and work them every day for several weeks 
 before expecting them to be well done. Do not hurry: 
 
Graded Lessons in Harmony 7 
 
 you will gain most by sticking to the scale and chord for 
 a long time — several months at least, in many cases. 
 Above all, do not be discouraged if you do not succeed at 
 the first attempt. 
 
 Especially, listen intelligently, not only to music that 
 is performed, but also to every tone you play or sing, and 
 with this listening will presently come a new perception of 
 music. 
 
 This work is to be done without the aid of an instru- 
 ment. Take any convenient tone for "Doh.'' (For the 
 first few days it is allowable to test the voice, by touching 
 the piano after the tone or interval has been sung, and 
 while still sounding.) 
 
 After the first six exercises, and when the scale and 
 chord have been fairly accurate (though not necessarily in 
 their "absolute pitch"*) and are easily executed, it is time 
 to commence to add the other exercises gradually, one, 
 two or more each week, as the case may require. But 
 do not drop the scale and chord or the simpler exercises 
 until the feeling of the tonal relationships is established, 
 no: before you can both sing and recognize them when 
 given by another person. 
 Do Not Hurry This Work. Give it Time to "Grow." 
 
 EXERCISES. 
 
 a) Doh Ray Me Fah Soh Lah Te Dohi. Dohi Te 
 
 Lah Soh Fah Me Ray Doh. 
 
 b) Doh Me Soh Doh^ Soh Me Doh. 
 
 Take breath at all commas. 
 
 (1) Doh Me Soh, Doh Me Soh Me Doh Me Soh Doh^ 
 
 (2) Doh Doh^ Doh Me Soh Doh^ Soh Me Doh. 
 
 (3) Doh Ray Me, Doh Me, Doh Me Ray Doh, Me 
 
 Doh. 
 
 * To help you to get Absolute Pitch, when you enter a room where there is 
 a piano, try to sing Middle C or some other convenient tone. Then strike it 
 upon the piano for comparison and correction. You will be pleased to see how 
 after a short time you will be able to sing very close to the right pitch. The 
 drill can be continued by using other tones as well as C. This makes one criti- 
 cal and thoughtful along these lines. 
 
Graded Lessons in Harmony 
 
 
 (4) 
 
 The 
 
 (5) 
 
 Scale 
 
 (6) 
 
 'S-rs^N^ 
 
 (7) 
 (8) 
 (9) 
 
 fl 
 
 (10) 
 
 m^ 
 
 
 r^ 
 
 (11) 
 
 DOH' 
 
 
 TE 
 
 (12) 
 
 ta le 
 LAH 
 
 (13) 
 
 la se 
 
 se 
 
 (14) 
 
 SOH 
 
 
 sa fe 
 ba 
 
 (15) 
 
 FAH 
 ME 
 
 (16) 
 
 ma re 
 
 (17) 
 
 RAY 
 
 ra de 
 
 (18) 
 
 DOH 
 
 
 ti 
 
 (19) 
 
 
 (20) 
 
 
 (21) 
 
 DoH Ray Me Fah, Doh Fah, Doh 
 
 Fah Me Ray Don. 
 Doh Me Soh, Doh Soh, Doh Soh 
 
 Fah Me Ray Doh. 
 Doh Me Soh Lah, Doh Lah, Doh 
 
 Lah, Te Doh'. 
 Doh Lah. 
 Doh' Lah. 
 Doh Fah, Doh Lah, Doh Fah Lah 
 
 Doh' Lah Fah Doh. 
 Doh Ray Me Fah Soh Lah Te, 
 
 Doh Te, Doh Te Doh' Te Don' 
 
 Doh. 
 Doh Doh' Te Doh', Doh Te Doh' 
 
 Te Doh', Doh Te Doh' Soh Me 
 
 Doh. 
 Doh Me Fah, Doh Me Fah, Doh 
 
 Me Doh Fah Doh Me Doh Fah. 
 Doh Me Soh Doh' Soh Me Doh 
 
 Fah Lah Doh' Lah Fah Doh. 
 
 (Repeat.) 
 Doh Ray Doh Me Doh Fah Doh 
 
 Soh Doh Lah Doh Te Doh 
 
 Doh'. 
 Doh' Te Doh' Lah Doh' Soh 
 
 Doh' Fah Doh' Me Doh' Ray 
 
 Doh' Doh. 
 Doh Te, Doh Ray Me Doh Te, 
 
 Ray Doh Me Soh Te, Doh. 
 Doh Soh Me Doh' Soh Doh Me 
 
 Soh Doh' Me Ray Doh. 
 Doh' Te Lah, Doh' Lah Doh' 
 
 Lah Soh Fah Soh Lah Fah 
 
 Ray Soh Doh. 
 
 Take a lower pitch if necessary. 
 Doh' Ray' Me' Ray' Doh' Soh 
 
 Doh' Me' Ray' Doh' Soh' Fah' 
 
 Me' Ray' Doh'. 
 Doh' Me' Ray' Fah' Me' Soh' 
 
 Fah' Ray' Te Ray' Doh'. 
 Doh' Soh Lah Te Doh' Soh Me' 
 
 Doh' Soh' Soh Doh'. 
 
Graded Lessons hi Harmony 9 
 
 COLLATERAL READING AND SUGGES- 
 TIVE NOTES.* 
 
 12. (1) The key to unlock the secrets of Nature, as mani- 
 fested in any art or science, is the study of relationships. 
 Mathematics is the science of the relationship of numbers ; 
 astronomy, that of the relations of different heavenly 
 bodies. Harmony should then be, though it has not been 
 so to any marked degree, the science of tone relationship. 
 It is my purpose to take the simpler manifestations of Na- 
 ture for examination in this regard, and to draw such de- 
 ductions from them as will be helpful in later study. It is 
 presumed that the construction of the Major scale is 
 familiar; but the study of the scale in respect to relation- 
 ships will reveal principles which reach to the uttermost 
 bounds of the structure and form of music. 
 
 SCALE CONSTRUCTION. 
 
 (2) Statement. The scale of Nature and of Science is 
 the Major scale, the Minor scale being considered an arti- 
 ficial, derivative scale, since it is formed from the Major 
 scale. The Major scale will therefore form the basis of 
 the present investigation. 
 
 (3) Statement. A Major scale is formed by a succes- 
 sion of eight tones (technically, by a succession of sec- 
 onds). Between the third and fourth degrees and be- 
 tween the seventh and eighth degrees are half-steps ; be- 
 tween all other degrees are whole-steps. For illustration, 
 play the scale of C Major. 
 
 (4) Statement. This is the rule for the formation of 
 any Major scale. Briefly expressed for memorizing it is: 
 "Between 3 and 4, and between 7 and 8 are half-steps ; all 
 others are whole-steps." 
 
 (5) Deduction. Since the stepS and half-steps fall at 
 the (correspondingly) same places, all Major scales must 
 be alike. More scientifically expressed, there is but one 
 Major scale, which appears in different notations for con- 
 venience. 
 
 * For further notes, drills, exercises, topics for discussion, ear-training, 
 questions and answers, the student is referred to A Key to Harmony Simplified 
 and a Classroom Manual, by F. H. Shepard. This book will be referred to as 
 the Key hereafter. 
 
10 Graded Lessons in Harmony 
 
 (6) Deduction. Since the different scales or keys are 
 merely duplicates of a single type or scale form, all chords 
 and chord relations appearing in one key may be dupli- 
 cated with similar effect in any other key. In other 
 words, as the scales are alike, so the chords and their rela- 
 tionships in all Major keys must be alike. This fact is of 
 much value in the study of harmony, since in effect, we 
 need only to learn the structure and use of the chords of 
 one key in order to know the principles obtaining in all 
 keys. The foundation principles of harmony are few and 
 simple. The great need is to recognize and apply them in 
 a practical manner. 
 
Graded Lessons in Harmon 1/ 11 
 
 LESSON 2. 
 
 Motto — Facility is as ncccssai-y as knoidcdgc. 
 
 SCALES (Cont.) 
 
 The Major Scale (Cont.) 
 
 13. SCALE DEGREES AND SPECIFIC NAMES. 
 
 Study H.S., §§33, 34 together. Try to find out why 
 this subject is important, 
 
 14. DRILL. 
 
 (As per the exercises in H. S., §§33, 34.) 
 Taking two or three keys each day, drill thoroughly, 
 both at the keyboard — touching the proper key as its num- 
 ber or specific name is mentioned — and by recitation away 
 from the keyboard. 
 
 Continue this exercise till facility is gained in all Major 
 keys. Probably several weeks' daily drill will be neces- 
 sary. 
 
 15. IMPORTANT NOTE. 
 
 Although familiar with the scales in the way of per- 
 forming them with speed and accuracy, but few know 
 the scales in the manner here required, which is most 
 important, as it leads to the understanding of many impor- 
 tant matters. It is really the basis of speed in selecting 
 chords, in harmonizing a melody or in improvising. Here 
 especially, we must have not only knowledge but facility. 
 
 Following the idea expressed in H. S., §§33, 34, take 
 each scale in turn and play successively the notes forming 
 the Tonic, then the Sub-dominant and then the Dominant. 
 It is a good plan to let the fingers rest upon three keys 
 (the Tonic, Sub-dominant and Dominant notes) together 
 — not necessarily sounding them — that the mind may take 
 them in as a group, representing the most prominent fea- 
 tures of each key. 
 
 Be prepared to give this exercise daily drill for several 
 weeks. 
 
12 Graded Lessons in Ilarmovi/ 
 
 16. EAR-TRAIXIXG. 
 
 You are supposed to know the syllable names of the 
 tones — Doh, Ray, Me, Fah, Soh, Lah, Te (or Se), Doh. 
 It will help you in listening, to associate the following de- 
 scriptive names with the scale* tones. 
 
 Doh is called the Firm Tone. 
 
 Ray is called the Rising Tone. (To illustrate, play Doh, 
 
 Ray, then pause.) 
 Me is called the Calm Tone. (Play Doh, Ray Me; or 
 
 Soh, Fah Me.) . 
 Fah is called the Drooping Tone. (Play Ray, Me, 
 
 Fah; or Me, Fah, Me.) 
 Soh is called the Bright Tone. (Play Doh, Soh, Doh, 
 
 Soh ; or any of the military and cavalry calls.) 
 Lah is called the Sad Tone. (Play [high] Doh, Te, 
 
 Lah ; or remember how the Minor scale is formed, 
 
 starting upon the sixth step — or Lah — of the Major 
 
 scale.) 
 Te is called the Leading, or Rising, or Piercing Tone. 
 
 (Play up the scale to Te and pause, when the 
 
 urgent demand will be felt to go on to the eighth 
 
 step.) 
 
 17. EXERCISE. 
 
 Play or sing the scale slowly, and try to hear and feel 
 these qualities in the different tones. 
 
 Note. The great importance of this principle will be 
 apparent in the selection of the proper scale tones to express 
 any given sentiment or mood. For example, it would not 
 be right to emphasize the sixth step, or Lah, in a bright or 
 martial composition. This comes close to the heart 
 
 OF MUSIC. 
 
 The appreciation of the above will help you to sing cor- 
 rectly the Ear-training Exercises in §n. Carry this point 
 into your future practice. 
 
 *If you are associating the Ear-training with the key of C exclusively and 
 thinking letter names chiefly, you will make a serious mistake. Be careful to 
 use the syllable names and to "think" by syllables and by figures (1-3, 1-6, 
 etc.) in connection with the thought of the letter names. Remember tliat 
 letter names (C, G, etc.) express no relationships whatever, although some 
 musicians who are fortunate unconsciously feel and associate relationships with 
 the letter names — by ear, as it were: but the use of the syllables and figures 
 forces the recognition of relationship of tones, and gives constant suggestion 
 of the relative position of each tone in the scale, which is a vitally important 
 feature. 
 
Graded Lessons in Harmony 13 
 
 The Minor Scales. 
 
 Motto — The basis of all music is the scale. When you 
 understand all that is involved in scale relationships, 
 you will have a solid foundation for your theoretical 
 studies. 
 
 18. STUDY. 
 
 Read and study H. S., §§35-42, 46; also Key, 35-42, 46. 
 
 WRITTEN EXERCISES. 
 
 (a) Write the exercises in H. S., §38. 
 
 (b) Write the Melodic Minor scales, following the 
 order shown in H. S., §38. (For illustration, see H, S., 
 Fig. 16.) 
 
 (c) Write thei scale of G Major. Then change it to 
 the Harmonic Minor form, by altering the proper notes 
 by accidentals. (N.B. To save writing the scale twice, 
 you may enclose these accidentals in parentheses.) 
 
 (d) Repeat (c) with four other scales. 
 
 (e) Write the scale of A Major. Then change it to 
 the Melodic Minor form, by using accidentals as above. 
 
 (f) Repeat (e) with four other scales. 
 
 KEYBOARD EXERCISES. 
 
 (a) Remembering the rule for placing the steps and 
 half-steps, form all the Harmonic Minor scales, following 
 the order of signatures; i.e., A Minor, E Minor, B Minor, 
 etc. 
 
 (b) Form the same scales in the Melodic Minor form. 
 Play the above once each day for one week. 
 
 Relative Minor and Relative Major. 
 
 19. WRITTEN EXERCISES. 
 
 Write as required in H. S., §§39, 40.- 
 
 RECITATION. 
 
 Recite (to yourself or to a friend) the above exercises. 
 
14 Graded Lessons in Harmonji 
 
 Signatures in the Minor. 
 
 20. STUDY H. S., §§41 and 46. 
 
 WRITTEN EXERCISES. 
 
 (a) Write the exercises in H. S., §41. 
 
 (b) Write the exercises in H. S., §42. 
 
 21. To Distinguish Major and Minor in Printed Music. 
 
 Any given signature may indicate either a Major key 
 or its Relative Minor key. To discover which is intended, 
 look for the note which would be the fifth degree (Domi- 
 nant) of the Major key. If this note is raised by an 
 accidental, the key is the Minor. If unchanged, it is 
 Major. The reason for this is that it is this note which 
 is raised to make the leading tone in the Minor scale. 
 
 EXERCISES. 
 
 Examine Sonatas and other classical music, for exam- 
 ples of Minor keys. 
 
 22. EAR-TRAINING. 
 
 (a) Playing slowly and thoughtfully, contrast Major, 
 Harmonic Minor and Melodic Minor forms of the same 
 scale. Note the "color" or general tonal effect of each 
 form. 
 
 (b) Observe the effect of melodies written in the 
 Minor mode, and contrast them with Major melodies. 
 
 (c) Try to distinguish whether the compositions you 
 may hear are in the Major or Minor mode. Listen care- 
 fully. 
 
 23. QUESTIONS. 
 
 (1) How is the Relative Minor formed? 
 
 (2) Where are the half-steps in the Harmonic Minor 
 scale? 
 
 (3) What is the difference between the Harmonic and 
 the Melodic Minor? 
 
 (4) Name the keys related to G TMajor and give 
 reason therefore. 
 
Graded Lessons in Harmoni/ 15 
 
 (5) How would you discover a key from the signature 
 in sharps or flats? 
 
 (6) What is the signature of any Minor key? 
 
 (7) What is the office of the half-step in scale con- 
 struction ? 
 
 (8) Why is there an accidental in every Harmonic 
 Minor scale? 
 
 (9) Why does not this accidental appear in the signa- 
 ture? (See answer below, §24.) 
 
 (10) Was it there originally? 
 
 (11) How would you change a Major scale to an Har- 
 monic Minor scale of the same letter name (Tonic 
 Minor) ? 
 
 (12) How would you change an Harmonic scale to 
 the Major scale of the same name? 
 
 (13) Name the Dominant and Sub-dominant in all 
 Major and Minor keys. 
 
 (14) What do you understand by the term "Tonality" ? 
 How is it developed and how does it differ from the term 
 "Key"? (Read Key, (16) p. 12, after forming your 
 
 • answer to this question.) 
 
 24. ANSWER TO QUESTION 9. 
 
 The accidental change to make a leading tone in the 
 Minor scale is not shown in the signature because : 
 
 (a) It is not inherited from scale to scale; for exam- 
 ple, G#, leading tone in the scale of A Minor, becomes Cl 
 — the sharp is not inherited — in the next scale, that of E 
 Minor. 
 
 (b) Careful examination of this and other points 
 (such as the Melodic and Harmonic tendencies, and the 
 fact that the Minor scales appear in several different 
 forms,) indicates clearly to my mind that the Minor scale 
 is not a true, nature scale, but is an artificial or man-made 
 scale. Further, that from the Minor scale we find no 
 such great principles of relationship as can be deduced 
 from the study of the Major scale. 
 
 So, in considering signatures, instead of letting each 
 Minor scale inherit the sharps of the preceding scale, we 
 carry along constantly the fact that the Minor scale is 
 chiefly a re-arrangement of the resting points oi the Major 
 
16 Graded Lessons in Harmony 
 
 scale (that is, beginning and ending upoii six of the scale 
 instead of upon one), and that the signature should be 
 constantly considered as having been evolved from the 
 Relative Major. We like to think that the Minor scale has 
 no real foundation of its own, either Melodically, Har- 
 monically or in its relationships, and therefore its signa- 
 tures are merely derived from the Major scale and not 
 inherent in the Minor scale itself. 
 
 25. THE OFFICE OF THE HALF-STEP. 
 
 (1) The half-steps by their location determine the 
 quality, or color, or individuality, of the scale. For exam- 
 ple, in the Major scale they fall at 3 — 4 and 7 — 8, but 
 when their position is changed to 2 — 3 and 5 — 6 a certain 
 kind of Minor scale is developed. Observe that the Minor 
 scale is produced by changing the location of the half- 
 steps. When to the above mentioned Minor scale another 
 half-step is added by accidentally raising the seventh de- 
 gree, the Harmonic Minor scale is formed. 
 
 Examination of the old Dorian, Phrygian, Lydian and 
 other ancient modes (so called) will show how the 
 difference between these modes resulted entirely from the 
 differing locations of the half-step in the scale. (N.B. 
 To represent the Dorian Mode upon the piano, play upon 
 the white keys exclusively from D to the D one octave 
 above. The Phrygian is represented by playing upon the 
 white keys, from E to the E above, etc. Observe how 
 the Dorian has the half-step at 2 — 3 and 6 — 7, while in 
 the Phrygian they are at 1 — 2 and 5 — 6.) 
 
 Now, if you will consider the Special Note on "Indi- 
 viduality of the Scale Degree and Principle of Melodic 
 Tendencies,' §26, you will see how the character of any 
 scale tone must depend upon its relative distance from its 
 neighboring tones above and below, and therefore how 
 the half-step has great power in giving quality to the 
 scale. 
 
 The point is further illustrated by the upward ten- 
 dency of the Leading Tone of the scale (see H. S.. §152), 
 and by the change in the effect of individual scale tones 
 when they are accidentally raised or lowered to effect a 
 modulation. (This may be frequently observed in the 
 raising of the fourth degree to modulate to the key of 
 the Dominant, and in the lowering of the seventh degree 
 
Graded Lessons in Harmony 17 
 
 to modulate to the key of the Sub-dominant. These 
 changes are often found in hymn tunes, to which the 
 student is referred.) 
 
 The Chromatic scale also illustrates the principle, for 
 by the absence of variety or contrast in the distances be- 
 tween the scale tones, no single tone differs in power or 
 quality from the others, and therefore the scale seems to 
 have no special place of beginning or of ending unless 
 such place is indicated by the rhythm or accompanying 
 chords. (See below Special Note on the Scale Ten- 
 dencies.) 
 
 (2) The coincidence of the melodic tendencies and 
 the locations of the half-steps in the scale has an impor- 
 tant bearing upon the "Office of the Half-step," when 
 considered in connection with the thought that the quality 
 of each scale tone depends upon its relative nearness to 
 its neighbors, and that by changing this relative nearness 
 — by changing the places of the half-steps in the scale — 
 we can change the quality of any given scale tone and so 
 change the quality of the whole scale. For example, by 
 lowering the third degree of a Major scale the upward 
 form of the Melodic Minor scale is formed. Or if the 
 fourth degree of a Major scale is raised a half-step, a 
 completely new scale, that of the Dominant, is formed. 
 
 (3) Another rich suggestion may be found in the fact 
 that whole chords may be changed, as from Major to 
 Minor, etc., by changing a single note by a half-step. 
 For example, C-E-G is the triad of C Major, while C-Eb-G 
 is the triad of C Minor. 
 
 The above thoughts illustrate some of the powers of 
 the half-step. The subject, though possibly somewhat 
 indefinite at first, will grow upon the mind as advancement 
 is made in the study. Occasional review should be made 
 of this and other foundation principles. 
 
 26. INDIVIDUALITY OF SCALE DEGREES. PRIN- 
 CIPLE OF MELODIC TENDENCIES. 
 
 See also H. S., §152 et scq. 
 
 See also Collateral Reading, Lesson 4, §39, (13)-(14). 
 
 The effect of a scale is found by considering several 
 tones in succession, or in relation to each other, not by 
 thinking of tones isolated one from the other. Each tone 
 of the scale may therefore be considered as lying between 
 
18 Graded Lessons in Harmony 
 
 two other tones, that is, between the tone next above and 
 the one next below (e.g., in the scale of C, the note D 
 lies between C and E). Now if a tone is nearer to its 
 neighbor on one side than on the other, it is found to have 
 a tendency to progress to that nearer neighbor rather than 
 to the other, and this is called melodic tendency. To 
 illustrate, in the scale of C Major, E is nearer to F than 
 to D, therefore it tends toward F rather than toward D. 
 If, however, the neighboring tones are equally distant 
 the tone is free to progress in either direction. For exam- 
 ple, in the same scale A is equally distant from G on the 
 one side and from B on the other. A is therefore a free 
 neutral and not a tendency note. 
 
 It should be observed that the above theory, while 
 differing in substance from that given in H. S., reaches 
 the same result, viz., that the tendency notes of the scale 
 are found where the half-steps occur. 
 
 A slightly different theory is advanced by Goetschius, 
 as follows: The Tonic chord (for example C-E-G-C in 
 the key of C) represents the chief points of rest in 
 the scale and key. These notes may also be called "in- 
 active" notes, and the other tones of the scale, because 
 each tends toward one of these points of rest, are called 
 "active" or tendency tones. The active tones tend always 
 toward the nearest point of rest. In results this theory 
 corresponds with the other except in the case of the sixth 
 degree of the scale, which is classed as an "active" tone, 
 as it is nearer to the fifth degree of the scale than to the 
 eighth. The theory advanced by Goetschius applies par- 
 ticularly to the treatment of melodies while the other 
 applies directly to harmonic progressions. 
 
 By carefully comparing these three slightly differing 
 theories, we trust you will gain a real insight into this 
 matter, which is one of the most important underlying 
 principles of musical theory, explaining in thousands of 
 cases the reasons of ineffective and unmusical progres- 
 sions. 
 
 Spectal Note I.* About Tendency Tones, Active Tones 
 and Resting Tones. If we think of the two tetrachords in the 
 pcale, it is easy to conceive of the third degree as a Leading 
 Tone to 4 just as 7 is tlie Leading Tone to 8. This upward 
 tendency of the third degree appears when we modulate to 
 the key of the Sub-dominant. 
 
 * From lessons to pupils, 1913. 
 
Graded Lessons in Ilarmonij 19 
 
 But: the restful quality of the Resting Tones (1, 3, S, 
 and 8) is most important, and more constantly in evidence; 
 and the activity of 3 is not evident unless we modulate or 
 manage the progressions rhythmically so as to come to a stop 
 on the Sub-dominant chord. Therefore I do not empha- 
 size the upward tendency of 3, although it is scientifically 
 correct, perhaps. I now think it more practical to call 3 a 
 Resting Tone and ignore the tendency ; so please forget, until 
 later, that 3 tends up to the fourth. 
 
 This point is about the only thing in Harmony Simpli- 
 fied that I would like to change. 
 
 Special Note II.* About the Tendency of the Third 
 Degree of the Scale. When we consider the tetrachords sep- 
 arately, we see that the third degree is to the fourth degree 
 (constructively) just what the seventh degree is to the eighth 
 degree. Consequently it is not difficult to recognize in the third 
 degree a sort of leading tone to the fourth degree. In fact this 
 becomes apparent as soon as we modulate to the key of the 
 Sub-dominant : hence the statement of the upward tendency 
 on the part of the third degree. This I was taught by Eugene 
 Thayer, a great philosopher as well as musician. But at that 
 time I knew nothing of the Resting and Active Tones of 
 the scale, and all that they mean in music. I now prefer 
 to frankly abandon the thought of a tendency on the part 
 of the third degree, since to make it effective we have to 
 depart from the key, to a certain extent at least. The classi- 
 fication and consideration of a tendency of the third degree are 
 unnecessary to the understanding of the fundamental dis- 
 sonant chords (Dom. Sevenths, Dim. Sevenths, Aug. Sixths, 
 etc.) ; and there is so much to be gained by taking the third as 
 a resting point in the scale as explained in the Key to Har- 
 mony Simplified, page 8, §48, that we will simply ignore this 
 tendency as a' far-fetched and disturbing element which we 
 will eliminate from our work, for the present. 
 
 (This point is about the only thing in Harmony Sim- 
 plified that I would like to change.) 
 
 Special Note III. We get perhaps most of the ten- 
 dency feeling unconsciously through long association with 
 chords. For example, nine out of ten pupils have never felt 
 or thought of tendencies — or at least have not mentally rec- 
 ognized them. So in the Minor we have less feeling for ten- 
 dency between II and III, or V and VI, since the chords do 
 not emphasize the feeling: I would recognize only very 
 slight melodic tendencies in the Minor at these points. In 
 fact, the absence of law in the Minor (as compared with 
 the Major) is evidence to me that it is only an arbitrary, 
 man-made form, contrasting with the divine law in the Major. 
 
 * From lessons to pupils, 1913. 
 
20 Graded Lessons in Harmony 
 
 27. NOTE ABOUT THE SIGNATURE OF Db MINOR. 
 As this scale is the Relative Minor of Fb Major it 
 
 would, logically, have the same signature, which is eight 
 flats, and would therefore include one double-flat ; but in 
 practice it is never used, or at least I have never seen it : 
 the enharmonic key (CS Minor) is used instead. If, 
 however, the laws of form require the key of Db Minor 
 instead of Ct Minor, it would be expressed by accidentals, 
 so far as I know. Yet, if someone were bold enough to 
 publish a piece in the key of Db Minor and include the 
 necessary double-flat in the signature, I would commend 
 it ; for I see no reason why double-flats or double-sharps 
 should not be used in the signature with perfect propriety. 
 In your written exercises you may, if you wish, write the 
 signature of Db Minor with the double-flat, although, as 
 I say, custom does not support us in this. 
 
 COLLATERAL READING. 
 
 28. INDIVIDUALITY OF SCALE TONES; INTER- 
 
 NAL RELATIONS. 
 
 (1) Statement. The Tonic or Key Center. When any 
 note is chosen as the Tonic, or starting point of a scale, 
 a key-center is established, and certain definite relation- 
 ships are developed between the different scale tones, 
 which are expressed by the terms Dominant, Leading 
 Tone, Sub-dominant, etc. These relationships are in- 
 herent in the scale, and are of importance in our study. 
 
 (2) Statement. Resulting from the relations just 
 mentioned, certain tones of the scale possess peculiar 
 qualities which may be called tendencies. Investigation 
 proves that there are marked tendencies on the part of the 
 tone on the seventh degree to ascend, and of the tone 
 on the fourth degree to descend, when used under certain 
 conditions in melodic passages. Another tendency, less 
 marked, is that of the third degree to ascend.* These are 
 called melodic tendencies, since they exist independently 
 of harmonic effects. They are not laws, and these tones 
 are not obliged always to follow the directions indicated; 
 they are simply tendencies, or influences, which point 
 Nature's way, and which, under the right conditions, may 
 become sufficiently powerful to control. 
 
 *Read Special Notes I and 11, §26. 
 
Graded Lessons in Harmon;/ 21 
 
 (3) Deduction. Since these tendencies are inherent 
 in the single tone, we may expect them to be effective when 
 tones are combined in chords. This fact, hitherto but 
 little considered, is one of the most potent forces in 
 Theory, and will be considered again after a short time. 
 
 (4) Exercise. Find the tendency notes in different 
 scales. 
 
22 Graded Lessons in Harmony 
 
 LESSON 3. 
 
 SCALES (Cont.) 
 
 Related Keys. 
 
 Motto — Many important relationships and laws of music 
 rest upon the scale as a basis. 
 
 29. The related keys of any Major key are: first, the 
 keys of the Dominant and Sub-dominant Major; then, 
 the related Minors of all three, (i.e., the Relative Minors 
 of the Tonic, Dominant, and Sub-dominant) ; and lastly 
 (added by some authorities,) the Parallel Minor, or Minor 
 key of the same name. To illustrate, the keys related to 
 C Major are: first, G Major and F Major (which are 
 respectively the key of the Dominant and Sub-dominant) ; 
 then, A Minor, E Minor and D Minor (which are respec- 
 tively the Relative Minors of C, G and F ; and lastly, 
 C Minor (which is the Parallel Minor). 
 
 WRITTEN EXERCISES. 
 
 Write the keys related to each of the following Major 
 keys : G ; D ; A ; E ; B ; F* ; CS : Db ; Ab ; Eb ; Bb ; F. 
 Read also H. S., §334. 
 
 30. The related keys of any Minor key are : first, the 
 Dominant and Sub-dominant Minor; next, the Relative 
 Majors of all three (the Tonic, Dominant and Sub-domi- 
 nant) ; and lastly, the Parallel Major key (Major key of 
 the same name). 
 
 WRITTEN EXERCISES. 
 
 Write the keys related to each of the following Minor 
 keys : A ; E ; B ; G ; C ; F« ; Bb ; Eb ; Ab ; Db. 
 
 The Chromatic Scale. 
 31. STUDY H. S., §43. 
 
 WRITE Chromatic scales in the following Major 
 keys, by first writing the regular (Diatonic) Major scale 
 
Graded Lessons in Harmony 23 
 
 in the key, using the signature, and then filHng in the 
 Chromatic notes: — In the key of D; of A; of Bb. 
 
 Write in figures a formula for the Chromatic scale 
 which will apply equally to all keys. 
 
 32. STUDY H. S., §44. 
 
 First read the synopsis in H. S., §44. Then, referring 
 to the text-book, make an original synopsis from the text- 
 book, trying to see how one subject grows out of another. 
 
 33. INTRODUCTION TO CHORD BUILDING. 
 
 It is well to associate the Tonic chord (or chord upon 
 the first degree of the scale) with the study of the scales. 
 It should be played with one hand alone, and in its three 
 positions ( for example, C-E-G ; E-G-C ; G-C-E ; play 
 these three forms). This is described in H. S., §96 and in 
 the Key, 96. 
 
 KEYBOARD EXERCISES. 
 
 Play the Tonic triad in its three positions in all Major 
 keys; also, if not too difficult, in all Minor keys. Com- 
 mence at a slow tempo (e.g., M. M. 60, with two beats to 
 each chord) and increase the speed only as the forms 
 become familiar. 
 
 N.B. This exercise does not logically belong here, but it 
 will save time later to become familiar with it now. 
 
 .34. QUESTIONS 11-20, Key, pp. 13-14. 
 
 35. ANSWERS TO QUESTIONS 11-20, Key, pp. 13-14. 
 
 (11) By the term Related Keys is understood keys 
 which have several notes in common ; or better still, sev- 
 eral chords in common, since nearly all scales have several 
 notes in common. 
 
 (12) In the simplest series of relationship each key 
 is a fifth above or below its nearest related key. This 
 forms what is called the series of "Quint Relationships." 
 The other series is the series of Relative Minor and Rela- 
 tive Major Relationship which might be described as the 
 series of "Tierce (or Third) Relationships." In these 
 two relationships we can again see something of the logic 
 
24 Graded Lessons in Harmony 
 
 of chord structure, as the above relationships are illus- 
 trated in simple triads. 
 
 (13) The word Chromatic might be explained in two 
 almost opposite ways. First explanation : The term 
 means color; and the Chromatic tone instead of being 
 an original entity, possessing relationship of its own with 
 other tones in the key, is merely a colored or altered form 
 of some actual scale tone. Second explanation: The 
 word Chromatic might be considered as a colorless scale 
 since the element of contrast is absent for the reason that 
 the steps of the scale are all alike. This might be con- 
 sidered to make the scale wanting in color contrast, which, 
 like a roll of tape can be cut off at any point and seems 
 to have no design in beginning or in ending. In the 
 Major Diatonic gcale the half-steps and whole-steps form 
 such contrast that we are conscious of the individuality 
 of the tones comprising the scale, which individuality is 
 entirely wanting in the Chromatic scale. Read very care- 
 fully "The Office of the Half-step," Lesson 2, §25, and 
 "Individuality of Scale Degrees," Lesson 2, §26. 
 
 (14) It should be clearly seen that the Chromatic 
 tones are simply laid upon or interposed between the 
 tones of the Diatonic scale, and that the Diatonic scale is 
 the essence of the Chromatic, and all its relationships are 
 just as present as when the Chromatic tones are omitted, 
 leaving simply the Diatonic scale. Read Key, 43. 
 
 (15) In general, sharps are used going upward and 
 flats are used going downward; but it should be remem- 
 bered that a natural may sometimes perform the office of 
 an accidental sharp or flat, if it is used after a sharp or 
 flat normal scale tone. 
 
 (16) When a letter with sharp or flat appears in the 
 regular course of a scale, it is just as natural to that scale 
 as any white key in the scale of C, since all are scale 
 tones. In singing, the throat does not recognize black 
 keys — all are alike natural to the ear if in the scale. A 
 little Hibernian conundrum illustrates the point; I fre- 
 quently give it in class work: "When is a sharp not a 
 sharp?" The simple answer is: "When it is natural to 
 the scale." Though it may be rather silly, it contains a 
 most important truth, which you may need to consider 
 seriously and persistently in order to gain the full 
 meaning. 
 
Graded Lcssuns in llarmunij 25 
 
 (17) This formula is really the same as the formula 
 for the Diatonic Major scale given in Lesson I with the 
 addition of the interposed Chromatic or accidentally 
 altered notes : 
 
 Upward: 1, IS, 2, 2t, 3, 4, 4*, 5, 58, 6, 6#, 7, 8. 
 Downward: 8, 7, 7b, 6, 6b, 5, 5b, 4, 3, 3b, 2, 2b, 1. 
 
 If you will follow this formula you can write the Chro- 
 matic scale correctly in any Major key. From this you 
 will understand what changes to make to write it in a 
 Minor key. In all cases remember that the Diatonic scale 
 should appear unchanged and the other notes represented 
 as Chromatics. 
 
 (18) The chromatically altered tones always appear 
 following the unaltered or scale form of the same letter, 
 and never before it. For example, in making a note we 
 would never use F# before F. 
 
 (19) Some composers use the sharp fourth and flat 
 seventh (in the key of C this would be FS and Bb) in 
 hath directions, not changing FS to Gb coming downward 
 or Bb to AJ going upward. Their reason, I believe, is 
 that these two tones are characteristic of the Dominant 
 and Sub-dominant keys respectively, and being so closely 
 related and being frequently used for modulating from the 
 key, they have a legitimate place of their own. The 
 writer does not fully agree with this and will show when 
 we study Attendant Chords in H. S., how Gtf or many 
 other accidentals may be shown to be juSt as close to the 
 key as are these two favored accidentals. 
 
 (20) Originally the word Diatonic meant "through all 
 the tones" or through all the keys. This would seem to 
 imply the longer scale consisting of two tetrachords as 
 contrasted with the short or single tetrachord scale. Its 
 applied meaning in modern music is a scale having one 
 tone upon each letter and using all the letters as in regu- 
 lar Major or Minor scales. It is also especially used in 
 contrast with the Chromatic scale, or scale in which there 
 are two sounds or two tones representing one letter. 
 
26 Graded Lessons in Ilarmonii 
 
 Comparison of Terms Diatonic, Chromatic, Enharmonic. 
 
 "A uiATONJC change means change of pitch and 
 change of letter." 
 
 "A CHROMATIC change means change of pitch hut not 
 change of letter." 
 
 "An ENHARMONIC change means change of letter hut 
 not change of pitch." 
 
 36. NOTE OX THE CHRO.M.\TIC XOTATIOX. 
 This formula might be called the Harmonic: 
 
 1, 2b, 2=1, 3b, 3 = , 4, 4#, 5, Ob, Q^, 7b, 7», 1. 
 
 This recognizes the flat Third and the flat Sixth as sug- 
 gested by the Minor mode ; the sharp Fourth and the sharp 
 Seventh as being the characteristic accidentals leading to 
 the keys of the Dominant and Sub-dominant respectively, 
 which keys are included in the group of related keys — 
 or what is sometimes called the Larger Tonality. The flat 
 Second is also included by reason of its use in the chord 
 of the Augmented Sixth based upon the Dominant and 
 also upon the Neapolitan Sixth, neither of which can be 
 made clear until you have studied further. 
 
 Frequently this harmonic form is combined with or 
 substituted for the regular ascending and descending 
 forms as first given in this lesson. After becoming ac- 
 quainted with these various forms of the Chromatic scale 
 and the erratic way in which it is often noted, you will be 
 inclined to think there is no positive rule, but you will at 
 least understand the principles upon which different com- 
 posers proceed. 
 
 37. EAR-TRAINING. 
 
 How to Distinguish Half and Whole-steps. 
 
 The following suggestions usually prove helpful. They 
 are built upon the law of association. 
 
 (1) The half-step upward suggests to the mind the 
 ascending Chromatic scale. 
 
 (2) The half-step downward suggests the desire to 
 immediately return to the starting tone. To illustrate, 
 play 8, 7, 8 of the scale a few times in succession and then 
 play 8, 7 alone, when the ear will demand the completion 
 of the group and the return to the Key Note. Singers 
 
Graded Lessons in Ilarmoni/ 27 
 
 \\ill recognize this under the syllable order of Doh', Tc, 
 Doh'. It is merely a completion of the upward tendency 
 of the leading tone. 
 
 (3) The whole-step upward will suggest to the mind 
 the continuation of the Diatonic Major scale. 
 
 (4) The whole-step downward will suggest another 
 whole-step (downward) to complete cadencing series of 
 tones like 3, 2, 1 of the scale. This is an outgrowth of 
 the consideration of the Resting and Active Scale Tones 
 as described in the Key, 48. 
 
 With the aid of the above the student will be enabled 
 to distinguish between an ascending half and ascending 
 whole-step, for the one will suggest the Chromatic scale, 
 while the other suggests the Diatonic -scale. Similarly, a 
 descending half-step can be distinguished from the de- 
 scending whole-step, for the half-step suggests the imme- 
 diate return, while the descending whole-step suggests 
 further descent. 
 
 Please study the above carefully. 
 
28 Graded Lessons in Harmony 
 
 LESSON 4. 
 
 SCALES (Cont.) 
 Special Advanced Work. 
 
 Note. This lesson is not obligatory or even positively 
 necessary. Yet, if you fully master it, you will understand 
 something of the wonderful symmetry of Nature as re- 
 vealed in Music. 
 
 38. THE MEANING OF SCALE RELATIONSHIPS. 
 STUDY H. S., §§13-29. Also Collateral Reading, §39. 
 
 EXERCISES. 
 
 Write out, and also work out at the keyboard, all the 
 illustrations and exercises mentioned. Try to prove or 
 illustrate each individual statement, and find its bearing 
 on the rest of the matter. If you understand the exposi- 
 tion, try and make an original demonstration of the same 
 principles, using (as far as possible) different keys to 
 illustrate. Use your own language as much as possible, 
 first saturating your mind with the ideas by repeated read- 
 ings of the text mentioned above. Then answer the fol- 
 lowing questions. 
 
 (1) Do you see that 7 of one scale (seventh de- 
 gree of the scale) is the same letter as the fourth in the 
 "preceding" scale? 
 
 (2) Knowing that only one tone is changed in going 
 from one scale to the next in order, do you see that the 
 change is made by creating a new leading tone (by the 
 use of a new sharp) ; or by restoring an old leading tone 
 (either by taking away a sharp or by adding a flat) ? 
 
 (3) In connection with question 2, do you see that 
 creating a new leading tone takes us to the key having one 
 more sharp (the next scale in ascending order), while 
 restoring an old leading tone by removing a sharp (or 
 adding a flat) takes us to the next key in descending 
 order? 
 
 (4) Does this mean to you that taking away a sharp 
 
Graded Lessons in Harmony 29 
 
 is equivalent to adding a flat, or that taking away a flat 
 is equivalent to adding a sharp? 
 
 (5) Do you recognize that by going upward a fifth 
 you will reach the same letter as by going downward a 
 fourth ? Can you see this in the arrangement of sharps 
 and flats in the signature? Do you also see that going 
 upward a fourth is the same as going downward a fifth? 
 
 (6) Do you realize that the "Order of Sharps" gives 
 a series of fifths similar to the order of scales, though 
 not commencing on the same letter? 
 
 (7) Can you describe and illustrate a portion of the 
 Circle of Keys — for example, the changes made and the 
 inner meanings involved in the keys of C-G-D-A? 
 (N.B.) Take for a model answer Collateral Reading, (1)- 
 (2), §39. 
 
 (8) Similarly describe the descending process of that 
 portion of the circle commencing with D (two sharps) 
 and taking in succession the keys of G-C-F-Bb. See 
 Collateral Reading, (6), §39. 
 
 (9) Describe the process, ascending, in the following 
 keys: Bb, F, C, G, D. 
 
 (10) Can you give your impression of the relations of 
 sharps and flats, as shown in this process? 
 
 SPECIAL QUESTION. 
 
 Do you know any practical reason for studying or 
 even for the existence of the keys with double-sharps and 
 double-flats, when there is a simpler expression for the 
 same thing? 
 
 Answer. To illustrate the need of double-sharp keys: 
 A law of form requires the frequent modulation into the key 
 of the Dominant. If, for example, the Tonic is the key 
 of C#, the Dominant would have to be the key of GS — not 
 the key of Ab. This is because the fifth degree of the scale 
 of CS is Off and not Ab. The key of GS (a double-sharp 
 key) is thus related to the key of Off, whereas the key of Ab 
 is totally unrelated. It is therefore on account of the rela- 
 tionship of the keys that it is necessary sometimes to use 
 a double-sharp or a double-flat key instead of its simpler 
 equivalent key. 
 
30 Graded Lessons in Harmony 
 
 COLLATERAL READING. 
 
 39. SCALE ASSOCIATIONS. EXTERNAL RELA- 
 TIONS. 
 
 (1) Statement. Successive scales are formed by 
 using the note upon the fifth degree of each scale as the 
 Tonic, or starting tone, of the next scale. Following this 
 plan, each scale will have one more sharp than the pre- 
 ceding scale. 
 
 (2) Exercise and Illustration. Starting with the note 
 C, form successive Major scales at the keyboard or in 
 writing, or both. The fifth degree of the scale of C is 
 the note G, which will become the Tonic, or starting note, 
 of the second scale. This scale of G will have one sharp. 
 The fifth note of the scale of G is D, which will become 
 the Tonic of the third scale. The scale of D has one 
 more sharp than G, or two sharps. Continue similarly 
 to use the fifth degree of each scale as the Tonic of the 
 next scale. 
 
 (3) Statement. This series may be continued, by 
 using double-sharps, to the scale of B-sharp. This is 
 called the circle of sharps and includes every key, white 
 or black, in the octave ; that is, twelve keys, and so twelve 
 scales. 
 
 (4) Statement and Deduction. In each scale all the 
 sharps of the previous scale are retained, and one new 
 one added. This new sharp is always placed on the sev- 
 enth degree, or leading tone, of the scale, and may be 
 called the "Characteristic Sharp." From this fact we are 
 able to recognize any Major scale instantly, by noting the 
 fact that the keynote of any scale is one half-step above 
 the seventh degree, or leading tone. The seventh degree 
 is revealed by the location of the new sharp, which is 
 always placed at the right in the signature, as it is the 
 only one added. Therefore, the key is recognized as 
 being one half-step above the right-hand sharp in the 
 signature. To illustrate : In the signature of four sharps, 
 D-sharp is found furthest to the right. The keynote will 
 therefore be one half-step higher than D-sharp, and must 
 be in the key of E. Another and far more useful appli- 
 cation of this principle will be shown later in the discov- 
 ery of any fundamental foreign chord, one of the most 
 vague and difficult matters in the study of Theory. 
 
Graded Lessons in Harmon;/ 31 
 
 (5) Deduction. Scales having most notes in common 
 (notes belonging to both scales) form what is called re- 
 lated keys. The related keys or scales are, then, the one 
 having one more sharp and the one having one less sharp, 
 since in each case only one note is altered to create the 
 next succeeding scale. For example, the keys most 
 closely related to the key of G are : key of D, since that 
 has one more sharp than G; and key of C, since that has 
 one less sharp than G. By a similar reasoning — the notes 
 in common — the key of the Relative Minor is also consid- 
 ered as a related key. These are the keys most closely 
 related to any given key ; the one having one more sharp, 
 which is the key of the Dominant; the one having one 
 less sharp, the Sub-dominant, and the Relative Minor. 
 To these may be added, to complete the list of related 
 keys, the Relative Minor of the Dominant and the Rela- 
 tive Minor of the Sub-dominant. These relationships, the 
 result of similarity of construction, form the basis of the 
 choice of keys in classical compositions. For example, 
 in the sonata form it is customary to place the second 
 theme in the key of the Dominant. Similarly, in fugue 
 the "answer" to the subject is placed in the Dominant. 
 In song form the phrases are found usually in one or 
 another of the related keys. This relationship, when 
 applied in composition, secures unity in variety. It also 
 illustrates how simple laws of Nature afifect and control 
 the highest art forms. 
 
 (6) Statement. Beginning with the key of C, the 
 circle of keys with sharps was constructed by taking the 
 fifth degree of one scale as the Tonic of the next succeed- 
 ing scale. This process may naturally be reversed, for if 
 we start with a key having one or more sharps we may 
 find the key which shall have one less sharp, by counting 
 downward as many degrees as were counted upward 
 before. For example, let us start with the scale of D, 
 having two sharps — F-sharp and C-sharp. (The student 
 should follow this carefully at the keyboard or in writing.) 
 To find the scale which shall have only one sharp, simply 
 follow the scale of D downward to the fifth note from the 
 top, thus : D, a, B, A, G. The fifth note touched is G, 
 which will be the Tonic of the scale having only one 
 sharp. Comparing the scales of D and G, we find that 
 since C-sharp is the leading tone of the scale of D, and 
 therefore the one to receive the new sharp in that key, it 
 
32 Graded Lessons in Harmony 
 
 will necessarily be the note to lose its sharp when return- 
 ing to the scale of G. Now note especially that this 
 altered (in this case, the restored) note is the fourth 
 degree of the scale of G. Let us continue by descending 
 fifths, when by a similar process, the scale having no 
 sharps will be the scale of C. Further, the F-sharp, which 
 is the leading tone in the scale of G, is altered (restored) 
 to form the fourth degree of the scale of C. 
 
 (7) Deduction. While in the ascending series the 
 added sharp always falls upon the seventh degree of the 
 new scale or leading tone, in the descending series the 
 one note to be altered in each case falls upon the fourth 
 degree of the new scale. But since in descending the 
 fourth note of the new scale is the same as the seventh 
 note of the old scale, therefore in both cases it is the same 
 note which is altered. 
 
 (8) Statement and Illustration. Let us now continue 
 the descending series of scales, notwithstanding the fact 
 that there are no more sharps to remove. Five notes 
 downward brings the note F as the new Tonic. This 
 scale, according to §12, (3) and (4), must have B-flat as 
 the fourth degree. Now notice that this flat is introduced 
 at the point where in the other scales the sharp was 
 removed. The flat therefore performs the same office in 
 this scale as was performed by the removal of the sharp 
 so long as there were sharps to remove. This is like 
 the impecunious man who paid his debts, a dollar at a 
 time, until his money was all gone, and was then obliged 
 to give his note in further payment. It is also illustrated 
 by the algebraic proposition that the addition of a minus 
 quantity is equal to the subtraction of a plus quantity, 
 since the addition of the flat creates the same result as 
 the removal or subtraction of a sharp. It is still better 
 illustrated by the register of the thermometer in which 
 the key of C, having neither sharps nor flats, may be com- 
 pared to the zero mark, while those keys with sharps 
 represent the corresponding numbers of degrees above 
 zero, and the flat keys represent degrees below zero. 
 This is a most important principle, for the "relative 
 sharpness" of different keys and notes will be in con- 
 stant use after a few lessons. 
 
 (9) Deduction. Flats are the opposites of sharps: 
 taking away a sharp from a signature is the equivalent 
 of adding a flat, and vice versa. 
 
Graded Lessons in Harmony 33 
 
 (10) Deduction. As by using double-sharps a com- 
 plete circle of keys was formed, so by continuing as above, 
 by descending fifths, using double-flats where necessary, 
 a complete circle of keys with flats may be formed, con- 
 tinuing till D-double-flat is reached. 
 
 (11) Deduction. Since keys having more than six 
 sharps or six flats are unnecessarily complicated, by uni- 
 versal consent the first half of the sharp circle is supple- 
 mented by the first half of the flat circle, thus using the 
 simpler half of each, and yet embracing every Chromatic 
 note. 
 
 (12) Deduction. The question now arises, "Why, 
 then, did you go to the extreme with what might have 
 been a simple matter?" First, to show how marvelously 
 perfect and complete are the operations of Nature. Noth- 
 ing produced by the finite mind of man could result in 
 such absolute correspondence, each part proving the 
 whole by its perfect fitting with every other part. There 
 is not a flaw in the logic of Nature. It forms one more 
 proof of the existence of a higher power; and secondty, 
 it was carried to the extreme for the reason that occa- 
 sionally the more complicated keys are needed for correct 
 grammatical expression. For example, the Dominant of 
 the key of C-sharp is not A-flat, but G-sharp. In a 
 sonata, if the first theme is in the key of C-sharp, the 
 second theme should be in the key of G-sharp. Examples 
 of this are found in Beethoven's sonatas, where the true 
 key of a passage is shown by about two measures of many 
 accidentals, followed by the enharmonic change into the 
 simpler corresponding key. 
 
 (13) THE OFFICE OF THE HALF-STEP. State- 
 ment. As compared with the Major scale the Minor 
 scale is formed by a different arrangement of the half- 
 steps. It will not be possible to explain the Minor scale 
 in detail at this time, but a full exposition may be found 
 in the text-book mentioned above. It is here particularly 
 desired to call attention to the office of the half-step and 
 its power in music. In the case of the Minor scale the 
 changed locations of the half-steps are sufficient to create 
 the peculiar Minor quality. Further, in Collateral Read- 
 ing, §28, (l)-(3), the tendency notes are in each case, only 
 a half-step distant from the note toward which they are 
 drawn, displaying a sort of magnetic attraction. This 
 quality of the half-step is further illustrated below. 
 
34 Graded Lessons in Ilarmoni/ 
 
 (14) Statement. The Major scale has been described 
 as being made up by the union of two short scales of four 
 notes each, called tetrachords by the Greeks— thus 
 
 1234 567 8. Notice that the half-step concludes 
 
 each tetrachord. Upward scales always conclude with a 
 half-step, to give the feeling of completion. 
 
 (15) Deduction. A Major scale is composed of two 
 tetrachords. The last, or upper, tetrachord of one scale 
 becomes the first tetrachord of the scale having one more 
 sharp. 
 
 (16) Deduction. Similarly, or conversely, the first 
 half of one scale becomes the last half of the scale having 
 one less sharp. These two deductions show still more 
 completely the intimate relations of the scales. 
 
 The study of the scales reveals the wonderful order, 
 symmetry and perfection of the simple laws of Nature. 
 
 40. Note. The scale appears to be the very epitome of key 
 relations as well as of the wonderful tone relations and 
 qualities expressed in itself. Let me explain my meaning 
 in detail. You have learned how there are six keys related 
 to any given key, viz : the Dominant and Sub-dominant Ma- 
 jor, the Relative Minors of all three (that is, including the 
 Tonic as well as the Dominant and Sub-dominant) and fur- 
 ther, the Tonic Minor. Let us see how this works out in 
 the scale of C. Please take a piece of paper and write on it 
 the letter names of the scale tones as follows : C, D, E, F, G, 
 A, B, C. If you like, you may omit the last C, which is 
 merely a duplicate of the keynote. Now check off from this 
 list, the Tonic, Sub-dominant and Dominant and you have 
 the three keys representing the Major group. Now check off 
 the Relative Minors : first, of C, which is A ; next, of F, 
 which is D ; last, of G, which is E. Now we find everything 
 checked off, except the seventh or leading tone; let us lay 
 aside the consideration of this leading tone for a moment. We 
 may say in passing that the Tonic Minor is not, strictly 
 speaking, a related key, but is rather the same key with a 
 change of mode. Let us look at results: we have three 
 Major and three Minor keys; that is, each Major has its 
 Relative Minor. It seems to me almost like dividing the 
 key in perfect balance between the masculine and feminine. 
 Now, further, if you understand just a little of chord build- 
 ing, and I am sure you do, if you build the simple triads 
 upon C, F and G, you will find that in this key. C, they are 
 Major chords; whereas the triads built upon the Relative 
 Minors, D, E, and .\, form Minor chords. So here we find 
 
Graded Lessons in Ilarmont/ 35 
 
 a correspondence in the key between its Major chords and 
 the related Major keys; and between its Minor chords and 
 the Minor related keys. Can you not see how the key in its 
 content is a wonderful epitome of the whole scheme of key 
 relationship? This is to me one of the most wonderful 
 and beautiful things in the subject of Theory. 
 
 But now you question : "How, then, do you account for 
 the oversight in the case of the seventh degree?" The answer 
 is this : "The seventh degree is the variable one, or the point 
 from which the key reaches out toward other keys. You will 
 remember that in each case it is a leading tone which is cre- 
 ated or destroyed in going upward or downward in our circle 
 of keys ; and so Nature left out this tone as the changeable 
 one in the scheme of representing the great relationships of 
 music, through, and in, the scale. 
 
 41. QUESTIONS 21-27, Key, p. 14. 
 
 Remark: Teachers will find the "Topics for Discus- 
 sion" at the end of each chapter of "Key" of suggestive 
 value for classroom work. 
 
 DAILY TECHNIQUE DRILL. 
 
 Motto — // "Theory and Practice go together" be sure to 
 let Practice go with this Theory. 
 
 42. SPECIAL DIRECTIONS. 
 
 After completing the study of a subject, do not drop 
 it, but continue to spend a few minutes daily in keeping it 
 in mind, with the aid of this DAILY DRILL. 
 
 Take one or two keys each day, never less than one. 
 This will complete the circle of keys in one or two weeks, 
 giving real Facility. 
 
 Specific Names. 
 
 (1) (a) Name and play the notes representing the 
 specific scale names, in the following order : Tonic, Octave, 
 Super-tonic, Leading Tone, Mediant, Sub-mediant, Sub- 
 dominant, Dominant. 
 
 Note. This order will not be difficult to remember, if 
 it be noticed that the successive tones start as far as possi- 
 ble from each other, and approach as closely as possible, 
 giving' the order 1,8, 2, 7, 3, 6, 4, S. 
 
 To illustrate the above, in the key of D. The student 
 will recite (and play) as follows: Tonic, D; Octave, D; 
 
36 Graded Lessons in Harmony 
 
 Super-tonic, E ; Leading Tone, C# ; Mediant, FS ; Sub- 
 mediant, B ; Sub-dominant, G ; Dominant, A. 
 
 (b) Recite the above without reference to a key- 
 board. 
 
 (2) Repeat the above in the Parallel Minor key. 
 
 (3) Comparing the Major and the Harmonic Minor 
 forms of the scale we are now considering, state which 
 notes of the Major scale are lowered to make the Minor 
 form. 
 
 (4) Name and touch scale notes in the following 
 order : 1, 6, 4, 2, 5, 3, 1. Learn this order by heart. Some- 
 times use the specific names instead of the numerals. 
 
 To illustrate in the key of D as above, the student will 
 play the notes as he says, "1 (or Tonic) is D; 6 (or Sub- 
 mediant) is B; 4 (or Sub-dominant) is G"; etc. 
 
 (5) Recite the sharps in the order found in the signa- 
 ture. Recite the flats in the order found in the signature. 
 
Graded Lessons in Harmony 37 
 
 LESSON 5. 
 
 INTERVALS.* 
 
 Motto — By the study of intervals the inner meaning and 
 
 the uses of chords are revealed. By it we reach 
 
 the heart of music. 
 
 General Names. 
 
 43. STUDY. Read and study daily H. S., §§53-57 ; Key, 
 56, and Collateral Reading, §46, (3)-(6). 
 
 EXERCISES. 
 
 Referring to the sections above mentioned, the student 
 will, according to his advancement, go through all re- 
 quired exercises, first at the keyboard and then in writing ; 
 or he will take a part at the keyboard and the rest in 
 writing. In any case, they should be continued until 
 facility is attained. 
 
 RECITATION. 
 
 It will assist the power of quick thinking to recite a 
 few of the exercises to a friend; or to recite without a 
 listener, by setting the metronome at a slow speed and 
 naming one note of the required interval with each beat, 
 or by giving the correct answer to a question within a 
 certain limited number of beats. 
 
 44. EAR-TRAINING. 
 
 Following the directions given in H. S., §81 ct seq., 
 work as well as you can by yourself or with the help of 
 another. 
 
 , Use particularly the Ear-training Exercises, realizing 
 that when you sing two tones in succession a melodic 
 interval is formed. Realize also that intervals are (usu- 
 ally) made from the natural scale tones. 
 
 ♦Special Note, In taking up this subject it is well to observe that it is 
 divided into four general sections, which at first are studied ratlier independently 
 of one another, viz.: (1) The General Names of Intervals; (2) The Specific 
 Names; (3) Inversions; (4) Consonant and Dissonant Intervals. 
 
 Try to keep these four lines of study distinct in the mind. 
 
38 Graded Lessons in Harmony 
 
 Special Note. Seconds and sevenths are harsh disso- 
 iianics : we can hardly help discerning them. Thirds and 
 sixths suggest a chord by their mellow consonance. 
 
 The sixth is distinguished easily from the third: it is 
 much further apart. Fourths and fifths both sound "empty": 
 note how the fifth "warms up" when the third is added. 
 
 Fifths remind one of tuning a violin — the effect of the 
 open strings. 
 
 The fourths suggest a cavalry call on a horn. 
 
 A unison is a single tone. 
 
 An octave is a. tone and its "shadow" — not something dif- 
 ferent, but still slightly "brightened" by the higher pitch. 
 
 Keep these in mind in ear-training and ask yourself : "Is 
 it a sharp dissonance?" If not it cannot be a second or 
 seventh. (Note. One is the inversion of the other, hence they 
 are both in the same class.) "Does it sound ernpty?" If not, 
 it is neither a fifth nor fourth (again inversions — therefore 
 in the same class). So you eliminate them two at a time, 
 till you can answer "yes" to the question 
 Is it harsh? 
 Is it empty? 
 Is it sweet like a chord? 
 
 45. QUESTIONS 1-10, Key, p. 23. 
 
 COLLATERAL READING. 
 
 46. (1) The office of the intervals is seldom formally 
 stated; it is this: As chords are composite, being made up 
 of several intervals, the character of a chord must neces- 
 sarily depend upon the character of its intervals. The 
 best approach to a true understanding of chord structure 
 is therefore through the study of intervals. The exposi- 
 tion here given differs radically from accepted methods, 
 the attempt being made to reach results of practical value 
 through an appeal to the reason instead of to the memory. 
 
 (2) Statement. An interval, in the physical sense, is 
 an expression of distance between two given tones sound- 
 ing either together or in immediate succession. Artis- 
 tically, it is the effect produced by the two tones. While 
 it is necessary to a discussion of the subject to refer 
 almost exclusively to the physical interval the student 
 should continually think also of the effect or artistic result. 
 
 When the two tones of an interval sound together, it 
 is called an harmonic interval ; when sounding in succes- 
 sion, it is called a melodic interval. 
 
Graded Lessons in Harmony 39 
 
 GENERAL NAMES OF INTERVALS. 
 
 (3) Statement. The general name of an interval is 
 determined by the number of degrees of the staff included 
 in its extent, counting extremes, or degrees upon which 
 the notes stand, as well as those between, e.g., C-A (the 
 lower note is mentioned first) is a sixth, since six degrees 
 are involved ; G-B is a third, etc. 
 
 (4) Exercises, (a) Name the following intervals: 
 F-B; B-D; E-D; C-B; D-F; B-F; B-G; A-G; G-A; A-C. 
 (The answers are, respectively, a fourth, third, seventh, 
 seventh, third, fifth, sixth, seventh, second, third.) 
 
 (b) First at the keyboard and afterward in writing, 
 form the intervals of a sixth, third, fifth, seventh, second, 
 fourth and ninth from each of the following notes : F, A, 
 D, G, B, E and C. 
 
 (c) Describe the intervals found in the chord 
 G-B-D-F. Ans. G-B is a third, G-D a fifth, and G-F 
 a seventh ; B-D is a third, B-F a fifth, and D-F a third. 
 (These intervals are found by taking the different notes 
 in turn and considering in connection with those above.) 
 
 Similarly, describe the intervals found in the chord 
 A-C-F ; in the chord F-G-B-D ; F-B-D ; F-A-C-D. 
 
 (d) Describe the intervals found in the various chords 
 in printed music ; for example, in a hymn tune. 
 
 (5) Statement. The presence or absence of sh.arps 
 and flats does not affect the general name of an interval, 
 though the specific name may be changed, as will be seen 
 later. 
 
 (6) Statement. Extended Intervals. Duplication of 
 Notes. When the notes of an interval are more than an 
 octave apart they are considered just as if they were in 
 the same octave. In Theory neither distance nor duplicates 
 of notes affect the result. The relationships are taken as 
 those of the seven notes of the scale, irrespective of pitch 
 or duplication. The chief exception to this is the interval 
 of the ninth, which in the chord of the ninth needs to 
 stand at the full distance from the root of the chord. 
 
40 Graded Lessons in Ilarmontj 
 
 LESSON 6. 
 
 INTERVALS (Cont.) 
 
 Specific (or Descriptive) Names. Measurement of 
 Intervals. 
 
 47. Following the plan outlined in preceding lessons, study 
 the matter in H. S., §§58-69 ; in the Key, §§58-69 ; and in 
 Collateral Reading, §51. 
 
 KEYBOARD DRILL as outlined in H. S., Key and 
 Collateral Reading. 
 
 WRITTEX EXERCISES as outlined in H. S., the 
 Key and Collateral Reading. 
 
 N.B. Do not lose sight of the General Name of the inter- 
 vals when studying the Specific Names. 
 
 Special Note. Here is a very simple view of the Normal 
 intervals. Comparing the interval C-G and the interval C-A, 
 the first is a Perfect fifth and the second is a Major sixth. 
 But why? Here is the answer: 
 
 First take the notes of the interval C-G. The letter G 
 belongs to the scale of C Major, therefore the interval is 
 Normal. Now let us reverse the test : does C belong to the 
 scale of G Major? We find that it does; and since each 
 letter belongs to the other's scale, we say that the interval 
 is Perfect as well as Normal. 
 
 Now let us try the interval C-A. A belongs to the scale 
 of C, therefore the interval is Normal. But the reverse is 
 not true, for C does not belong to the scale of .^ Major (Cf 
 being the required note). Therefore we say that C-A is a 
 Normal interval, because the upper note belongs to the scale 
 of the lower note; but it is not a Perfect interval, since the 
 lower note does not belong to the Major scale of the upper 
 note. From the above we can deduce these rules : 
 
 Considering any given interval, if the upper note belongs 
 to the Major scale of the lower note, the interval is at least 
 Normal ; and if the lower note also belongs to the Major 
 scale of the upper note, the interval is also Perfect. In other 
 words, when the relationship is Normal in both directions. 
 it is the most complete relationship possible, and the interval 
 
Graded Lessons in Harmony 41 
 
 is called Perfect; but when the relationship is Normal in 
 only one direction (when only, one belongs to the scale of 
 the other), the relationship is not so complete and the intervals 
 are not called Perfect, but simply Major. 
 
 48. EAR-TRAINING. 
 
 Form with the voice Major thirds, starting in turn 
 from each (chromatic) degree within the octave. 
 
 After working for a few days with Major thirds, try 
 in turn Minor thirds. Perfect fourths, Perfect fifths, 
 Major sixths. Minor sixths, Major sevenths, Minor sev- 
 enths and Perfect octaves. Let this drill be carried 
 through possibly six months. 
 
 Please note that this drill has to do with intervals in 
 abstract; that is, having no relationship to any key. For 
 some musicians it is difficult to dissociate the tones from 
 Key Sense, but it is a very desirable power to have. It 
 is curious that with an unmusical person we have to 
 labor a long time to create this sense of Key Relationship 
 (for they hear almost nothing of it) ; and then that we 
 reverse the process and try to dissociate the hearing of 
 tones from Key Sense, in order to measure them more 
 accurately. 
 
 Note. In this chapter try to make no break in the daily 
 study, as it is desirable to gain a complete view of the subject 
 as soon as possible after undertaking it. The daily drill in 
 Lesson 8 will fix the matter in the mind and insure facility 
 if it should seem difficult at first. 
 
 -Remember that this {^'foundation work, and that the prin- 
 ciples here developed will be used always. 
 
 49. QUESTIONS 11-21, Key, pp. 23, 25, 26. 
 
 50. ANSWERS TO QUESTIONS 11-21, Key, pp. 23, 
 
 25, 26. 
 
 (11) The terms Major, Minor, Diminished and Aug- 
 mented may be called "comparative" or "descriptive" 
 terms, since by them we may compare . or describe the 
 various forms possible to any given interval. 
 
 (12) The Major is the standard of comparison, for 
 we say : "The Minor is one half-step smaller than Ma- 
 jor," etc. 
 
 (13) A Normal interval is an interval formed by 
 
42 Graded Lessons in Ilarmony 
 
 taking the first degree of any Major scale in connection 
 with any degree of the same scale. 
 
 (14) A simple way of measuring intervals is as fol- 
 lows : Compare with the Normal intervals, using the lower 
 note as a Tonic. This is more particularly described in 
 H. S., §§ 59-62, also §§ 65-07. 
 
 (15) The following intervals are called Perfect when 
 Normal ; primes, fourths, fifths and octaves. 
 
 (16) A convenient way of remembering which are 
 Perfect intervals is: (1) Think of the nearest related 
 keys (Dominant and Sub-dominant), remembering that 
 the octave is merely a duplication of the Tonic. An- 
 other way for more advanced students to remember is 
 to think of the chief chords of a key. Read Key, 75 (a). 
 
 (17) The Normal Major intervals are seconds, thirds, 
 sixths and sevenths. 
 
 Note. Both the Perfect and the Major intervals are more 
 easily remembered by observing that they occur in pairs; or, 
 in other words, in complementary groups as follows : (a) 
 Perfect intervals: Unisons and octaves, fourths and fifths; 
 (b) Major intervals : seconds and sevenths, thirds and sixths. 
 
 (18) The opinion of the writer is that Perfect inter- 
 vals may be considered in practical theory as a subdivi- 
 sion, rather than radically different from Major inter- 
 vals, since they are equally normal. 
 
 (19) Two reductions are required to change Major 
 intervals to their Diminished form. 
 
 (20) One reduction is required to change Perfect in- 
 tervals to their Diminished form. 
 
 (21) In this respect the Perfect intervals may be said 
 to differ, in that they have no Minor form. Read Key, 
 76. 
 
 COLLATERAL READING. 
 
 51. (1) Statement. Chords are dependent upon their 
 component intervals for their names, as "chord of the 
 sixth," "of the six-four," etc. Chords are similarly de- 
 pendent upon their intervals for their qualities, as Major, 
 Minor, Diminished or Augmented, being often named 
 from the most characteristic interval contained. There 
 are then, Major, Minor, Diminished and Augmented in- 
 
Grcidcd Lessons in Harmony 43 
 
 tervals. The Major interval is tal^eii as unit of com- 
 parison, Minor meaning an interval a half-step smaller 
 than the Major; Diminished, still smaller; and Augmented 
 meaning larger than Major. Formally stated, and more 
 accurately, the various intervals are : 
 
 _ . >• The standard of measurement. 
 Perfect j ^ 
 
 (The difference between the two is explained below.) 
 
 Minor, meaning less by a half-step than Major. 
 
 Diminished, meaning still less, or less by a half-step 
 than Minor or Perfect. 
 
 Augmented, meaning increased, or greater by a half- 
 step than Major or Perfect. 
 
 Note. A momentarily helpful explanation of the term 
 "Perfect" is that "those Major intervals which have no Minor 
 form are called Perfect." A more accurate statement is that 
 "those Normal intervals which have no Minor form are 
 called Perfect." But the meaning of the word Normal is 
 not yet clear, and the chief point at present is to consider 
 Perfect intervals, not as essentially different from Major, 
 but as a sub-division of the same class, the full distinction 
 to be seen later. Just now think of them as "those which 
 have no Minor form." 
 
 MEASUREMENT OF INTERVALS. 
 
 (2) The older way of measuring intervals is to count 
 the half-steps included in their extent, first memorizing 
 the number of half-steps in each of the different inter- 
 vals — a feat too difficult for the average person. The 
 following is offered as a simple, practical and valuable 
 method, involving, as it does, a constant comparison of 
 the different forms of the intervals. 
 
 (3) Statement. The Standard of Measurement. Con- 
 sider the scale of C upon the keyboard. From C to any 
 other degree of the scale of C Major, or from C to any 
 white key, is a Major or a Perfect interval, i.e., a Normal 
 interval ; e.g., the following are all Normal intervals : 
 C-D; C-E; C-F; C-G; C-A ; C-B ; C-C. Some of 
 these are Major intervals and some are Perfect, but 
 all are Normal. This gives us a practical standard of 
 measurement, by which any interval can be measured 
 
44 Graded Lessons in Harmony 
 
 and its quality determined; for by the definitions above, 
 a Minor interval is a half-step smaller than a Major in- 
 terval, an Augmented a half-step larger than the Major, 
 etc. To illustrate: C-A is a Major sixth; one half-step 
 less, or C-Ab, is a Minor sixth. When reduced again by 
 a half-step, to either C-Abb (double-flat) or CJf-Ab 
 (for either the upper or lower note may be altered), it 
 becomes a Diminished sixth. Again, compared with the 
 Major form, by increasing the distances by one half- 
 step an Augmented sixth is formed, C-Alt. (Note. The 
 Diminished sixth is seldom used in composition; it is 
 found here only for illustration.) For exercises see (7) 
 below. 
 
 (4) Major, Perfect, Minor, Diminished and Aug- 
 mented are comparative terms, being considered in re- 
 lation to the Normal, or standard of measurement. 
 
 (5) Statement. From the note C to any note of the 
 scale of C is a Normal interval. Similarly, from the key- 
 note of any Major scale to any note of the same scale, is 
 just as Normal, since the scales are simply duplicates one 
 of the other. (See §12.) For example, from F to any 
 note of the scale of F is a Normal interval ; from D to 
 any note of the scale of D, or from Bb to any note of 
 the scale of Bb, is a Normal interval. Therefore : 
 
 (6) Statement, (a) To form any required interval, 
 ask: "What would be the Normal interval?" Count from 
 the lower note, and then modify this Normal note as may 
 be required. 
 
 (b) To describe a given interval, find the Normal 
 interval, as above, and compare it with the given interval. 
 
 Illustration of (a). "Form an Augmented sixth from 
 E." Process: "The Normal sixth from E would be the 
 sixth degree of the scale of E Major, which is CS. As an 
 Augmented sixth is a half-step larger than the Normal, it 
 must be E-Cx (double-sharp). 
 
 Illustration of (b). "Describe the interval D-Bb." 
 Process: "The general name of this interval is a sixth; 
 the Normal sixth from the lower note, D, is B^. As 
 the given interval is a half-step smaller it must be a Minor 
 sixth." (N.B. (8) shows that the Normal sixth is 
 Major, and therefore has a Minor form. 
 
 (7) Exercises, (a) E-C* is a Major sixth. Change 
 it first to a Minor, and then to an Augmented sixth. (Ans. 
 
Graded Lesscnis in Harmony 45 
 
 The Minor sixth from E is E-C^ ; the Augmented sixth is 
 E-Cx.) Change the Major third F-A to a Minor third. 
 Change the Major sixth F-D to an Augmented sixth. 
 Change the Augmented second D-ES to a Major second; 
 to a Minor second. 
 
 (b) Form an Augmented sixth from F; from A; 
 from C ; from D ; from G ; from B. From the same notes 
 form Augmented fourths ; also Augmented fifths. 
 
 (8) Statement. The Perfect intervals are the Nor- 
 mal unisons, fourths, fifths and octaves. (Note. This 
 statement should be memorized. It will appeal to the 
 memory better by noting that the unison and octave are 
 complementary intervals, as are also the fourth and fifth. 
 Further, it should be observed that these intervals cor- 
 respond to the chief tones of the scale, namely, the Tonic, 
 Sub-dominant and Dominant — the octave being in scale 
 study the duplicate of the Tonic.) These figures, one, 
 four, five and eight, representing the Perfect intervals, 
 and also the chief tones of the scale, will be very fre- 
 quently under consideration. 
 
 The Major intervals are Normal seconds, thirds, 
 sixths and sevenths. Observe that the seconds and sev- 
 enths are complementary, as are the thirds and sixths. 
 There are then two pairs of Perfect intervals and two 
 pairs of Major intervals, if two complementary intervals 
 are taken as a pair. 
 
 (9) Exercise, (a) State whether the following inter- 
 vals are Normal, and if so, whether Major or Perfect. 
 Further describe these which are not Normal, as Minor, 
 Diminished, or Augmented ; C-G ; C-D ; D-C ; E-B ; B-F 
 B-E; E-F; FS-A#; FS-B; Fll-C; A-F; A-E; A-Ot; F-Bb 
 F-A; F-D; F-Eb. 
 
 (b) Form a Major sixth (upward) from each of 
 the following notes : D ; G ; C ; F ; B ; CS ; Eb ; Dt ; Ab ; Gb. 
 
 (c) Form Augmented fourths from the same 
 notes ; also Diminished fifths. Augmented sixths and 
 Minor sevenths. 
 
 (d) Form a Major third from D, and change to a 
 Minor third. 
 
 Form a Major sixth from E, and change to an 
 
 Augmented sixth. 
 Form a Perfect fifth from Ft, and change to an 
 
 Augmented fifth. 
 
46 Graded Lessons in Harmony 
 
 Form a Perfect fourth from Bb, and change to a 
 Diminished fourth. 
 
 (e) Describe each interval in the following chords: 
 C-E-G-Bb ; Ab-C-E-Flf ; C-D-FS-A; B-D-F-Ab ; GS-B-D-E. 
 
 (f) Similarly describe chords seen in your daily mu- 
 sical experience. (Make this your daily practice until 
 facility is acquired. He who would attain real familiarity 
 and facility with chords in analysis and at the keyboard 
 must first acquire the power suggested by these exercises.) 
 
Graded Lessons in Harmony 47 
 
 LESSON 7. 
 
 INTERVALS (Cont.) 
 Inversions in General. 
 
 52. STUDY: H. S., §§70-72; Addendum to §72, p. 42; 
 and Collateral Reading, §58 (l)-(6). 
 
 KEYBOARD EXERCISES. 
 
 Take the exercise in §70 of H. S., and play each inter- 
 val, giving the general name as it is played, and then play 
 it inverted, giving the general name of the inversion. 
 
 Continue this exercise by taking intervals from other 
 keys, remembering that the addition of sharps or flats can 
 never alter the generql name of an interval. 
 
 RECITATION. 
 
 Recite the above or similar exercises. 
 
 Inversion of Specific Intervals. 
 
 53. STUDY. Read and study daily, H. S., §§73-74, and 
 Collateral Reading, §58, (7)-(10). 
 
 KEYBOARD EXERCISES. 
 
 (a) Play the interval D-FS; describe it (that is, give 
 its specific name) ; invert it, and describe the inversion. 
 (Illustration: The general name of this interval is a third, 
 since three letters are involved. The specific name is a 
 Major third, since FJ is the Normal third in the scale of 
 D. (Remember th^t we "think" in the scale of the lower 
 note.) Inverted, the general name will be a sixth 
 (9 — 3^0) : and the specified name will be a Minor sixth, 
 since a Major interval becomes Minor when inverted. To 
 prove that this is a Minor sixth, by thinking in the scale 
 of the lower note we will find DS to be the Normal sixth. 
 from F# (remember that F# is now the lower note), and 
 
48 Graded Lessons in Harmony 
 
 therefore the Major sixth from F(. Now as D is a half- 
 step nearer to the lower note, the interval Fft-D is a Minor 
 sixth. Hence, we may conclude that D-FS is a Major 
 third, which inverted becomes F#-D, a Minor sixth.) 
 
 (b) Proceeding as in the above illustration, take each 
 of the following intervals, describe it, then invert and de- 
 scribe the inversion (the lower note of the interval is 
 mentioned first): E-C; G-B ; G-C; G-E; G-F; G-FS; 
 C-A • C-Ab ; C-Bb ; F-G« ; F-Ab ; F-B ; F-D ; F-DS ; F-Eb ; 
 D-D*; FS-C«; DJt-CIf; C»-Bb ; D«-G; Db-G; D-ES; G»-F. 
 
 54. WRITTEN EXERCISES. 
 
 Write the more difficult of the preceding exercises, 
 particularly those of which you are not absolutely sure. 
 Write at least one complete description, following the 
 foregoing illustration. In all of these written exercises 
 describe carefully the interval and its inversion. 
 
 RECITATION. 
 
 Recite some of the above with the metronome as pre- 
 viously suggested. 
 
 55 EAR-TRAINING. 
 
 Continue the study of the different intervals (see H. S., 
 §§87-88). The help of another person is valuable at this 
 point. If it cannot be obtained, try to concentrate the 
 attention upon the quality or character of the dififerent 
 intervals as you strike them at the piano. Also try to 
 sing the intervals— for example, taking the note C from 
 the piano, try to sing the Major Third and then the Minor 
 third. Proceed similarly with other intervals. Also learn 
 to listen to the quality of the different intervals and so dis- 
 tinguish them. This will be more fully treated in the 
 next lesson. 
 
 5G. QUESTIONS 22-29, Key. p. 2G. 
 
 Special Note. The usual cause of failure to grasp and 
 use the specific intervals and inversions is that we forget 
 to "think" in the scale on the lou'er note. Tf you have trouble 
 at this point, reread carefully H. S.. §§59-62, and Key. 59, 62. 
 
 .^.7. ANSWER TO QUESTION 22, Key. p. 20. 
 
 Extended Internals are those in which the two tones 
 are more than an octave apart, being considered as dupli- 
 
Graded Lessons in Ilarmoni/ 49 
 
 cations or extensions of similar intervals within the 
 octave. Their relationships are precisely the same as in 
 the cases of their smaller forms. Consequently, through 
 the action of this principle, when we construct a 
 large chord (even covering many octaves, as in the cases 
 of the orchestra or grand organ) no new principles are 
 introduced and no new relationships are developed. On 
 the contrary, the chord is considered merely as an enlarge- 
 ment of the simple form, resulting from the duplication 
 of notes in several octaves. (To analyze such a chord 
 this simple rule will suffice : Place all notes within the 
 compass of one octave, strike out duplicates of all letters, 
 and so reduce the chord to its simplest form.) 
 
 ANSWER TO QUESTION 25, Key, p. 26. 
 
 This question is intended to bring out the wonderful 
 quality of chords, in the following respect : that vvhen 
 inverted they do not change their real quality, in spite 
 of the fact that by inversion all the Major intervals in the 
 chord become Minor intervals, all the Diminished become 
 Augmented, and vice versa. To illustrate more clearly, 
 let us take the triad C-E-G and invert it, so that it be- 
 comes E-G-C. Now observe that the Major interval C-E 
 of the first form becomes Minor E-C in the inverted form. 
 Now observe that the chord E-G-C is just as much Major 
 now as it was in the original form, C-E-G. This brings 
 us to the thought that it is not mere presence of the Major 
 or Minor interval in the chord which makes that chord 
 Major or Minor, but it is the relation of each tone in the 
 chord to the root, which gives the real character to the 
 chord. This correlative quality of intervals, by which a 
 Major third may become a Minor sixth and yet not give 
 a Minor quality to the chord, is one of the most wonderful 
 provisions of Nature. Without this quality we would be 
 entirely unable to use chords in their various inversions 
 and positions, for every new form would necessarily give 
 a new character to the chord. Please think very deeply 
 upon this. 
 
 ANSWER TO QUESTION 27, Key, p. 20. 
 
 A Discord is simply a disagreeable sound ^ a Disso- 
 nance means something unfinished, or incomplete, or un- 
 restful. 
 
50 Graded Lessons in Harmony 
 
 A dissonance may be very beautiful in effect, for exam- 
 ple: The chord of the Dominant seventh is a dissonant 
 chord and yet it is a favorite chord; it is dissonant be- 
 cause it is unrestful or needs something to follow to com- 
 plete the thought. Dissonance is the proper technical 
 term to use, not discord. 
 
 COLLATERAL READING. 
 
 58. INVERSION OF INTERVALS. 
 
 (1) Statement. An interval is inverted by changing 
 the relative positions of the two notes; the upper one • 
 being lowered one or more octaves till it stands below the 
 other note, or, the lower note being raised till it stands 
 higher than the other ; e.g., C-F by inversion will become 
 F-C; D-F becomes F-D, etc. The use of this principle 
 becomes apparent when we observe that the different 
 notes of a chord appear in various order, first one note 
 and then another being highest or lowest. 
 
 (2) Exercise. First at the keyboard and then in 
 writing, invert the following intervals : C-E, B-F, F-C, 
 E-D, D-B, E-F, G-B, etc. 
 
 (3) Statement. To determine the interval which shall 
 result by inversion, subtract the number of the interval 
 from 9 ; e.g., a third by inversion will become a sixth, 
 since 9 — 3=6. 
 
 (4) Exercises. What interval will result by inverting 
 D-F? Answer; D-F is a third, and the inversion will be 
 F-D, a sixth, since 9 — 3^6. Similarly, describe the in- 
 versions given in (2). 
 
 (5) Statement. Complementary Intervals.* Any in- 
 terval and its inversion taken together form what are 
 called complementary intervals, or intervals necessary to 
 complete the octave. Read Key, p. 21: "Complementary 
 Intervals." 
 
 *The term "Complementary Interval" is in a way only another expression 
 of the word "inversion." Its special office, however, is to call attention to the 
 fact that the two intervals (i.e., the given interval and its inversion), together 
 always extend over exactly an octave, each one complementing the other and 
 rounding out the octave. 
 
 The deeper meaning implied is that the whole of music taken as a science 
 is in a sense contained within the octave. It is a little difficult to make this point 
 clear in words. It is rather something which is gradually absorbed as these 
 various principles are studied in their relations and interrelations with each 
 other. 
 
Graded Lessons in Harmony 51 
 
 (6) Exercises. What is the interval complementary 
 to the fourth? To the seventh? To the fifth? To the 
 unison? To the sixth? To the third? To the second? 
 To the octave? 
 
 (7) Statement. 
 
 By inversion Major intervals become Minor. 
 
 By inversion Minor intervals become Major. 
 
 By inversion Augmented intervals become Diminished. 
 
 By inversion Diminished intervals become Augmented. 
 
 By inversion Perfect intervals remain Perfect. 
 
 (8) Observation. In the foregoing table the correla- 
 tive or complementary quality of Major and Minor, and 
 of Augmented and Diminished, become very clear. The 
 importance of the principle will be noted when the differ- 
 ent chord forms (positions and inversions) are under con- 
 sideration, for in the absence of these complementary or 
 correlative qualities a chord would often completely 
 change its character by inversion. To illustrate :' In the 
 chord G-B-D-F is a Diminished fifth, B-F. In the inver- 
 sion of this chord, D-F-G-B, the same letters, B-F, by 
 inversion become F-B, which is an Augmented fourth. 
 Now, if Diminished and Augmented intervals were not 
 complementary or correlative, the character of the chord 
 would necessarily be changed by the inversion. That the 
 character is not changed is one more illustration of the 
 perfect working of Nature's laws. 
 
 (9) Observation. While Major and Minor are cor- 
 relative, as are also Diminished and Augmented, the Per- 
 fect intervals remain in a class by themselves. This is 
 an important difference between Major and Perfect, that 
 while Major intervals by inversion become Minor, the 
 Perfect intervals remain Perfect when inverted. 
 
 (10) Exercises. Prove experimentally the statement 
 in (7) and (9), by inverting at the keyboard, and also 
 in writing, various Major, Minor, Augmented and Dimin- 
 ished intervals. 
 
52 Graded Lessons in Harmony 
 
 LESSON 8. 
 
 INTERVALS (Cont.) 
 
 Consonant and Dissonant Intervals. 
 
 .Motto — To fully understand the principle here giirn and 
 its application as shown in later lessons, is to come 
 vcrv near the Heart of Music, and to sec the z^'ork- 
 ings of one of Nature's great Lan's. 
 
 J'J. STUDY. Learn thoroughly §75 of H. S., with this 
 reservation — that it is not important to know which are 
 perfect and which are imperfect consonances, as the two 
 are treated aHke in Harmony. Read Key, ~'> (b). 
 
 EXERCISES. 
 
 Turn to all the exercises in notation in this chapter, 
 and observe each interval, giving its specific name and 
 stating whether it is consonant or dissonant. Write a 
 few examples from among them, especially the more 
 difficult. 
 
 WRITTEN EXERCISES. 
 
 Write the series of consonant intervals from the note 
 C as the lower tone. Illustration and answer : We must 
 remember that all of the intervals are represented as 
 contained within the octave, so that if we take a given 
 note, for example C, and place it in connection with 
 every other tone of the octave, we will have all the inter- 
 vals (all of the different kinds). C-C is a Perfect uni- 
 son ; C-C# is an Augmented unison ; C-Db is a Minor 
 second, etc. (Note that some of the intervals are ex- 
 pressed in two different ways, as C-C* and C-Db.) 
 (Observe also the abbreviations occasionally used — Maj., 
 Min., Dim. and Aug. for Major, Minor, Diminished and 
 Augmented; also Perf. for Perfect.) 
 
 With this explanation, let us take the Xolo C in con- 
 nection with every other (chromatic) tone of the octave 
 in turn, and select those intervals which according to §75 
 
Graded Lessons in Ilarmoni/ 53 
 
 of //. 6'., are consonant, with the following result: C-C, 
 
 IVrf. unison; C-Eb, Min. third; C-E, Maj. third; C-F, 
 
 Terf. fourth; C-G, Perf. fifth; C-Ab, IVfin. sixth; C-A, 
 Alaj. sixth; and C-C, Perf. octave. 
 
 XoTK. To form the series of dissonant intervals, we need 
 only to take the remaining intervals of the octave, as all 
 intervals must fall under one of these two classes. ■ For 
 example: C-CS, Aug. unison; C-Db, Min. second; C-D, Maj. 
 second; C-FC, Aug. fourth; C-Gb, Dim. fifth; C-AJ, Aug. 
 sixth; C-Bb, Min. seventh; C-B, Maj. seventh; and C-Cb. 
 Dim. octave, are all dissonant intervals. Now proceed with 
 the following. 
 
 60. WRITTEN EXERCISE. 
 
 Write, as shown above, first the consonant and then 
 the dissonant intervals from the following notes : G ; F ; 
 Eb; E; Ab; B; Db ; FS. (Continue from other notes 
 until facility is gained.) 
 
 KEYBOARD EXERCISES. 
 
 Proceeding as above, form the series of consonant 
 intervals and then the series of dissonant intervals, from 
 each of the following notes; C; D; Bb; A; Gb ; GS etc. 
 If possible, use the metronome in forming the series and 
 note the speed of the first and the later attempts. 
 
 RECITATION. 
 
 Recite the series of consonant and dissonant intervals 
 as above, noting the speed attained. 
 
 61. EAR-TRAINING. 
 
 Continue as directed in previous lessons ; try particu- 
 larly to sing them. From now on try to observe from 
 the effect which are consonant and which dissonant. Let 
 a friend play different intervals (write out a promiscuous 
 series for him to play, if necessary) while you listen 
 carefully as each one is repeatedly played, and decide 
 as to its specific name, which will of course determine 
 its consonance or dissonance. 
 
 Note. When played by themselves you will be unable to 
 distinguish between certain intervals (for example, the Aug. 
 fifth and Min. sixth, or the Aug. second and Min. third, 
 or the Aug. fourth and Dim. fifth), for the sound will be 
 identical. Yet this never makes confusion in hearing music. 
 
54 Graded Lessons in Harmony 
 
 for the other tone or tones present will unfailingly indicate 
 which is intended. This is like interpreting a sentence by the 
 context. 
 
 62. QUESTIONS. 
 
 Write answers to questions 30-35, Key, p. 26. 
 
 63. ANSWERS TO QUESTIONS 30-32, 34-35, p. 26, 
 Key. 
 
 ANSWER TO QUESTION 30. 
 
 Consonant Intervals in a Key. 
 
 Perfect Unisons. Perfect Fifths. 
 
 Minor Thirds. Minor Sixths. 
 
 Major Thirds. Major Sixths. 
 
 Perfect Fourths. 
 
 Perfect Octaves. 
 
 Dissonant Intervals in a Key. 
 
 Aug. Unisons. 
 Dim. Seconds 
 
 Dim. Fifths. 
 Aug. Fifths. 
 
 (not in common use). 
 Min. Seconds. 
 Maj. Seconds. 
 Aug. Seconds. 
 Dim. Thirds. 
 Aug. Thirds 
 
 Dim. Sixths (seldom used) 
 Aug. Sixths. 
 Dim. Sevenths. 
 Min. Sevenths. 
 Maj. Sevenths. 
 
 (not in common use). 
 Dim. Fourths. 
 
 Aug. Sevenths 
 
 Aug. Fourths. 
 
 (not in common use). 
 Dim. Octaves. 
 
 ANSWER TO QUESTION 31. 
 
 This is intended to bring out the idea that all chords 
 must be classified under one of these two heads (conso- 
 nant or dissonant) and treated accordingly. 
 
 It will simplify matters very much in future to bear 
 this point constantly in mind : that all consonant chords 
 are treated according to certain principles, and all disso- 
 nant chords are treated according to entirely different 
 principles. 
 
 ANSWER TO QUESTION 32. 
 
 In the Major scale the intervals formed by the Tonic 
 
Graded Lessons in Harmony 55 
 
 and Third and the Tonic and Sixth taken together are 
 Major, while in the Minor scale these intervals are Minor. 
 Further, to change a Major to a Minor scale, we lower 
 the third and sixth degrees a half-step. Now as the inter- 
 vals of a Maj. third and Major sixth are changed to 
 Minor in the same way as the Major scales are changed 
 to Minor scales, the relation between the Major scales 
 with their Major third and Major sixth, and the Minor 
 scales with their Minor third and Minor sixth becomes 
 apparent. 
 
 ANSWER TO QUESTION 34. 
 
 By color is usually meant the degree of cheerfulness, 
 or brightness, upon the one side ; or of sadness, etc., upon 
 the other side. You will find as you go on in the study 
 of music, a close connection between Major intervals 
 and the brighter compositions, and between Minor inter- 
 vals and Minor compositions ; but you must not think that 
 this means that we cannot find any Minor intervals in a 
 bright composition, for we can. 
 
 ANSWER TO QUESTION 35. 
 
 As we trace the subject further, we find that the large 
 intervals in the motive of a composition (intervals like a 
 fifth, a sixth, or an octave) tend to make the composi- 
 tion more robust, rugged and aggressive in character; 
 while the smaller intervals like the half-step, or a second 
 or third, tend to make the composition quiet, meditative 
 or sad. It is particularly interesting to study the motives 
 in Wagner's operas with this in view. 
 
 64. SPECIAL NOTE. 
 
 Did you ever observe that it is the fifth of a chord which 
 is most important in determining whether it is to be Aug- 
 mented or Diminished, while the quality of Major or Minor 
 depends chiefly upon the third? To illustrate, let us take 
 the chord C-E-G. To make the chord Augmented, raise the 
 fifth (please also note that the Major third must be asso- 
 ciated with the Augmented fifth to make an Augmented 
 Triad; or, in other words, the extra large fifth requires a 
 large third to accompany it). Now return to C-E-(j for a 
 fresh start. To change this to a Minor triad the third 
 must be altered. And if we now wish to change this Minor 
 triad to a Diminished seventh the change is made by lower- 
 ing the fifth. So that whenever Augmented or Diminished 
 
56 (iriidcd Lessons in Ilarmovij 
 
 is mentioned my mind at once goes to the fifth of the chord, 
 while if Major or Minor is mentioned my mind goes at once 
 to the third. This becomes very simple and practical if 
 we remember at the same time that the extra large fifth 
 requires the large (Major) third while the Diminished fifth 
 requires the small (Minor) third. 
 
 It may be noted, in a broader way that the quality of 
 Major or Minor either in chord, interval, scale or melody 
 depends most directly and essentially upon the 'quality of the 
 third of the scale (if the scale or melody is under discus- 
 sion), or upon the third of the chord if the chord or interval 
 is under discussion. The third is even more important in 
 this connection than its complement, the sixth, as is illus- 
 trated in the Melodic Minor scale, which has a Alinor third, 
 while the sixth is not lowered. So we may conclude that 
 it is not the second or seventh or any other interval but the 
 third (and in a lesser degree the sixth), which is primarily 
 the source of the Major and Minor modes. 
 
 65. DISSONANT INTERVALS THAT SOUND WELL. 
 
 Students often ask why an Augmented second or an 
 Augmented fifth is called a dissonant interval when the 
 Minor third or Minor sixth, sounding like them, are 
 classed as consonant. 
 
 This might be called a "Grammatical" or "Theoretical" 
 classification, since a few dissonant intervals do sound like 
 consonances when taken alone. But considered with the 
 "context" the dissonance is usually apparent. For exam- 
 ple, C-GS sounds consonant ; but take C-E-G and holding 
 the C and E, change G to GS, when the dissonance will be 
 extreme. This is what I mean by "context." But this 
 kind of illustration does not ahi'ays work. For example, 
 the Diminished fourth does not readily yield an illustra- 
 tion ; the best I can do is : Take Ab-CT-F, the C-F being 
 the Perfect fourth ; now flat F, and you have a clear 
 dissonance. But if you take A^i as context, the resulting 
 chord sounds like an ordinary Minor triad. 
 
 Like most musicians, you have possibly thought that 
 a dissonance is the same as a discord, but there is a 
 marked difference. While a discord is an unpleasant 
 sound, you should realize that "dissonance" does not 
 necessarily mean the bad sound you have always thought, 
 hut rather an interval or chord requiring some other to 
 follow to give repose ; and you will aways find these 
 Augmented seconds, etc., followed by consonances. 
 
Graded Lessons in Harmony 57 
 
 COLLATERAL READING. 
 
 66. DIFFERE\XES BETWEEN MAJOR AND PER- 
 FECT INTERVALS. 
 
 (1) Statement, (a) Perfect intervals have no Minor 
 form. That those Normal intervals which have no Minor 
 form should be called Perfect seems at first thought illog- 
 ical ; since they are apparently more limited than the 
 Major intervals. The significance of the term Perfect is 
 found largely in the mathematical relations of the vibra- 
 tion numbers of the two tones of a Perfect interval. 
 
 (b) Perfect intervals become Diminished by being 
 reduced one half-step, whereas a Major interval requires 
 two such reductions to become Diminished. (This is 
 merely another statement of (a), though it has special 
 significance in practice work.) This is shown by the sub- 
 joined comparison of the intervals: 
 
 (1) Augmented (2) Augmented 
 
 i\/r- Perfect 
 
 Mmor ■' 
 
 Diminished Diminished 
 
 (c) Perfect intervals, when inverted, remain Per- 
 fect, or Normal, while Major intervals by inversion 
 become Minor; i.e., not Normal. 
 
 (d) Perfect intervals cannot be made smaller with- 
 out destroying their quality of "consonance"' (see (2) be- 
 low), while the consonant Major intervals do not lose this 
 consonant quality when made Minor. This fact has a most 
 important bearing upon the structure of chords as illus- 
 trated in the following : Play the chord C-E-G, noting the 
 consonant effect; then change G to Gb, playing the other 
 notes as before, when the dissonant character of the chord 
 with the altered fifth will be apparent. Note that C-G 
 is a Perfect fifth, which is consonant (see (2) below), 
 and loses its consonant character when made smaller, 
 C-Gb. In contrast to this, we will change the Major 
 interval C-E, chord C-E-G. Play it as before, noting the 
 consonant quality ; then change E to Eb, playing the other 
 notes as before. As this last form (C-Eb-G) is conso- 
 nant, it is clear that a consonant Major interval may be 
 made smaller without destroying its quality, or classifica- 
 tion, as described in the following sections; while the 
 
58 
 
 Graded Lessons in liarmony 
 
 Perfect intervals might well be called "sensitive'' inter- 
 vals, since they cannot be altered in any manner without 
 altering their character. (Note — This section should be 
 read again after (2) -(3) below.) 
 
 INTERVALS— CONSONANT AND DISSONANT. 
 
 In the preceding sections we have considered the sub- 
 ject of intervals, the general names, specific names, and 
 the measurement and comparison of intervals. We now 
 have to consider the subject from a new point of view, 
 namely, the qualities of consonance and dissonance. 
 
 (2) Statement. Intervals are classed according to 
 their musical effect, as — 
 
 (a) Consonant, meaning those intervals upon 
 which it is agreeable to pause, and which do not need to 
 be followed by another interval to produce a pleasant 
 effect; and 
 
 (b) Dissonant, or those which are not satisfactory 
 to dwell upon, or to use in the final chord of any compo- 
 sition. 
 
 (c) Consonances are further divided into Perfect 
 and Imperfect consonances, with reference to the degree 
 of concord, as follows: 
 
 All Perfect intervals, viz. : 
 Perfect Prime (or Unison), 
 Perfect : i Perfect Octave, 
 Perfect Fourth, 
 Perfect Fifth. 
 
 Major Thirds and Sixths. 
 
 Minor Thirds and Sixths. 
 Seconds and Sevenths, together with all 
 Augmented and Diminished intervals; 
 Dissonances, -j i.e., all intervals other than the Perfect 
 intervals and Major and Minor Thirds 
 and Sixths. 
 
 (3) Exercises, (a) Form and describe various inter- 
 vals as consonant or dissonant. Particularly, form illus- 
 trations with different chords, similar to that shown in 
 (1) above. 
 
 Consonances." 
 
 Imperfect 
 
 ■■{ 
 
Graded Lessons in Harmony 59 
 
 (b) Find and describe dissonant intervals in 
 chords or printed music, carrying the practice into the 
 daily musical life. 
 
 (4) Statement. Referring to the statement (see 
 Collateral Reading, Lesson 5, [1]), that chords are com- 
 posite, and for their character depend upon the character 
 of their constituent intervals, it should now be understood 
 that (1) When all the intervals of a chord are consonant, 
 that chord will be consonant; and (2) When even one 
 dissonant interval is found in a chord, that chord will be 
 dissonant. This leads to the division of chords into two 
 great classes: (1) independent, or consonant chords, 
 which do not require to be followed by another chord, 
 and which indicate the quality of repose or inaction ; and 
 (2) dependent, or dissonant chords, which must be fol- 
 lowed by a consonant chord to give the feeling of rest 
 or completion. One of these qualities (consonance or 
 dissonance) is characteristic of every chord in music, 
 leading logically to a consideration of the great principle 
 of Resolution, or the progression of dissonance to conso- 
 nance in successive chords, or intervals. Read also Key, 
 75 (c). 
 
 67. QUESTIONS ON INTERVALS : Key, p. 23. 
 ADDITIONAL QUESTIONS : Key, p. 25. 
 
 68. DAILY TECHNIQUE DRILL IN THEORY. 
 
 (Note. All illustrations are here given in the key of D.) 
 
 (1) (a) Form all the 'Perfect intervals from the key- 
 note. 
 
 (b) Change each of these Perfect intervals to 
 
 Augmented. 
 
 (c) Change each of these Perfect intervals to 
 
 Diminished. 
 
 Illustration : D-D is a Perfect prime ; D-G, a Perfect 
 fourth; D-A, a Perfect fifth, and D-D, the Perfect 
 octave. Changed to Augmented, they will be, respec- 
 tively; D-DS; D-GJ; D-A)t and D-DJt. Changed to Di- 
 minished, they will be, respectively: (there is no Dimin- 
 ished prime) ; D-Gb ; D-Ab and D-Db. 
 
60 Graded Lessons in Harmoni/ 
 
 (2) (a) Form all the jNIajor intervals from the kej- 
 note. 
 
 (b) Change these to Augmented. 
 
 (c) Change these to Diminished. 
 
 (d) Change these to Minor. 
 
 Illustration: D-E is the Major second; D-F$, the Ma- 
 jor third; D-B, the Major sixth, and D-Qt, the Major 
 seventh. The change to Augmented gives, respectively : 
 1)-E#; D-Fx (double-sharp); D-BS and D-Cx. The 
 change to Diminished gives: D-Ebb (double-flat); D-Fb ; 
 D-Bbb; D-Cb. The change to Minor gives: D-Eb ; D-F; 
 D-Bb, and D-C. 
 
Graded Lessons in Harmony 61 
 
 LESSON 9. 
 
 TRIADS. 
 
 The Principle of Chord Building. 
 
 Motto — All chord forms grow out of the Triad. There- 
 fore, facility in forming the triads is indispensable to 
 later success. Be thorough. 
 
 69. NOTE. 
 
 We will first study triads in general, learning how to form 
 any and every one, afterward associating them in keys and 
 using them. 
 
 Note. So many are unable to readily "think" triads that 
 we dare not take anything for granted. Therefore we will 
 first take the simple drill which has been found most helpful 
 in class work, particularly with children. 
 
 The "Alternate" Letter Principle. 
 
 Whereas a scale consists of consecutive letters, the 
 elemental principle of chord forming is the use of alter- 
 nate letters. Preliminary to the regular study of triads 
 we will therefore learn to think quickly of the letters in- 
 volved in any and all triads, excluding all thought of the 
 sharps or flats. (Note. This point is much like the 
 difference between the general and the specific name of 
 intervals.) To illustrate, the letters used in the triad of 
 D are D, F and A. Note that it is not F» but F. If the 
 Major triad were required we would use FS, but we have 
 not yet come to that. 
 
 EXERCISES. 
 
 Recite the entire series of triad letter forms, as fol- 
 lows: C-E-G; D-F-A; E-G-B; F-A-C; G-B-D ; A-C-E; 
 B-D-F; C. (The last letter, C, is included for the rhyth- 
 mic efifect.) Continue to recite this series till a speed of 
 100 or more is attained, saying a whole group of three 
 letters for each beat. Also reverse the order, as follows : 
 C-E-G ; B-D-F ; A-C-E ; G-B-D ; F-A-C ; E-G-B ; D-F-A ; 
 C. 
 
62 Graded Lessons in Harmony 
 
 Another form of the exercise is to recite all of the 
 letters in alternating form, thus : C-E-G-B-D-F-A-C, etc. ; 
 then from D, D-F-A-C-E-G-B-D, etc. ; then from E ; from 
 F, etc. 
 
 Note. This alternating order of letters in a chord is never 
 violated, even when sharps or flats are introduced. (Even the 
 inversions of the chords are traced back to this fundamental 
 form.) 
 
 Remembering this principle, we are less likely to name the 
 notes of a chord wrong by substituting the flat of one letter 
 for the sharp of another, to say, for example, Gb when we 
 mean Fit, as might easily occur if we first touch the keys 
 upon the piano and then name them without system. Looking 
 upon the piano at the notes B-DS-FS, we could not say if 
 we remember this principle of alternate notes that the triad 
 of B is formed by the notes, B, Eb and Gb, but by B, DS and 
 FJf. 
 
 It is most important that this principle be thoroughly ap- 
 plied, as if is so necessary in all later work. Remember, 
 that although we may add sharps or flats we cannot change 
 the letter name of a note and still retain the original name of 
 the chord. Now a question : What letters are required to 
 form the triad of Gb? (Note. Before reading further please 
 mentally answer the question.) The usual classroom answer 
 is Gb, Bb, Db, but we should remember that flats and sharps 
 have nothing to do with the letter, and the true answer 
 is G, B and D. 
 
 70. EXERCISES. 
 
 Name the letters forming the triad of F#. (Ans. : F, 
 A and C. Do not be confused by the absence of the 
 sharps.) 
 
 Similarly, name the letters used in forming the triads 
 of Ab ; of Bb ; C# ; GJ ; ES ; BS. Write the answers to the 
 last four. 
 
 Chord Structure in General. 
 
 71. STUDY: H. S., §91 (to the Exercises only) ; Key. 91 ; 
 Collateral Reading, §75, (l)-(3). Advanced students 
 also read H. S., §90. 
 
 DRILL upon the above. In the triad C-E-G, which 
 note is the root, and which the third, which the fifth ? 
 (Ans.: C is the root, E the third, and G the fifth.) 
 Similarly name the root, third and fiftli of each of the 
 following triads: A-C#-E; F#-A-C; B-D-F; F-A-C. 
 
Graded Lessons in Harmony C3 
 
 Note. This exercise, though absurdly simple, is given to 
 establish the identity of the three' elements of the triad. It 
 will soon be necessary to have the point to use. 
 
 72. THE MATERIAL OF MUSIC; OR, THE SCALE 
 
 AS THE BASIS OF ALL MUSIC. 
 
 In the scale are contained all the materials from which 
 music is constructed. In the single tones of the scale are 
 found the melody or the chief part of it, since the Chro- 
 matic passing tones appear not as the real substance of 
 the melody but are like unimportant decorations. By 
 combining the scale tones into chords the harmonic struc- 
 ture is developed, therefore we may say that both melody 
 and harmony are developed from the scale. Further, 
 following the principle of alternate letters and choosing 
 only TONES BELONGING TO THE SCALE, wc may build a triad 
 upon EACH DEGREE OF THE SCALE; that IS, we Can use each 
 scale tone in turn as the root, upon which to build a triad 
 by adding the third and fifth above, as shown in H. S., 
 Fig. 25. We make therefore seven different chords, one 
 upon each degree of the scale. Note that these seven dif- 
 ferent triads are all in the key. Do not think that the 
 triad upon the first degree is more truly in the key than 
 the triad upon any other degree. Now — 
 
 STUDY: Collateral Reading, §75, (7)-(8), and H. S., 
 §91 (the Exercises), and §92. 
 
 OBSERVE: (1) That the triads upon the different 
 scale degrees differ in their sound; and (2), that they 
 differ in the kinds of thirds and fifths contained. This 
 leads to the consideration of 
 
 The Specific Forms of Triads — Major, Minor, 
 Diminished and Augmented. 
 
 73. STUDY: f/. 5., §93; Collateral Reading, §76, (5) and 
 (9) ; Key, 93. 
 
 Note 1. The abbreviations Maj., Min., Dim. and Aug. will 
 be used for the four kind of triads. 
 
 Note 2. In the following work the triads are not supposed 
 to be in any particular key, but simply formed from any re- 
 quired note by adding the proper "intervals. 
 
64 Graded Lessons in Harmon;/ 
 
 XoTE 3. It will be easier to renieiiiber tlie inlemuls re- 
 quired for tlie Dim. and Aug. triads if we note that tlie "extra 
 small" (or Dim.) fifth is u.sed with the "small" (or Min.) 
 third, to form the Dim. triad, while the "extra large" fifth 
 and the "large" third work together to form the largest form 
 of the triad, or Aug. triad. 
 
 SPECIAL DRILL. 
 
 (a) Why is C-E-G a Maj. triad? (Ans. for illustra- 
 tion: "Because it has a Maj. third and Perf. fifth.") 
 Why is C-Eb-G a Min. triad? Because it has a Min. 
 third, C-Eb, and a Perf. fifth, C-G. Why is B-D-F a 
 Dim. triad? Why is D-F#-Af an Aug. triad? Why is 
 A-C-E a Min. triad? 
 
 (b) Describe the triad C-E-GS. Ans.: It has a Maj. 
 third, C-E, and an Aug. fifth, C-(i5, and is therefore an 
 Aug. triad. 
 
 Describe similarly D-F-Ab ; FS-A-CC ; FS-A-C; 
 Bb-D-F#; Bb-Db-Fb; A-C-Eb ; Af-CS-E ; A-CS-E. 
 
 (c) Write the Maj. triad upon each of the following 
 notes : D ; Eb ; G ; C ; Ab ; F ; Db ; A : F£ ; D« ; B ; GS ; E ; 
 Cf. 
 
 (d) Write Min. triads upon the same notes. 
 
 (e) Write Dim. and Aug. triads upon the same notes. 
 KEYBOARD EXERCISES. 
 
 (1) (a) Repeat (c), (d), (e) at the keyboard. 
 
 (b) Form the triad of C Maj. Next change it to 
 Aug., then back to Maj., then to Min., then to Dim. 
 
 (c) Proceed similarly with the triad on Db, giving 
 it the four forms in succession, then with the triad of D, 
 and continue through all the chromatic tones in the octave. 
 
 (d) Also write this exercise complete and note 
 speed attained with the same at the keyboard. 
 
 (2) Form various Aug. and Dim. triads unthout first 
 giving the Maj. form. Also write examples of the same. 
 
 74. QUESTIOXS 1-10, Key, pp. 5(1-,-!. 
 
 COLLATERAL READING. 
 
 75. It is not intended to go into the formation, positions 
 and inversions of triads and common chords, as the sub- 
 ject is covered in many text-books, but rather to take 
 up a few thoughts relating to the subject, which may 
 not be found in all books. 
 
Graded Lessons in Harmony 65 
 
 (1) Statement. A chord, in the general sense of the 
 term, and as generally used, is an imitation of the Great 
 Chord of Nature, as shown by comparison with what is 
 known as the "Harmonic Series," or "Overtones." (Na- 
 ture's Chord is illustrated by the series of tones produced 
 from a keyless brass horn, or by those produced by a 
 vibrating string.) The chord of three different notes 
 (the triad) has its counterpart in the first notes of the 
 Harmonic Series. Being so closely in accordance with 
 Nature would seem to argue strongly in favor of the 
 claim of superiority of our musical system as compared 
 with other systems, such as the Chinese. 
 
 (2) Chord structure in general. A chord is formed 
 by adding the intervals of a third and fifth ; or a third, 
 fifth and seventh ; or a third, fifth, seventh and ninth 
 to any note which is taken as a root. In other words, a 
 chord is composed of a series of thirds superimposed, or 
 placed one above the other. 
 
 (3) Parenthetically, it might be observed that where- 
 as a scale is formed of consecutive letters, a chord is 
 formed of alternate letters. The chord of three different 
 notes is called a Triad. This is the simplest and original 
 form of the chord principle, or harmonious combination 
 of different pitches. (Note. Two tones in combination 
 form an interval; three or more tones form a chord.) 
 When one note of the triad is doubled to make four-part 
 hannony, the triad becomes a common chord. When a 
 chord is composed of four different notes, being composed 
 of alternate letters, it is called a chord of the seventh. 
 Similarly, by a process of adding thirds, a chord of the 
 ninth, a chord of the eleventh, or a chord of the thir- 
 teenth may be formed. The latter chords, however, are 
 not in very general use. 
 
 (4) Statement. Chords are composite, being made 
 up of intervals. The character of a chord depends upon 
 the character of the intervals contained. (See Collateral 
 Reading, §51, [1]). 
 
 (5) Statement. Specific Names of Triads. There 
 are four kinds of triads — Major, Minor, Augmented and 
 Diminished. They are named from the most characteris- 
 tic interval contained, as follows: A Major triad has a 
 Major third and Perfect fifth, counting from the root. 
 .■\ Minor triad has a Minor third and Perfect fifth,, 
 
66 Graded Lessons in Harmony 
 
 counting from the root. A Diminished triad has a Minor 
 third and Diminished fifth. An Augmented triad has a 
 Major third and Augmented fifth, counting from the 
 root. (The characteristic intervals in each of the four 
 kinds of triads is here in italics.) It is desired that the 
 relation between the chord and its most characteristic 
 interval should be clearly seen, as it has a most important 
 bearing upon the whole structure and practice of music. 
 
 (6) Exercises. Form examples of each of the four 
 kinds of triads from each chromatic note of the octave. 
 (Note. This exercise is most valuable when taken in sys- 
 tematic form and with increasing speed, controlled by the 
 metrotiome.) 
 
 (7) Statement. To be in the key, a chord must be 
 composed exclusively of scale notes. If even one note is 
 not a scale note, the chord cannot be said to be strictly 
 in the key. 
 
 (8) Statement. The Material of Music. A chord, 
 either a triad, chord of the seventh, or other chord, may 
 be formed upon each degree of the scale. The seven 
 notes of the scale and the chords built upon these seven 
 notes, may be said to be the alphabet, or the prime ele- 
 ments of music, which are combined much as language 
 is formed to express every emotion possible to human 
 experience. 
 
 (9) Statement. Of the triads formed upon the seven 
 scale notes, there are three kinds. Major, Minor and 
 Diminished, found in the Major mode (or scale) ; and all 
 four kinds are found in the Minor mode. It might, at 
 first thought, seem strange that a Minor triad should form 
 part of a Major key. In this, as well as in other respects, 
 a key represents a family which is composed of dissimilar 
 elements. 
 
 (10) Exercises. Form a triad upon each degree of 
 several Major and Minor scales, and describe each triad 
 in turn. 
 
 (11) Note. Positions, Inversions, Marking Chords, 
 Connecting Chords, Figuring Chords. It is suggested 
 that the earnest student should make thorough drill, par- 
 ticularly at the keyboard, of each point in turn. Detailed 
 directions may be found in H. S. In general it should be 
 noted that it is possible to place the different notes of 
 the chord in auv desired order. 
 
Graded Lessons in Harmony 67 
 
 LESSON 10. 
 
 TRIADS (Cont.) 
 
 Motto — Be thorough and patient. As soon as a new 
 thought is grasped take it to the keyboard and use 
 it; compare it ivith the points previously gained — 
 that is, co-ordinate it — and find its relations to the 
 subject as a ivhole. Especially here, learn by 
 Doing. "Do" each point as it unfolds to your 
 mind. 
 
 76. SPECIAL DIRECTIONS. 
 
 Read zvith a hand upon the keys, and follow the un- 
 folding of the idea by having the hand go through the 
 chord forms described. This is most practical and helpful. 
 
 The four kinds of triads, Maj., Min., Dim. and Aug., 
 continued from preceding lesson. You are supposed to 
 have written the series of triads required in the Key- 
 board Exercises, Lesson 9, §73, where we take the triad 
 of C Major, change it to Augmented, back to Maj.; to 
 Min. ; to Dim., and then progress to the triad of Db and 
 go through the same process, etc. Below are given the 
 triads in their proper order, for comparison with the one 
 written by the student. 
 
 Fifths: G ,Gii,G ,G ,Gb ; Ab,-A ,Al),Ab,Al'b; A ,AS,A ,A ,Ab 
 
 Thirds: E ,E ,E .Eb.Eb ; F ,F ,F ,Fb,Fb ; Fii,F#,Fit,F ,F 
 
 Roots: C ,C ,C ,C ,C ; Db.Db.Db.Db.Db ; D ,D ,D ,D ,D 
 
 1234:5 12345 12345 
 
 Fifths: Bi»,B ,Bb,Bb,Bl,l>; B ,B#,B ,B , Bb 
 Thirds: G ,G ,G .Gb.Gb ; GS,G#,G«,G ,G 
 Roots: El7,E|7,Eb,Eb,Eb ; E ,E ,E ,E ,E ■ 
 
 C ,Ci:,C ,C ,Cb 
 A ,A ,A ,Ab,Ab 
 F ,F ,F ,F ,F 
 
 1234 5 12345 12345 
 
 Fifths: CS,Cx,Cii,CS,C ; D ,DS,D ,D ,Db; Eb,E ,Eb,Eb,Ebb 
 
 Thirds: .Aif,AS,Atf,A ,A ; B ,B ,B ,Bb ,Bb; C ,C ,C ,Cb,Cb 
 
 Roots; F-t,F#,F*t,FS,F-t ; G ,G ,G ,G ,G ; Ab, Ab,Ab,Ab,Ab 
 
 12 3 4 5 12 3 4 5 12 3 4 5 
 
 Fifths: E ,E#,E ,E ,Eb ; F ,FS,F ,F ,Fb; F#, Fx, Fij, F#, F ; G. 
 
 Thirds: Cif,C#,C#,C ,C ; D ,D ,D ,Db ,Db; DS,D#,Dit,D ,D ; E. 
 
 Roots: A ,A ,A ,A ,A ; Bb,Bb,Bb,Bb ,Bb; B ,B ,B ,B ,B ; C. 
 
 12345 1234 5 12345 1 
 
68 (iraded Lessons in Ildrmoni/ 
 
 ^VRITTE^■ EXERCISES. 
 
 If you have not already done so, or if incorrect at the 
 previous attempt, write the above in notes, on the treble 
 staff. Write from memory, or rather from understand- 
 ing — not by copying. 
 
 XoTE that the roots of the series above form a chromat- 
 ically ascending series, C, Db, D, Eb, etc. Note further that 
 Db could also have been written CS, Eb as DS, etc. In the 
 above the simpler form was taken in each case — the one re- 
 quiring fewest double-sharps or double-flats in the triads. But 
 it is advisable for the student who is somewhat advanced to 
 write and recite the above series first with the "flat" root and 
 then with the "sharp" root, changing it enharmonically. (For 
 definition of "enharmonic," see H. S., §§24, 78.) 
 
 77. KEYBO.-\RD EXERCISES. 
 
 Play the foregoing series of triads, without referring 
 to the printed or written copy. This will not be difficult 
 if you will first fix the series in mind: Maj., Aug., Maj., 
 Min., Dim. ; "progress" (to the next root) and note also 
 that in passing from one form to the next in order, only 
 one note is changed. 
 
 TWO AIETHODS OF PRACTICING THE ABOVE. 
 
 (a) As each successive form is struck, say "Maj., 
 Aug., Maj., Min., Dim.," naming each form and striving 
 to be conscious of (1) its sound, (2) its feeling under the 
 fingers, (3) its variations from the Normal or Major 
 form, and (4) of its appearance on the printed page, or 
 the way it would be written. 
 
 (b) As the successive forms are struck, name the 
 single note which is altered to create the new form each 
 time. For example, playing C-E-G, say "'Major C-E-G."' 
 Then when you change to the Aug. form, say "GJf" as 
 you play the Aug. triad. If you were to change from the 
 Maj. to the Min. form, you would say "Eb" or "Min. Eb" 
 as the Min. triad is struck. Then, as you strike the next 
 triad, Db-F-Ab, you would say "Maj. "Db-F-.\b." Begin 
 this practice slowly, M.M. ,50, and tivo beats to each chord. 
 Then, as facility is gained, increase to a rapid speed, say 
 120-160, with one beat to each triad. 
 
 PRACTICE THIS EXERCISE BOTH ASCENDING 
 AXn DESCENDING. Note that in descending, when 
 
Graded Lessons in Harmony 69 
 
 you change from the Dim. form of one triad to the Maj. 
 form of the next one below — e.g., from C-Eb-Gb to 
 B-DJ-FS, only one note is really changed, the upper two 
 being enharmonically altered. Practice it also with the 
 left hand. Continue the training daily for from one to 
 three weeks, putting most of the time upon the weaker 
 points. 
 
 AXOTHER ASCENDING FORM is as follows: Maj., 
 Min., Dim., Min., Maj., Aug. "Progress," e.g., C-E-6, 
 C-Eb-G, C-Eb-Gb, 'C-Eb-G, C-E-G, C-E-G#; now "pro- 
 gress" to Db-F-Ab, and continue as before. Practice this 
 in the two ways. 
 
 Note. The above series becomes more or less ''mechani- 
 cal" in a short time, and does not call upon the reasoning 
 powers sufficiently. So we must devise a training to fill this 
 requirement, one that will not allow the fingers or mind to 
 reach a conclusion without direct and independent thought. 
 This point is gained by taking the triads in such a series as 
 to prevent each one from being formed from the preceding, 
 but on the contrary, formed directly by the knowledge of the 
 intervals composing it. Therefore you should now review 
 the statements in H. S., §93, about the component intervals of 
 each kind of triad. 
 
 78. RECITATION. 
 
 (a) Recite the notes of the triad of C Major (C-E-G). 
 Then pass upward a whole-step from C to D, and recite 
 the notes of the Major triad on D. Pass upward a whole- 
 step again and recite the notes of the Major triad, con- 
 tinuing the process until C is reached an octave higher. 
 Then commence upon C( (also sometimes calling it Db) 
 and proceed as before, naming the notes of the Major 
 triad in each case. 
 
 (b) Repeat the process, but this time naming the notes 
 of the Minor triad each time. 
 
 (c) Proceed as before, but naming the notes of the 
 Aug. triads. Note here that you should not mentally first 
 form the Maj. triad and then change it, but you should go 
 straight to the Aug. form and name each note, remember- 
 ing that a Maj. third and Aug. fifth from the given 
 root — whatever it may be — are required. 
 
 (d) Name similarly the Dim. triads, remembering that 
 the Min. third and Dim. fifth are required — do not first 
 
70 Graded Lessons in Harmony 
 
 form the Maj.or Min,, that is, if you are able to do it 
 without this help. 
 
 WRITE three examples of Maj. triads, three of Min., 
 three of Aug. and three of Dim. triads. If you will pro- 
 ceed chromatically upward from C to C, writing the triad 
 of C Maj., then of C*f Min., D Aug., Eb Dim., E Maj., etc., 
 the twelve required examples will use every chromatic 
 note of the octave. 
 
 KEYBOARD EXERCISES. 
 
 Repeat the foregoing exercises in recitation at the key- 
 board, using the metronome, and reporting accurately 
 upon the speed attained. Do not try to go through 
 the whole of the above in one day. Rather, use it as a 
 drill to be carried from ten to twenty-five days, till facility 
 is gained. 
 
 79. WRITTEN EXERCISES. 
 
 This is a test for speed and accuracy. Write out in 
 capital letters the notes constituting the following triads, 
 timing yourself accurately by the watch, writing plainly 
 and making no corrections, not even to add a sharp or 
 flat. (You may afterward place a ring around any wrong 
 notes and write the correction outside to show that you 
 understand.) Note the time required for the whole exer- 
 cise — not for each triad. You may do this exercise once 
 as soon as you see this, and then again when the lesson 
 is mastered, to note the progress. 
 
 The Test. Write the notes of the following triads: 
 B Min., F» Maj., C» Aug., A Dim., G Aug., D Aug., Gb 
 Min., C# Dim., Ab Dim., B Aug., G» Min., DS Maj., Gb 
 Dim., Db Min., DS Maj. Remember, no corrections 
 except with rings. 
 
 KEYBOARD EXERCISES. 
 
 Play the preceding triads, noting the metronome speed 
 attained upon the" first attempt and also the last. Do not 
 forget to use the left hand part of the time upon all exer- 
 cises. 
 
 80. VARIETY OF DRILT.. 
 
 As the study of the formation of triads in their four 
 
Graded Lessons in Ilarmoni/ 71 
 
 forms is to be continued till facility is gained, it is well 
 accomplished by changing the order of the roots ; e.g., 
 instead of taking a series whose roots are a whole-step 
 apart, we may pass upward (or downward) a Minor third 
 for the following triad, and continue to pass upward (or 
 downward) a Minor third each time. Then similarly we 
 can progress a Major third each time, or b^ any desired 
 skip or combination of skips. One of the most useful 
 skips is that of the Perfect fifth, either upward or down- 
 ward. This develops knowledge which will presently be 
 useful in another way. 
 
 KEYBOARD DRILL. 
 
 (a) Following the above suggestion, form a series of 
 Major triads, using one or more of the suggested ways 
 and note the speed attained. In every case include the 
 progressions of the Perfect fifth up and down. 
 
 (b) Form a similar series with Minor triads, choosing 
 a different progression. 
 
 (c) Form a similar series with Diminished triads. 
 
 (d) Form a series with Augmented triads. 
 
 WRITTEN EXERCISES. 
 
 Write out the series with Augmented triads, progress- 
 ing by the Perfect fifths upward, then by Perfect fifths 
 downward. 
 
 RECITATION. 
 
 Recite the series of Diminished triads, progressing by 
 Perfect fifths upward and then downward. 
 
 Special Note. If difficulty is experienced with the forma- 
 tion of the different kinds of triads, the drill must be con- 
 tinued daily for some time. Do not expect facility simply 
 by understanding them. You must think and do them many 
 times before the mind and fingers will work quickly. And, 
 further, do not discontinue this drill as soon as the next 
 subject is undertaken, but return frequently to this portion 
 for a review and drill. 
 
 81. EAR-TRAINING. 
 
 To ask at this point that ear-training be carried on 
 from the beginning of the study of triads is nearly like 
 
72 (iyadcd I^essoiis in Ilarmonij 
 
 the postscript of Pat's letter: "If yez don't receive this 
 yez may know thot I'm well." Yet it is desired in connec- 
 tion with the daily study in each and every day's practice. 
 It is especially desired that this be done to make each fact 
 and principle more tangible and real, and that the ear as 
 well as the eye and the understanding may be called into 
 activity. 
 
 S2. QUESTIONS 37-28, Key, pp. :.l-.'>2. 
 
 83. ABOUT THE TERM POSITION. 
 
 "Position" does not relate to the order of the notes 
 in the chord, but it relates to the highest note only, or 
 Soprano, and not to any other note, or to any order of 
 notes. The above statement is made as strong as possible 
 to ward off any possible misunderstanding, for pupils are 
 very frequently confused about this for some little time. 
 
 When a triad is taken with one hand, changing the 
 position does naturally bring about an apparent change in 
 the order of the notes, but this change in the order of the 
 inner notes has nothing to do with "position," as will be 
 seen if you use two hands and spread the chord out over 
 three octaves, when you will see that the order of the 
 lower three parts may be freely changed without affecting 
 the position. 
 
 It must be clearly understood, then, that position re- 
 lates to one tone only and that the highest in the chord. 
 Read H. S., 00 ; also7^n', 90. 
 
 84. EAR-TR.\INING. 
 
 (a) Strike the triad of C Major upon the piano; then 
 listen intently, striving to hear the individual tones con- 
 stituting the chord, but not striking them individually; 
 try to sing the third and fifth (the top note is always 
 the easiest one). Now strike other triads and try to 
 sing the tones in turn — to commence with the third is to 
 show a good ear. 
 
 (b) Similarly sound Minor triads and try to sing their 
 tones. 
 
 (c) Similarly sound Diminished triads and try to sing 
 their tones. 
 
 (d) Similarly sound Augmented triads and try to sing 
 their tones. 
 
Graded Lessons in Harmoni/ 73 
 
 \0TE. These exercises will help you to listen with con- 
 centration and intelligence to the different kinds of triads, and 
 will help you to recognize them when played. It is less impor- 
 tant that you succeed with those exercises than that you make 
 the attempt, and so come to listen more intently, and that you 
 learn how to listen. 
 
 (e) Play different kinds of triads in different parts of 
 the keyboard, noting the different color of the different 
 kinds of triads, and also how the same kind of a triad 
 gives a different effect in different pitches, which makes 
 the subject more diflficult. 
 
 By "color" is meant that a Major triad gives the effect 
 of brightness and satisfaction, a Minor triad of sadness 
 or darkness, a Diminished triad of dissonance or com- 
 pression (the notes are pressed together), and an Aug- 
 mented triad of most violent dissonance, together with 
 the effect of expanding, tearing apart or openness. Ob- 
 serve that both Major and Minor triads are consonant, 
 while Augmented and Diminished are both dissonant but 
 quite opposite in character. 
 
 (f) While a second person plays the various triads 
 upon the piano, write out the series given in Lesson 10, 
 §76. If necessary, you may decide as to the character of 
 each one as it is repeatedly played. 
 
 Note. If a second person is not available, then play these 
 different kinds of triads, with intensely concentrated thought 
 and attention, striving to hear and feel the qualities or colors as 
 described. After reaching this point we should take every 
 opportunity of recognizing the various kinds of triads when 
 listening to music. Such careful listening to music is really 
 the beginning of self-production of musical thoughts. And 
 now we come to the more difficult Ear-training Exercises. 
 which will not be done by more than a quarter of the students 
 at the first attempt, and by not more than one-half after many 
 attempts — yet the attempt is worth while, even if you fail. 
 
 (g) Sound the note C as a root, and while holding this 
 note, sing in succession the root, third and fifth of the 
 Major triad. Do not help yourself by sounding the other 
 tones till after the voice has taken the tone and then only 
 to prove the result. Repeat with other notes which lie 
 in the range of the voice. 
 
 (h) Proceed similarly with the Min. triads, 
 (i) Proceed similarly with the Dim. triads, 
 (j) Proceed similarly with the Aug. triads. 
 
74 Graded Lessons in Harmony 
 
 Do not hesitate to carry on the above exercises for 
 three months or even a year, for they are potent influ- 
 ences in developing true musicianship, whether you ever 
 succeed or not. Do not worry about that part. 
 
 If you do not readily succeed with the above, a com- 
 promise may be made or a preliminary training secured, 
 if a second person will play the various triads in "broken" 
 form while the student endeavors to decide the nature of 
 the triad from hearing it in the broken form. In this 
 way the ear becomes accustomed to hearing the melodic 
 side of chord building, which is recognized by but few. 
 
Graded Lessons in Harmony IS 
 
 LESSON 11. 
 
 TRIADS (Cont.) 
 
 85. IMPROVISATION. 
 
 This is one of the most important lines of work pos- 
 sible to the Theory student, and should form a part of 
 every day's practice to the end of the course. True 
 familiarity with the material of music can only be at- 
 tained by using, at the keyboard, each new element as it 
 is studied, adding to our working material item by item, 
 until we can use all the ordinary chords freely and almost 
 unconsciously, to express musical ideas. The common 
 fault with efforts in this line is that they do not begin at 
 the beginning, but attempt too many things at once to 
 succeed. 
 
 As a child commences his use of language with single 
 words of the simplest character, so will we first use single, 
 disconnected chords in the simplest form without gram- 
 matical significance. But this simple work can be in- 
 vested with real charm, and teachers will find it of the 
 greatest advantage to use the following exercises with all 
 piano pupils, children or adults. For the children the 
 original forms of the exercise were called the "Bounding" 
 and. the "Rocking" chords, the reason of which names 
 will be apparent later. 
 
 "Bounding" and "Rocking" Chords. 
 
 The term "Bounding'' chord, as here used, sirnply de- 
 notes the repetition of the chord in a higher octave. 
 There are various ways of performing this chord, one 
 which is shown in Fig. 2 below. (Note — The illustra- 
 tion shows the chord in only one key, but it will be played 
 by the student in all keys to gain facility, for which it is 
 one of the most important means yet devised.) 
 
 A "Rocking" chord is simply a form of the "broken" 
 chord as shown in Fig. 3. 
 
 KEYBOARD EXERCISES. 
 
 (a) Following the illustrations in Fig. 2, form 
 
76 
 
 Graded Le.i,tO)is in Harmony 
 
 "Bounding" chords from all the Major triads, progressing 
 upward by half-steps. 
 
 (b) Form a similar series, progressing downward by 
 half-steps. As soon as it is fairly familiar, work with the 
 metronome, repeating the more difficult ones as many 
 times as may be necessary, and give a report of the speed 
 which can be attained, playing in quarter and half-notes 
 as indicated in the illustration, one beat to each quarter. 
 
 (c) Form a similar series, but progressing by skips 
 of a Perfect fifth each time. 
 
 (d) Form a similar series, progressing downward by 
 a skip of a Perfect fifth. 
 
 WRITTEN EXERCISES. 
 
 Write examples of "Bounding" and "Rocking'' chords 
 in at least four keys. Be sure to write them exactly as 
 you play them, for the correctness of the keyboard work 
 can only be judged in this way. Write also all those 
 chords about which vou may be in doubt. 
 
 ROrxniXG CHORDS.' 
 
 Fig. 2 
 
 Repeat in all keys. 
 
 Fig. 3. 
 
 m 
 
 'ROCKING CHORDS.' 
 
 EEEE 
 
 Ped. 
 
 J 
 
 # Ped. 
 
 # Ped. 
 
 Repeat in all keys. 
 
Graded Lessons in Harmony 
 CONNECTION OF " BOUNDING CHORDS." 
 
 77 
 
 Fig. 4. 1^ 
 
 l:5T: 
 
 1 •^ 
 
 i::EEl3_^l 
 
 i 
 
 ^ 
 
 S 
 
 S-n 
 
 g^ 
 
 i£fcSi5=s 
 
 ^ 
 
 ^t 
 
 5ri 
 
 -=1-1^ — ?-=)• 
 
 # 
 
 jg ^_ 
 
 :4; 
 
 I 
 
 
 1 
 
 i 
 
 -a-=i^- 
 
 
 •c^JSl 
 
 3=- 
 
 ^1-V- 
 
 ^6r^ 
 
 ^= 
 
 -«— ^- 
 
 V7 
 
 I 
 
78 Graded Lessons in Harmony 
 
 LESSON 12. 
 
 TRIADS: THEIR POSITIONS AND 
 INVERSIONS. 
 
 86. Note. Before taking up the study of position, the student 
 should understand the terms, Principal and Secondary Triads 
 and Doubting. 
 
 Principal and Secondary Triads. 
 
 STUDY H. S., §94. 
 
 WRITTEN EXERCISES. 
 
 Write the seven triads in the scale of D I\Iajor; 
 describe each one as required under the head of Exercises, 
 H. S., §94. 
 
 Doubling. 
 
 87. STUDY H. S., §95. 
 
 WRITTEN EXERCISES. 
 
 Write the chord of G Major in four parts in several 
 different ways ; that is, doubling different notes, indica- 
 ting which forms are best and which are poorest. 
 
 Position. 
 
 88. STUDY H. S., §9(;; also Key. OC. 
 
 WRITTEN EXERCISES: H. S.. §9(1. 
 
 KEYBOARD EXERCISES. 
 
 Following H. S., Fig. 27, as a pattern, play every 
 Major and Minor triad in its three positions. 
 
 Note. Instead of sludyiiig part-writing at this point, the 
 student will skip for the moment from J{. S., §97 to §125. We 
 will do this for the purpose of studyini;' the construction of 
 chords more tlinronghly lieforc t.nking up tlic stuilv nf part- 
 writing. 
 
Graded Lessons in Harmoni/ 79 
 
 89. EAR-TRAINING. 
 
 In the second lesson, §10, the individual qualities of 
 the scale tones were shown. The student will now be 
 able to use this knowledge in determining the different 
 positions of a chord. By listening intently to the upper 
 tones, the quality of either rest or incompleteness may 
 be heard. By singing the upper tone when playing the 
 three positions in succession the quality may become more 
 marked. The student should, however, be warned that 
 this is not an easy matter for a large proportion of musi- 
 cians, and it may require six months or longer to become 
 proficient in this line. Those gifted with accurate hearing 
 may be able to distinguish almost at the first attempt. It 
 would be well in this exercise if a friend could play chords 
 in different positions. 
 
 To "Hear" or Sing Any Required Tone of a Chord 
 When All Are Played Together — Not Broken. 
 
 To successfully distinguish the various chords in their 
 different positions and inversions, it is essential that the 
 student should first be able to sing at will any one of the 
 tones of a common chord, picking- out any tone from the 
 mass as the chord is sounded with all its tones together. 
 For some persons this is very easy, for others, extremely 
 difficult. Therefore, each student is required to report 
 specifically upon this point, and if any particular difficulty 
 is found, do not try to go on with the next exercise till 
 after several weeks, or even months, of training in this 
 line. The above exercise is one that the student can do 
 with considerable success by himself, striking any chord 
 upon the piano (not forgetting to try the different posi- 
 tions and inversions), and especially striking all the tones 
 together and then trying to sing the different tones of the 
 chord at will, attempting particularly the inner tones, 
 which are more difficult than the highest or lowest tones 
 of the chord. 
 
 Positions. 
 
 The student will remember that in the second lesson, 
 §16, the individual qualities of the scale tones were dis- 
 cussed, the Tonic being firm, the Third calm and the 
 Fifth bright. By listening carefully, you will be able to tell 
 
80 Graded Lessons in Harmony 
 
 which tone of a chord is highest, that is, to determine 
 the position of the chord. Other helps may occur to you, 
 as for example, to try to think how far it is down or up 
 to Doh, or the point of rest; or to notice as you sing the 
 various notes upward or downward, what the intervals 
 are. For illustrations, when the fifth of a chord is high- 
 est, it will be a Minor third above the next note below ; 
 or if the octave is highest, it will be a fourth above the 
 next highest note, and if you were to add (experimen- 
 tally) another note above, it would be a Major third. 
 Some people with unusually keen musical hearing can dis- 
 tinguish the positions of a chord without reasoning, but 
 this is not expected of the student. It is a faculty to be 
 gained by hard work and plenty of it. 
 
 Inversions. 
 
 The principles discussed above will apply equally to 
 the lowest tone in a chord, and the student should give 
 especial attention to the lowest as well as the highest note. 
 When these two tones become clear in the mind it is 
 comparatively easy to decide upon the intervening tones, 
 which will result in a real knowledge of the complete 
 chord. Remember that this work cannot be accomplished 
 in a short time, and those not gifted with especially good 
 hearing should frequently review the simplest exercises of 
 the descending tones of the scale and the simplest inter- 
 vals, for upon this foundation the ability to hear as well 
 as the ability to construct chords is developed. 
 
 90. QUESTIONS 29-31, Key. p. .".2. 
 
 91. NOTE ABOUT AIIXING POSITIOXS AND IXVER- 
 
 SIOXS. 
 
 Although students make the statement and believe it, that 
 position refers to Soprano and inversion relates to the Bass, 
 yet when the position is allowed to change with the changing 
 inversion, one is forced to suspect that in the subconscious 
 mind of the student the position is affected by the inversion. 
 This should not be and the student should give careful atten- 
 tion to this point, for it will be met, either in his own study 
 or in his experience as a teacher : think it out carefully. 
 
 In teaching and drilling the inversions, you will find a 
 tendency on the part of your pupils to shift the position every 
 time the Bass is changed, letting the Soprano go up as fast 
 
Graded Lessons in Harmony 81 
 
 as the Bass does. This will give the wrong impression, for 
 we wish to confine the thought to the change in the Bass. 
 Therefore, always require pupils to keep the same position 
 as far as possible throughout the different inversions; or 
 rather, ask them to play through the different inversions, 
 first retaining one position, then repeat it with a changed 
 position and so on till each position has been used for all the 
 inversions. 
 
82 Graded Lessons in Harmony 
 
 LESSON 13. 
 
 INVERSION OF TRIADS. 
 
 92. STUDY H. S., §125. Observe particularly the foot- 
 note. 
 
 WRITTEN EXERCISES: H. S., §125. 
 
 KEYBOARD EXERCISES. 
 
 Using two hands, play every Major and Minor chord 
 in its direct form and two inversions, as shown in Fig. 38, 
 H. S. Note the speed attained. 
 
 Note 1. It should be observed that the whole substance of 
 "positions" and "inversions" resolves itself into this : That 
 as the tones of an interval may be inverted without destroying 
 its character, so the tones of a chord may be inverted or used 
 in different orders withoiit destroying the character of the 
 chord; and that the relationships of the different tones of a 
 chord to the root are not essentially altered, regardless of the 
 order in which the tones appear. The student should now 
 review the lessons on the inversions of intervals and trace out 
 the logical connection between the intervals and chords, 
 remembering particularly that chords are composed of inter- 
 vals and the intervals give character to the chords. There- 
 fore, the principles which govern the relationships of the tones 
 of an interval will continue in force when intervals are 
 grouped into chords. 
 
 Note 2. The student should further observe that in study- 
 ing positions, inversions and doubling, we have but three 
 tones to consider, — the root, third and fifth which we 
 studied in our first lesson on triads. These three tones, root, 
 third and fifth, may occur in any desired order, but the rela- 
 tionships of the tones one to the other remain unchanged 
 throughout these many different forms. 
 
 If these points are held carefully in mind the subject will 
 take a far simpler form in the mind than is otherwise possible. 
 
 93. FIGURING TRIADS. 
 
 Note. Very frequently students become confused when 
 studying the figuring of triads because ihey forget that there 
 
Graded Lessons in Harmonij 83 
 
 are but three different notes and that these notes are 
 not changed although the chord appears to be quite different. 
 Further, let us remember that figuring triads is simply 
 a process of showing whether the root, third or fifth is in 
 the bass. 
 
 STUDY H. S., §§127-128, also §130. 
 
 WRITTEN EXERCISES: H. S., §128. (See Key, 
 128.) 
 
 To Find the Root of An Inverted Triad. 
 
 94 STUDY H. S., §129. 
 
 WRITTEN EXERCISES: H. S., §129. (See Key, 
 129.) 
 
 DRILL. 
 
 Turn to various simple hymn tunes and find the roots 
 of the inverted chords, and write out the chords (contain- 
 ing not more than three different letters) the roots of 
 which you may be unable to find. 
 
 Read H. S., §131, but do not study it, as you will come 
 to it again later on in connection with part-writing. 
 
 Note. I would like you now to be able to speak of the 
 chord of the "sixth," meaning the first inversion of the 
 chord ; or the chord of the "six four," meaning the second 
 inversion of the chord, as those are terms frequently used 
 by musicians. Remember that both the figures and the inver- 
 sions relate only to the bass or lowest note, and do not in 
 the least determine which note shall be highest. 
 
 95. EAR-TRAINING. 
 
 As you play (or a friend plays) the chords in their 
 different inversions, listen intently to the lowest tone, 
 trying to determine whether a root, third or fifth is in 
 the bass. The different qualities of rest or incompleteness 
 will aid in determining the form of the chord. Remem- 
 ber, however, that with most students it is a work of 
 months to gain facility in these lines. Sut if you learn to 
 listen more intelligently as you play or hear music, you 
 will find a great gain in musicianship is attained, whether 
 you succeed immediately in this work or not. To aid you 
 in distinguishing the various kinds of triads by hearing, 
 the following may be of assistance. 
 
84 Graded Lessons in Ilarmont/ 
 
 Instead of trying to measure the tones of the chord 
 by distance or by trying to detect which tone is altered 
 in changing from Major to Minor, Diminished or Aug- 
 mented, it is better to listen to the general effect or color 
 of the chord and try to notice the individual qualities of 
 each kind of triad. 
 
 The first step might be to bring the chord in question 
 into one of the great groups as follows: the Major and 
 Minor triads are restful, that is consonant, as described 
 at the end of Chapter II, H. S., while the Diminished and 
 Augmented triads are unrestful or dissonant and there- 
 fore show a decided tendency to progress to some other 
 chord. So, by noticing whether the chords are restful or 
 unrestful, we can reduce them to one of the two classes in 
 each of which there is but one choice. Let us suppose we 
 have decided the chord to be unrestful or dissonant : It 
 must be then either Diminished or Augmented. The 
 Diminished triad gives a sense of narrowness, or small- 
 ness, or contraction, and if we listen carefully to the ten- 
 dencies we will find, if the triad is not inverted (and for 
 the first exercises it should not be inverted) that they 
 tend to approach each other, the upper note to go down- 
 ward and the lower note to . go upward. In the Aug- 
 mented triad we feel the effect more of breadth, and the 
 tendency of the Augmented fifth is to go upward and to 
 expand. In this way we can distinguish one from the 
 other. 
 
 To distinguish between Major and Minor, one way is 
 to listen to the general effect whether cheerful or somber. 
 The Major gives the effect of floating, or of brightness, 
 while the Minor gives the effect of depression, or sadness. 
 Another way to distinguish between Major and Minor 
 triads is to mentally ( or audibly) sing the three tones of the 
 triad, beginning with the lowest, when it is quite easy to 
 distinguish whether we are singing 1-3-5 of the Major 
 scale or 1-3-5 of the Minor scale. Experiment along 
 these lines. 
 
 96. QUESTION-S 1-29, Key, pp. 69-70. 
 
 Improvisation. 
 
 97. "BOUNDING" AND "ROCKING" CHORDS. 
 
 In Lesson 11 the subject of "Bounding" and "Rocking" 
 chords was introduced, and drill was given upon the sim- 
 
Graded Lessons in Harmony 85 
 
 pier forms of the chord. The student should consider this 
 the beginning of a most important work, to be prosecuted 
 daily if he would achieve practical success. 
 
 DRILL. 
 
 Go over each exercise in the various lessons upon the 
 chords in their different positions and inversions, and 
 make a thorough drill upon each exercise in every Major 
 key, using the metronome if possible, and note the speed 
 attained. in each exercise. 
 
 WRITTEN EXERCISES. 
 
 Write in one key, a complete example of each form in 
 which you practiced the above exercises. 
 
 KEYBOARD DRILL. 
 
 Repeat the above exercises in all Minor keys if you 
 are an advanced student. If found too difficult, this work 
 may be postponed for a time. 
 
 98. KEYBOARD DRILL. 
 
 Return to H. S., §105 and try to connect the chords 
 there given, continuing the use of the "Bounding" and 
 "Rocking" forms which you have learned. This should 
 be done in all keys including Minor, if the pupil is suf- 
 ficiently advanced. One example of each kind and of all 
 the forms where special difficulty is found are to be writ- 
 ten out. 
 
 Using first the "Bounding" and then the "Rocking" 
 chord forms, the pupil should connect chords in the key 
 of C in the following order: 8, 6, 4, 2, 5, 3, 1; that is, 
 connect the chord of C Major with the chord of A Minor, 
 which in turn will be connected with the chord of F 
 Major, which in turn will connect with the chord of D 
 Minor, then to the chord of G Major, then to E Minor, 
 then to C Major. (This is not designed as the conven- 
 tional Closing Formula, which will come later, but is a 
 practical drill in employing the various triads of the key.) 
 
 Repeat this exercise in both "Bounding" and "Rock- 
 ing" chord forms in all Major, and if possible, all Minor 
 keys. 
 
 99. REVIEW AND SYNOPSIS. 
 
 At this point the pupil should review triads from the 
 beginning and should write a complete synopsis. 
 
86 (Iraded Lessons in Ilarvwni/ 
 
 LESSON 14. 
 
 PART-WRITING— TRIADS. 
 Connection of Triads in Simplest Form. 
 
 100. STUDY. 
 
 Skip for the moment H. S., §§95-101. Study H. S., 
 §^§102-104 and Key, 103. 
 
 ^\•RITTEX EXERCISES. 
 
 (a) Write ten examples, H. S., §105. 
 
 (b) Write five examples. Transpose to other keys. 
 
 KEYBOARD EXERCISES. 
 
 Do all the exercises in H. S., §105, (a), (b) and (c). 
 
 Special Note. This lesson, although very short in appear- 
 ance, is one of the most important in the whole course and 
 should receive many hours of drill. The ambitious student 
 will do these exercises not only in the key of C but in all 
 other keys. He will also do them with the left hand alone as 
 well as with the right hand, and also with two hands, letting 
 the left hand take the bass part, as illustrated in H. S.. 
 Fig 30. 
 
 To Connect Triads When There Is No Common 
 Note. 
 
 101. STUDY H. S., §§106-108. 
 WRITTEN EXERCISES. 
 
 (1) Copy the exercises in H. S., §109, and fill up the 
 vacant parts as there required. 
 
 (2) Write the exercises in H. S., §109, (a) and (b). 
 
 KEYBOARD EXERCISES. 
 
 Do the exercises in H. S., §109, as shown in Fig. 32. 
 Also §109, (a), (b) and (c). See Key*, p. 3;l Fig. 32. 
 
 *HOW TO USE THE " KEY." 
 
 SUGGESTION. 
 
 ta) In doing part-writing, it is desirable to use tliree staves for each exercise; 
 write tile bass upon tlie lower one of the three, your own setting upon tl^e 
 middle staff, and reserve tlte upper staff for tlie Kry, copying in from the Key 
 
(irndcd Lessans in narmniii/ 87 
 
 102. STUDY H. S., §§95-101; also Key, pp. 29-32. 
 
 WRITTEN EXERCISES. 
 
 Now go over the written exercises already completed 
 for this recitation, examine to find the consecutive fifths 
 and octaves, and correct the same as best you can. 
 
 103. QUESTIONS 6, 7, 8, 13, Key, p. 71. 
 
 only those chords which differ from your own setting. Be sure to have the bar 
 lines go through the three staves, so that the copied chords from the Key will 
 be over the proper bass notes. This plan not only brings the Key setting Into 
 proper place for easy comparison with your own but it is essential for future 
 reference and study. . It also makes it easy to discuss the advantages of one 
 setting over the other and it makes a deeper and more musicianly worker 
 of yourself. 
 
 (b) Pupils are placed upon their honor not to consult the Key until after 
 the part-writing or other exercises under consideration are completed. Then 
 as the next step they are to compare their work with the solution in the Key: 
 Note each difference and give the reason in writing: 
 
 (1) For the superiority of the setting in the Key; 
 
 (2) For the (possible) superiority of his own setting; 
 
 (3) For the acceptability of both settings, if possible; and if you 
 think a still different setting could be used, tell why. 
 
 This process saves the teacher time in the routine clerical work of writing 
 out a correct solution and brings the discussion right to the points of difficulty; 
 making possible a much more thorough and searching discussion of underly- 
 ing principles than is possible in re-writing an incorrect exercise. To make 
 such discussion with a class is most educational. This removes the danger 
 of the pupil's having a Key, for its use becomes a part of the educational process 
 and forces him to find underlying reasons and principles. 
 
88 Graded Lessons in Ilarmonij 
 
 LESSON 15. 
 
 PART-WRITING— TRIADS (Cont.) 
 
 104. NOTE. 
 
 We now come to a new department of our work — the only 
 one recognized in older methods, but which is only one of 
 several important departments in their course. "Part-writing" 
 means writing chords from a given bass or from a given 
 melody, the latter beirig commonly called "Harmonizing Melo- 
 dies." 
 
 The older methods gave us many positive rules, chiefly 
 prohibitions, for part-writing, and then furnished so many 
 exceptions to each rule that the average student became be- 
 wildered and lost all confidence. In this course it will be 
 attempted to show the principles which govern not only the 
 applications but also the exceptions to the rules. But the 
 student must remember that skill in part-writing is less a 
 matter of rule than of judgment, or a balancing of one force 
 against another, — a steering one's boat along a channel filled 
 with obstacles, where in steering around one rock we must 
 be careful not to collide with another. 
 
 The work in part-writing is in a certain sense like a review 
 of the subject, since we return to the subject of triads and 
 cover the same ground as before, but with a different end in 
 view. While the exercises in part-writing are being carried 
 on, the student should, without fail, make a thorough review 
 of all the constructive work at the keyboard covered in the 
 previous lessons. These exercises should now be carried into 
 more difficult keys, and higher speed and more accurate think- 
 ing should be required. 
 
 STUDY H. S., §§161-169; also Key, pp. 64-67. 
 
 Note. The above pages should give the student a general 
 idea of the principles of part-writing which will make the 
 corrections of the written work more intelligent. 
 
 REVIEW H. 5., §§95-114. 
 
Graded Lessons in Harmonij 89 
 
 WRITTEN EXERCISES.* 
 
 (a) Write the exercises in H. S., §115. Compare with 
 Key, pp. 33-34. (For best results, do not consult Key 
 until all the exercises are written.) 
 
 (b) Write the exercises in H. S., §116, then compare 
 with Key, pp. 36-38. 
 
 How to Discover Consecutive Fifths and Octaves in 
 the Written Work. 
 
 105. Very frequently students do not know how to go to 
 work to find consecutive fifths and octaves in the written 
 exercises. The following will be found of great assist- 
 ance : A consecutive fifth or octave implies that the in- 
 terval of a fifth or octave shall have appeared between 
 the same voices in two consecutive chords. The first thing 
 is to understand what the term "same two voices" means. 
 It is this : If between the Bass and Tenor of a chord the 
 interval of a fifth is found, and the same interval is 
 found between the same'two voices in the next chord fol- 
 lowing, consecutive fifths have been formed. On the 
 other hand, if in the first chord the fifth is between the 
 Bass and Alto, while in the second chord the fifth is 
 between the Bass and Tenor, they cannot be called con- 
 secutive fifths, since consecutive fifths require that the 
 interval shall be found between the same two voices in 
 consecutive chords. (Of course, in the above illustration 
 other voices than Bass or Tenor could be used. The chief 
 point is, that whichever voices have the octave or fifth 
 in the first chord, must have it in the next chord to make 
 the fifths or octaves consecutive.) 
 
 The student should remember especially that a fifth 
 in a single chord is not wrong, nor are octaves or fifths 
 
 *NOTE TO TEACHERS. 
 
 The work in part-writing should be even more personal and individual 
 than the preceding work, for the exercises written by the student must be 
 carefully corrected. 
 NOTE TO STUDENTS. 
 
 ■ Part-writing is a matter oi facility, and we need to do work not only correctly, 
 but quickly. The best way to gain the desired results is to take a limited 
 numlDer of exercises, not more than six or eight, and write them once through. 
 The next day do the same work without reference to the work of the day before. 
 Repeat this every day for a week. Remember that your progress is not measured 
 by the length of the lesson but by the way in which it is studied; that is, by 
 repealed workings of each exercise. 
 
90 Graded Lessons in Jlarmonij 
 
 wrong in two successive chords, but — and here is tlic 
 great point — they must not appear between the same 
 voices in both chords. 
 
 SPECIAL DIRECTIONS. 
 
 When writing an exercise, as soon as each exercise is 
 written the student should stop and examine the progres- 
 sion from the previous chord somewhat as follows : 
 
 Are there consecutive fifths or octaves formed between 
 Bass and Tenor ? 
 
 Are there consecutive fifths or octaves formed between 
 Bass and Alto? 
 
 Are there consecutive fifths or octaves formed between 
 Bass and Soprano ? 
 
 Are there consecutive fifths or octaves formed between 
 Tenor and Alto? 
 
 Are there consecutive fifths or octaves formed between 
 Tenor and Soprano? 
 
 Are there consecutive fifths or octaves formed between 
 Alto and Soprano? 
 
 In this way the student will learn to watch the leading 
 of the voices almost unconsciously and so avoid the pit- 
 falls of consecutive fifths and octaves. 
 
 STUDY //. S., §§97-111, and Key. pp. 29-32. 
 106. QUESTION'S 1-5, Key, p. 71. 
 
Graded Ijcssoiis in Ilarmonij 91 
 
 LESSON 16. 
 
 PART-WRITING— TRIADS (Cont.) 
 
 107. After writing tiie exercises required in Lesson 15, 
 the student is urgently advised to read again H. S.. 
 §§96-114, and §§161-169; Key, pp. 29-32, 64-67. 
 
 WRITTEN EXERCISES. 
 
 Write the exercises in H. S., §120. (See Key, p. 42.) 
 
 To Avoid the Augmented Second From 6 to 7 of the 
 Minor Scale. 
 
 108. STUDY. Students often have difficulty at this point, 
 so the following statements must be as emphatic as pos- 
 sible. To avoid the Augmented second, the seventh 
 must be approached from above ; or at least if from below 
 it must be by a skip; that is, we must not proceed directly 
 from 6 to /. Please heed this. We can go from 5 to 7, 
 but not from 6 to 7. It is, however, better to go from 
 8 to 7. 
 
 If you find that you have made this mistake you can 
 correct it by changing the voice that moves to J. For 
 example, take the chord D-F-B, followed by E-GS-B, here 
 you see the Alto of the first chord, F, has moved an 
 Augmented second to G# in the second chord; to correct 
 this, let the Soprano proceed to G8 and let the Alto go 
 downward, making the second chord B-E-G#. Now you 
 will see that we have followed the rule to let a different 
 voice approach 7. You will see that the Alto which in 
 the first example made the Augmented second upward, 
 now makes a half-step doivnward. Do not be confused 
 by the fact that GS is in the second chord and F is in the 
 first chord. This does not make the Augmented second 
 unless the same voice sings both tones. 
 
 READ Key, p. 43, and do the Additional Exercises as 
 outlined. 
 
 WRITE the exercises from the Figured Bass in //. .S"., 
 §123. (See Key. 123, pp. 43-49.) 
 
92 Graded Lessons in Harmony 
 
 109. KEYBO.VRD EXERCISES. 
 
 Working from the Bass in H. S., §§115-ll(j, try to play 
 the required chords with the right hand. Work slowly 
 at first and try to make the individual voices move as 
 smoothly as in the written exercises. 
 
 110. SPECIAL NOTES. 
 
 (1) Doubling the Third. One of the most frequent diffi- 
 culties encountered by the student is to know when to double 
 the third in a chord and when not to do so. The question 
 is thoroughly answered in //. S., §§162-166, and in Key, 162- 
 166, pp. 64-66. 
 
 (2) Concerning the Rule Which Required the Common 
 Note to Remain in the Same Voice. This difficulty is fre- 
 qiiently encountered but will be conquered in a very short 
 time. Study H. S., §167, carefully. Sometimes by changing 
 the position of a previous chord, the common note may be 
 so managed as to remain in the same voice, but it frequently 
 happens in a cadence (the chord of the Dominant seventh 
 followed by the Tonic) that this rule must be broken. Read 
 pp. 35-36 in Key. 
 
 (3) How to Choose Betureen Two Possible Progressions. 
 
 (a) Look ahead to see how the following chords will take 
 shape, measuring the comparative smoothness of the two ways. 
 
 (b) Study the tendencies of the individual tones contained 
 in the chord, particularly of the outer voices. It is quite pos- 
 sible that the progression in which the tendencies of the indi- 
 vidual tones are best observed will be the better progression. 
 But in this progression do not forget the "Tendency of Con- 
 tinuity" as that very frequently overrules the melodic ten- 
 dencies of the tones of the chord. 
 
 Hidden Fifths and Octaves. 
 
 111. Note 1. Students frequently have trouble to discover 
 consecutive or hidden fifths and octaves in their work unless 
 especial attention be given to the point. Let us begin with 
 a conventional definition of the term "Hidden Fifths." 
 
 Definition. "When two voices, moving in the same 
 direction, arrive at the interval of a fifth. Hidden Fifths 
 are produced." (The student will please learn the fore- 
 going definition by heart.) 
 
 Note 2. Tests in the classroom prove conclusively that 
 with such a definition as the above not one student in five 
 will get a complete and correct impression until the individual 
 points are brought out by the teacher's questions. Read the 
 
Graded Lessons in Harmoni/ 93 
 
 above definition carefully and then see if the points mentioned 
 below are already in your mind, or whether the following 
 description helps to give a clear impression. 
 
 DESCRIPTION OF THE ABOVE DEFINITION. 
 
 (a) "When two voices." Note that two voices are 
 indicated. By this is meant, not that any two voices may 
 start to progress in the same direction and some other 
 voices arrive at the interval of a fifth, but that the same 
 two voices shall progress in a similar direction and arrive 
 at the interval of the fifth. 
 
 (b) "Moving in the same direction." It will never 
 be a hidden fifth if two voices, moving by contrary or 
 oblique motion, strike the interval of a fifth. 
 
 (c) "Arrive at the interval of a fifth." This does 
 not mean that the first of the two intervals may be a 
 fifth and the second interval something else, but that 
 the first shall be "something else" and the latter of the 
 two intervals shall be a fifth. 
 
 Note*. Many students do not thoroughly understand hid- 
 den fifths and octaves. A hidden fifth occurs where 
 two notes which are not a fifth apart moving in the same 
 direction rest upon a fifth. For example: Play the notes 
 D-B. If B moves upward a half-step to C, and D moves 
 upward two degrees to F, a hidden fifth will be produced. 
 Note the following points : 
 
 (1) The notes must not be a fifth apart, since there would 
 be open or consecutive fifths if the interval of a fifth were 
 found both in the first and last interval. 
 
 (2) They must move in the same direction; that is, both 
 must go up or both go down. If two notes moving in con- 
 trary motion should arrive at the interval of a fifth it could 
 not be considered a hidden fifth. 
 
 Further, if one note should remain still and the other move 
 to the interval of a fifth, it could not be considered a hidden 
 fifth. 
 
 (3) The second of the two intervals must be the fifth, 
 not the first. 
 
 SPECIAL NOTE. 
 
 It should be remembered that all hidden fifths and 
 octaves are not faulty. On the contrary, many hidden 
 
 * From special lessons to pupils, 1913. 
 
94 Graded Lessons in Ilarmonij 
 
 fifths and octaves must be used else the progression will 
 be angular and awkward. The faulty hidden fifths are: 
 
 (1) Those in which both parts skip (where one voice 
 moves diatonically the hidden fifth or octave is usually 
 agreeable and therefore allowed) ; 
 
 (2) Those which in their effect contradict the melodic 
 or the harmonic tendencies (the effect is likely to be dis- 
 agreeable and therefore faulty). 
 
 The student should read H. S., §§134, 163, 165 ; also 
 Key. 134, pp. 62-64. 
 
 Note*. Hidden octaves and hidden fifths are not always 
 bad. To avoid them in every case will often result in pro- 
 ducing worse faults in the awkward progressions arising. 
 There are many rules in various books concerning which 
 hidden octaves and fifths are permitted and which are not 
 permitted. The following to my mind covers the ground with 
 sufficient thoroughness for all practical purposes : 
 
 (1) Hidden fifths or octaves in which both voices skip 
 are not good and should not be used. In connection with this 
 point, it should be remembered that the outer voices are 
 more prominent than the inner voices, and that which might 
 sound badly in the Soprano is sometimes quite satisfactory 
 when found in the Tenor or Alto. 
 
 (2) Where the natural melodic tendencies of the scale 
 tones are disregarded, the effect of the hidden fifth or 
 octave is usually not good, and such hidden fifths or 
 octaves should not be employed. It may be observed that 
 the natural tendency of a scale tone is brought more into 
 prominence by the hidden fifth, or octave, and that which 
 might have passed unnoticed under ordinary circumstances 
 is developed through the doubtful progression into a positive 
 fault. So it is my plan to judge the hidden fifths and 
 octaves by the above tests, whether both voices skip, and 
 whether any tendency is violated. If these tests are met I 
 admit the hidden fifth or hidden octave as correct. 
 
 EXERCISES. Write three examples showing hid- 
 den fifths, making as much variety in the form as you 
 can. 
 
 Hidden octaves are described similarly to hidden fifths. 
 
 EXERCISES. Write three examples of hidden 
 octaves. 
 
 .Should you, after this, fail to understand thoroughly 
 
 * From a special k-sson to a pupil, 1^1.^ 
 
Graded Lessons in Harmony 95 
 
 the hidden fifths and octaves, read the above twice 
 carefully. Also study again H. S., §134, and Key, 134, 
 pp. 62-64. 
 
 COLLATERAL READING. 
 
 112. (1) Statement. Broken Chords. The notes of a 
 chord, instead of sounding together, may be given in 
 succession, and in any desired order, with any desired 
 duplication of notes, and through as many octaves as 
 desired. For example, an arpeggio is simply a broken 
 chord led through several octaves. Similarly, the left 
 hand, in rnuch piano music, performs chiefly broken 
 chords. It is important to realize that these extended 
 forms are usually nothing more than simple chords. 
 
 (2) Exercises. 
 
 (a) Form examples of as many different figures in 
 broken chords as possible. 
 
 (b) Look for examples of broken chords in instru- 
 mental music. 
 
 (3) Statement. To -find the root of an inverted triad 
 or chord of the seventh. Continue to invert (try in dif- 
 ferent inversions) until the intervals of a third and 
 fifth are found for the triad, or of a third, fifth and sev- 
 enth for a chord of the seventh. The lowest note will 
 then be the root of the chord. 
 
 OBSERVATIONS. 
 
 (Study the following with special care.) 
 
 (4) Of Chord Individuality. It should be noted that 
 the identity of a chord is not destroyed by inversion, or 
 by adding more notes, although the characteristic form 
 and appearance of the chord may be entirely altered. 
 The principal chords of a scale retain their relative im- 
 portance, whether appearing in the form of a triad, chord 
 of the seventh, chord of the ninth, Diminished seventh 
 or Augmented sixth. Similarly, an unimportant chord 
 retains its relative condition in any of the above mentioned 
 forms. So the individuality of a chord is never lost. 
 
 (5) Of Chord Connections. Governing the connec- 
 tions and use of common chords, there appear to be sev- 
 eral important influences at work, somewhat as follows; 
 
96 Graded Lessons in Ilarmoni/ 
 
 (a) There is a physical connection between differ- 
 ent triads or common chords, regardless of their asso- 
 ciation in a key, which is caused by the fact that there 
 are notes common to both chords. (Note. It is largely 
 owing to this fact that different keys, apparently unrelated, 
 can be connected in a smooth manner.) 
 
 (b) There is a latent connection or relation be- 
 tween chords which have no common note or notes, when 
 they are members of the same key. (Note. It is this fact 
 that explains the connection of two triads which have no 
 note in common, as for example, in connecting the triad 
 of C Major with that of D Minor, the first and second 
 degrees of the key of C.) 
 
 (c) There is a certain conventionality about the 
 succession of chords, which seems to proclaim certain pro- 
 gressions good and others bad. That which makes many 
 progressions disagreeable, and forbidden in Harmony 
 text-books, is that some harmonic or melodic ten- 
 dency is thereby violated. (The writer will attempt 
 to show later how the melodic and harmonic tendencies 
 already described control all of the regular resolutions in 
 music, and also explain the origin and reasonableness of 
 many otherwise inexplicable rules of harmony.) This 
 conventional line of progression of chords may be com- 
 pared to the idiomatic form of language, where certain 
 expressions, in themselves perfectly correct, seem strange, 
 for the reason that they do not follow the idiomatic form. 
 When the student appreciates this conventional form of 
 expression he will be able to comprehend many things 
 which are not fully clear as the operation of principle. 
 
 (d) The writer is inclined toward the belief that 
 tonality, or key, is largely the result of the natural affin- 
 ity of certain chords for each other, and not the contrary, 
 i.e., that chords are related for the reason that they 
 happen to be in the same key. This presumption is illus- 
 trated most forcibly by the fact that in the development 
 of music the feeling of tonality was exceedingly vague, as 
 well as the use of signatures, until the chord of the Domi- 
 nant seventh was introduced. The use of this chord, 
 although against the judgment of the musicians of the 
 day, brought a distinct impression of tonality. 
 
 (6) Of the Correlative Character of the Different 
 Chord Forms. Referring to Collateral Reading. §58, 
 (7) -(8), it is found that Major intervals when inverted 
 
Graded Lessons in Harmony 97 
 
 become Minor, Minor become Major, Diminished become 
 Augmented, and Augmented become Diminished. Further, 
 it is found that Major and Minor, and Augmented and 
 Diminished, are correlative terms; that is, when a Major 
 interval becomes Minor by inversion, it remains in the 
 same class as before; i.e., if the given Major interval is 
 consonant, its correlative Minor will also be consonant, 
 while if the given Major is dissonant, its correlative Minor 
 will be dissonant. And similarly, the Augmented and 
 Diminished intervals are correlative. Applying the fore- 
 going to the structure of chords, it will be noticed that 
 when a triad, for example, is inverted, some of its 
 component intervals are thereby inverted. But as the 
 inversion of an interval does not alter its quality of 
 consonance or dissonance, so the inversion of a chord 
 does not alter its quality of consonance or disso- 
 nance, on account of this wonderful correlative quality 
 in its component intervals. To illustrate this point, 
 consider the simplest triad, C-E-G. C-E is a Major 
 third, which by inversion becomes a Minor sixth, E-C. 
 Now, if the Major third and Minor sixth were not both 
 members of the consonant family (or if they were not 
 correlative), the inversion of the triad would change it 
 from a consonant to a dissonant triad, and so change all 
 its relations with other chords. It is by such facts as the 
 above that a clear impression is gained of the symmetry 
 and logical completeness of the structure of music. 
 
 (7) Frequent reviews of the subject, independent of 
 any interruption, are of great assistance in keeping in mind 
 the thread of thought, the logical development of one prin- 
 ciple from another. A most important aid in a review 
 is to make a careful synopsis of each subject; that is, of 
 scales, of intervals, of triads. Illustrations of these 
 synopses may be found at the end of several chapters of 
 H. S. and the Key. It is not necessary to construct a 
 synopsis from memory, but rather from the text, compar- 
 ing one section with another, until the relations of the 
 parts to each other are discovered, and the logical out- 
 growth of one thought into another is understood. Facts 
 and principles do not stand alone, but one leads to another, 
 making a chain of logic, which, when understood, is per- 
 fectly simple. This is most particularly^ the case with our 
 subject, and the student is urged to find this thread, which 
 will make this a most fascinating and profitable study. 
 
98 Graded Lessons in Harmonii 
 
 (8) Exercises, (a) Refer to the previous lessons, 
 read the text carefully and thoughtfully, and do every 
 exercise, choosing, if possible, different keys from those 
 used before. 
 
 (b) Make a synopsis of scales, of intervals, and of 
 triads, first referring to the examples mentioned above, 
 and then proceeding from the text. Afterward compare 
 with the synopses in H. S. and Key. (N.B. Work of 
 this nature will greatly assist the memory in retaining the 
 foundation principles of harmony.) 
 
 (9) Exercises. Drill yourself in the formation of 
 various intervals and triads, in every key, continuing until 
 perfect familiarity and good speed are attained. (N.B. 
 This familiarity with the formation of all kinds of triads 
 is indispensable in the more complicated forms of later 
 study, for if the simple forms are not under control the 
 larger forms developed from them will simply be impos- 
 sible in any practical and useful sense.) 
 
 (10) In the drill for review, particular attention 
 should be given to the connection of triads. Unlike other 
 methods of harmony study, it is here intended that the 
 student shall learn to connect triads at the keyboard. This 
 is a direct step toward the realization of one of our sub- 
 jects: viz., to be able to use the knowledge of the theory 
 and structure of music. Detailed directions of much value 
 to the beginner in chord connection may be found in 
 H. S. and Key. 
 
 (11) Exercises, (a) Taking the different keys in 
 turn, connect the triads upon the first degree with the 
 triads on as many other degrees of the same key as 
 possible. 
 
 (b) Connect the triad on the second degree with 
 as many other triads in the same key as possible. 
 
 (c) Continue similarly from each of the remaining 
 degrees of the scale and repeat in other keys. 
 
 113. QUESTIONS 9-12, 14-29, Key, pp. 71-72. 
 
 (In Lesson 27 you will later be asked to answer Ques- 
 tions 14-29 more completely.) 
 
Graded Lessons in Ilarmonij 99 
 
 LESSON 17. 
 
 PART-WRITING— TRIADS (Cont.) 
 
 114. Following the directions about using the Key (see 
 Lesson 14), write Exercise 1, H. S., §133, compare with 
 Key, p. 57 and write your opinion of every point of differ- 
 ence immediately under your work. Proceed similarly 
 with the remaining exercises of §133. 
 
 Should you find any difficulty in interpreting the fig- 
 ures, refer to the Key, p. 54, and study pp. 54-56, giving 
 especial attention to the exercises there found. 
 
100 Graded Lessons in Harmony 
 
 LESSON 18. 
 
 PART-WRITING— TRIADS (Cont.) 
 
 115. In future each part-writing exercise as soon as 
 completed should be compared with the Key and your ob- 
 servations made upon each point of difference, as shown 
 in the directions on "How to Use the Key," Lesson 14. 
 Following this plan, work the exercises in H. S., §134. 
 
 N.B. Do not harmonize the scales at present. This is de- 
 signed for a later lesson. 
 
 A Little Lesson in Transposition. 
 
 116. The secret in transposition is to recognize locations in 
 the key and to be able to express corresponding locations 
 in any required key. The proper preliminary study of the 
 relative names (Tonic, Super-tonic, Mediant, etc.), or of 
 the scale degrees (first, second, third, fourth, etc.), and 
 the subconscious recognition of these relative names will 
 go far toward making transposition easy. Commence with 
 the transposition of melodies. If the melody can be car- 
 ried in the mind and mentally or audibly sung while being 
 written it will make the best possible drill. Let us take 
 for example the melody of "Old Hundred." Expressed in 
 figures (without the rhythm) it will be: 1, 1, 7,, 6,, 5,, 1, 
 2, 3; 3, 3, 3, 2, 1, 4, 3, 2 ; 1, 2, 3, 2, 1, 6,, 7,, 1; 5, 3, 1, 2, 
 4, 3, 2, 1. 
 
 The pupil should first mentally sing this through, 
 trying to associate the numerals with the tones of the 
 melody and with the notes, as written, for example, in the 
 key of G. After doing this try to write it in the key of 
 F, mentally singing the melody with the appropriate num- 
 bers. Now write it successively in every Major key — first 
 vidthout the signature, that is, writing in each sharp or 
 flat as required, and afterward writing the signature in 
 its place. Similarly wrilo in four different keys two dif- 
 ferent melodies, for example, "Old Folks at Home" and 
 "^^ankee Doodle," 
 
Graded Lessons in Harmony 101 
 
 LESSON 19. 
 
 CHORDS OF THE SEVENTH. 
 
 117. STUDY H. S., §§147-149, and Key, 147, p. 73. 
 
 COLLATERAL READING. §122, (l)-(6) inclusive. 
 
 Special Note. Remember that in forming chords, alter- 
 nate letters are used. This applies to chords of the seventh 
 just as much as to triads. 
 
 DRILL. 
 
 What letters are required to build a chord of the sev- 
 enth upon each of the following notes used as a root 
 (remember that sharps and flats are not required, but only 
 the letter name) : G? D? B? F? A? C? E? 
 
 Note. As chords of the seventh may be built upon each 
 and every note of the scale, it is necessary to become practi- 
 cally familiar with this point, through the following. 
 
 EXERCISES. H. S., §148, (a), (b), (c) ; write. 
 
 Compare the various chords of the seventh in the key, 
 as described in H. S., §149, and required in the following. 
 
 118. EXERCISES. 
 
 Analyze all the chords of the seventh in the key of 
 G, describing in each case the third, fifth and seventh 
 (that is, stating whether Major or Minor, etc.). 
 
 OBSERVATION. 
 
 The student should observe that the chord of the seventh 
 upon the fifth degree of the scale is more agreeable and satis- 
 factory than the others. The fifth degree of the scale is called 
 the Dominant, and the chord of the seventh upon the fifth 
 degree is called the chord of the Dominant seventh. (The 
 reason for this term "Dominant" will appear in a later lesson.) 
 
102 Graded Lessons in Ilarmoni/ 
 
 119. KEYBOARD EXERCISES. 
 
 Form the chords of the Dominant seventh in every 
 key, proceeding systematically from key to key. Note 
 specifically whether you can strike all the notes of the 
 chord instantly, or whether you hesitate in some of the 
 keys. Use the metronome. 
 
 WRITTEN EXERCISES. 
 
 Write the chord of the Dominant seventh in every key. 
 P>e sure that the chords you play correspond with the 
 written forms. 
 
 120. EAR-TRAINING. 
 
 (a) Play a Major triad and immediately afterward 
 add the Minor seventh, changing it into a chord of the 
 Dominant seventh. Note very carefully, the restfulness 
 of the triad and the lack in the chord of the seventh. 
 
 (b) Ask a friend to play triads and chords of the 
 seventh while you try to distinguish one from the other, 
 by observing the quality of rest or its absence. 
 
 (c) Listen very intently for this point when hearing 
 music performed. 
 
 121. QUESTIONS 1-10, Key, p. 81. 
 
 COLLATERAL READING. 
 
 122. (1) The chord of the seventh may be said to repre- 
 sent, as a type, the great family of dissonant chord struc- 
 ture. As such the chord suggests motion, as contrasted 
 with the rest of the consonant triad. (See Collateral 
 Reading, §(i(i, [2]-[4].) It represents labor, and strife, 
 and longings, which are satisfied when it is "resolved" or 
 led in a natural way into the condition of consonance. 
 
 For the student, as for the scientist, it forms one of 
 the most important parts of harmony study, for it epito- 
 mizes within itself most of the principles of musical 
 structure and the relations of the tone world. Think 
 about this last statement. 
 
 (2) Construction of the chord of the seventh. State- 
 ment. It is formed from the triad by adding another 
 tone, following the previous order of adding tones by suc- 
 cessive thirds. (See Collateral Reading, §75, [2] -[3].) 
 
Graded Lessons in Ilarmoni/ KU 
 
 It will have, as a result of this building, four different 
 tones, and will therefore always be dissonant, three differ- 
 ent tones being the limit of consonant combinations. 
 
 (3) Statement. A chord of the seventh, like the 
 triads, may be formed upon each and every note of the 
 scale. The chords formed upon the different degrees will 
 differ in their character, just as do the various triads 
 of the key, and for the same reasons : viz., that the con- 
 stituent intervals differ. For example, the chord of the 
 seventh upon the first degree of the scale of C, composed 
 of the tones C-E-G-B, has a Major third, a Perfect fifth 
 and Major seventh, while the chord of the seventh upon 
 the second degree of the same key has a Minor third, 
 Perfect fifth and Minor seventh, otherwise described as 
 Minor triad with Minor seventh. Other degrees of the 
 scale will exhibit other forms, the Minor scale showing 
 some that are extremely disagreeable in their dissonance. 
 This differing character in the various chords of the 
 seventh should not be considered a defect in the system, 
 but a great excellence, for differing characteristics arc 
 requisite in music as in social life. 
 
 (4) Observation. Some chords of the seventh; while 
 called dissonant, are still very pleasant to the ear. This 
 is explained by the fact that a dissonance does not neces- 
 sarily represent a discord, but the quality of unrest or 
 incompleteness, as shown in Collateral Reading, §66, (2). 
 
 (5) Statement. In the following exercises only scale 
 tones should be used, regardless of the effect or form of 
 chord which results. These chords must all be in the 
 key, and this is only possible when every tone belongs 
 to the scale.- 
 
 (6) Exercises, (a) Taking in turn each degree of 
 the scale of C Major as a root, form a chord of the 
 seventh, and describe as shown above in (3). 
 
 (b) Proceed similarly in all other Major keys. 
 
 (c) Proceed similarly in all Minor keys. 
 
104 Graded Lessons in Harmony 
 
 LESSON 20. 
 
 CHORDS OF THE SEVENTH (Cont.) 
 
 Different Positions of the Chords of the Seventh. 
 
 123. Note 1. It is thought best to take the diflferent positions 
 and inversions of the triads — or to learn thoroughly to con- 
 struct the chords in diiiferent forms — before taking up the 
 subject of the resolutions. For this reason we will skip over 
 a few pages of H. S., returning to them after a few lessons. 
 
 Note 2. As with triads, the chords of the seventh may 
 appear in different positions; that is, different notes may 
 appear in the upper voice. Positions are named similarly to 
 those of the triads : position of the third, position of the 
 fifth, position of the seventh and position of tlie octave. 
 
 WRITTEN EXERCISES. 
 
 Write the chord of the Dominant seventh upon G in 
 its four positions, marking each one and using two staves. 
 
 KEYBOARD EXERCISES. 
 
 Using two hands, play the chord of the Dominant sev- 
 enth on G in its different positions, naming each position 
 as played. Proceed similarly with all other chords of the 
 Dominant seventh, moving either chromatically through 
 the octave or following the circle of fifths. 
 
 Special Note. Be careful to distinguish between the 
 Dominant in the key and the Dominant on a given root; for 
 example, the chord of the Dominant seventh in the key of G 
 is very different from the Dominant seventh on G. The 
 Dominant in the key of G is D-FJ-A-C, while the Dominant 
 on G is G-B-D-F. 
 
 124. KEYBOARD EXERCISES. 
 
 It is comparatively easy to play the different positions 
 of the chord of the Dominant seventh when taken in 
 regular order. It is more difficult to take any required 
 position without having previously played through the 
 
Graded Lessons in Ilarmonij 105 
 
 various positions of the chord. 'J"o gain facility in this 
 department the student should take one position (for 
 example, the position of the third), and play every chord 
 of the Dominant seventh in this position vi^ithout having 
 previously played it in its natural form of 1-3-5-7. This 
 exercise should be practiced by taking successive chords, 
 following the circle of fifths. Similarly practice the 
 chord in the position of the fifth ; in the octave. 
 
 Note metronome speed attained in all of the above 
 exercises. 
 
 Special Note. If the pupil has any difficulty in finding the 
 various positions of these chords, he should first do the above 
 exercises in writing before proceeding with the keyboard drill. 
 
 Inversions of the Chords of the Seventh. 
 
 125. As with the triads, chords of the seventh are used 
 in their various inversions. 
 
 STUDY H. S., §172. 
 
 WRITTEN EXERCISES. 
 
 Write exercises as given in H. S., §172. 
 
 KEYBOARD EXERCISES : H. S., §172. 
 
 Combining the Various Positions and Inversions. 
 
 126. KEYBOARD EXERCISES. 
 
 Taking the position of the octave, play the chord of 
 the Dominant seventh on G in all its different inversions, 
 making with the direct form, four different forms of the 
 chord. 
 
 Next, take the chord in the position of the third and 
 play it in all its inversions. 
 
 Next, proceed in the position of the fifth, then in the 
 position of the seventh, taking all inversions with each 
 position. 
 
 Next, let us invert the foregoing process by taking 
 the direct form (Root in the bass) and playing the chord 
 successively in its different positions. 
 
 Next, taking the chord in the first inversion (with 
 third in bass) play with this bass all the different posi- 
 
106 Graded Lessons in Harmon;) 
 
 tions. Proceed similarly with the second and third inver- 
 sions. 
 
 Repeat the above with all the chords of the Dominant 
 seventh. 
 
 Special Note. Advanced students in playing above may 
 try to avoid doubling the third of the chord ; that is, when 
 the third is in the bass, try to omit it from the upper parts. 
 
 Note. The pupil should write the above exercises complete 
 in one key. 
 
 127. KEYBOARD EXERCISES. 
 
 It becomes increasingly difficult to combine any re- 
 quired inversion of the chord of the seventh with any 
 required position of the same. The following exercises 
 will therefore require continued drill, possibly for several 
 months, in order to gain real facility. 
 
 (a) Play the chord of the Dominant seventh upon 
 the root D in the first inversion and position of the fifth. 
 
 (b) Similarly, play the chord of the Dominant seventh 
 on the root D in its second inversion and position of the 
 third. 
 
 (c) Similarly, play the same chord in the third inver- 
 sion and position of the octave. 
 
 Special Note. Remember that inversion relates to the 
 Bass (or left hand), while position relates to the Soprano (or 
 highest note in the right hand). It will therefore be less 
 confusing in the following exercises to think first : "What 
 is the chord?" (i.e., name to yourself the notes required for 
 the given chord). For example, if some inversion and posi- 
 tion of the chord upon the root G is required, it is well to 
 think of the letters forming the chord (G-B-D-F) before 
 commencing to think of the required inversion and position. 
 Next, think of the required inversion. For example, taking 
 the same chord, the second inversion will bring D as the 
 lowest (or left-hand note). Next think of the position. 
 "Position of the third" would bring B as the highest note in 
 the above chord. The reason for the above is that if the 
 student is required to do two or three things at one time he 
 will probably do none of them well. It is better to attack the 
 obstacles one at a time. Therefore, in placing chords of the 
 
Graded Lessons in Harmony 107 
 
 sevtiUh in different inversions and positions, we think (a) 
 "What are the notes of a chord?" (b) "Which inversion?'' 
 (This places the left hand in position.) (c) "Which posi- 
 tion?" (This places the highest note.) Then we proceed to 
 "fill in" the inner voices. 
 
 128. KEYBOARD EXERCISES. 
 
 (a) Beginning with the chord of the Dominant sev- 
 enth upon the root C and proceeding through the circle 
 of fifths, play each chord in the first inversion and the 
 position of the fifth. 
 
 (b) Similarly, play through the circle of the fifths 
 the chord of the Dominant seventh in the second inver- 
 sion and position of the octave. 
 
 (c) Similarly combine the third inversion with the 
 position of the fifth. 
 
 (d) Similarly combine all positions and inversions, 
 working through the circle of fifths. 
 
 Note. Do not attenipt to take this complete drill at one 
 time, but spread it over several days, and continue through 
 a long period. Facility in the above is one of the most neces- 
 sary lines of work for those who would attain real success in 
 the use of chords. 
 
 129. QUESTIONS 11-1.5, Kev. pp. 81, 83; 1-12, Key, pp. 
 91-92. 
 
 Where There Are Two Sets of Figures Over One 
 Bass Note. 
 
 130. Observe the following points carefully : 
 
 (1) See H. S., §131, especially (d) and (g). 
 
 (2) When no figures are given, the Common Chord 
 is intended. {H. S., §131 [a].) 
 
 (3) When following or preceding other figures, the 
 figures 3-5-8 in any combination are used to indicate the 
 common chord as shown in the illustration, H. S., §131 
 
 (g). 
 
 (4) It should be observed that some figures must be 
 given, otherwise the six-four chord would have neces- 
 sarily continued for the whole time. 
 
 (5) Observe further, that instead of two sets of fig- 
 ures over one bass note, it would be possible to divide the 
 
108 Graded Lessons in Harmony 
 
 bass note into two shorter notes, connecting them by a 
 tie and placing one set of figures over each note. This 
 would amount to the same thing as having two sets of 
 figures over the one longer bass note ; and this is really 
 what is meant by the two sets of figures — two different 
 chords in succession which chance to have the same bass 
 note. 
 
 EXERCISES. 
 
 Write out in three positions each of the following exer- 
 cises : 
 
 Fig. 5, A 
 
 (a) 8 1 («) t 3 (c) 3 2 
 
 e 
 
 (6) 2 means chord of the seventh (its third inver- 
 sion). The 2 is enough to give a clue to the whole chord. 
 Eor example: 
 
 B 
 
 w 
 
 The figure 2 means here the second from F, which is 
 G. Now G and F can get into the same chord only when 
 sion of this chord is F-G-B-D. From F to G is a second, 
 there is a chord of the seventh, G-B-D-F, and the inver- 
 shown by the figure 2. Now two successive letters like 
 F-G can only occur in an inversion of a seventh chord; 
 and the upper one of the two letters is always the root 
 of the chord. 
 
 It is the same way when we find two successive figures 
 
 4 6 
 
 as 3 g-, the note indicated by the upper figure will be 
 
 the root of the chord. This makes a very short and easy 
 way to find the root of an inversion of the chord of the 
 seventh ; and after we have the root of any chord, it is 
 easy to add the other tones. The figure 2 really indicates 
 two successive letters since the figure 1 is always "under- 
 stood" ; it is the bass note itself and therefore requires no 
 figure. When the figure 2 is given, the note indicated by 
 the "2" will therefore naturally be the root. 
 
Graded Lessons in Harmony 109 
 
 The figuring of chords is a kind of musical shorthand 
 writing: as much as possible is omitted, leaving just 
 enough to give a clue to the chord. 
 
 COLLATERAL READING. 
 
 131. (1) Positions and Inversions of Chords of the Sev- 
 enth. Statement. As with triads, the chords of the sev- 
 enth are used in all positions and inversions. There will 
 necessarily be four different positions and three inversions 
 in addition to the direct form, as the chord contains four 
 tones and each may become in turn the highest or lowest 
 note. (For illustration of positions and inversions, see 
 any text-book on harmony.) 
 
 (2) Observation. The most important training in the 
 whole study of harmony, the one that holds the key to all 
 use of the knowledge at the keyboard in improvising and 
 modulating, as well as of all success in later studies, is 
 that of forming the chords of the seventh in every key, 
 in every position and inversion. He who can do this need 
 fear no difficulties to come. 
 
 (3) Exercises, (a) Taking in turn each chord of the 
 seventh in the key of C, place it in all its different posi- 
 tions, while keeping the left hand on the root note. 
 
 (b) Similarly combine each position of the above 
 with every inversion, by keeping the right hand upon the 
 same position of the chord while forming the different in- 
 versions with the left hand. 
 
 (c) Proceed similarly in all Major and Minor 
 keys. (In this exercise is sufficient material for several 
 months of study.) 
 
 (d) Without referring to the keyboard, recite the 
 chords of the seventh in their different inversions. 
 
 (e) Make thorough drill at the keyboard in form- 
 ing quickly any required position and inversion of any sev- 
 enth chord; e.g., What is the second inversion of the 
 chord of the seventh upon the root E (in the key of C) ? 
 To answer this, the student should quickly play the notes 
 B-D-E-G. 
 
 (4) Important Observation. The student should give 
 especial attention to forming and recognizing the chord 
 of the seventh which is found upon the fifth degree of 
 every scale, called the Dominant, for this is the most 
 important and most frequently used chord in music. 
 
no Graded Lessons in Harmonij 
 
 LESSON 21. 
 
 CHORDS OF THE SEVENTH (Cont.) 
 
 Consonance and Dissonance as a Principle. 
 
 132. Note. This is one of the most important points in the 
 study of Theory. Work slowly and go over this part repeat- 
 edly, trying to absorb it point by point. 
 
 STUDY H. S., §§149-151 ; also Key, 150, p. 73. 
 COLLATERAL READING, §137, (l)-(2). 
 
 Important Note. By this great principle we can divide 
 the whole of the material of music into these two divisions, 
 and so simplify the theory of music in a marvelous way. 
 Since the Independent Chords are treated in just as definite 
 (though different) a way, consequently, when we determine 
 the character of a chord, the appropriate treatment of that 
 chord will follow as a matter of course. 
 
 Let us next proceed to find, through analysis of chords, 
 how they are to be treated. First, let us make sure that the 
 proceeding is clear by answering at this point : 
 
 (a) How many chords of the Dominant seventh may 
 be found in any one key? 
 
 (b) Describe the intervals required to form a chord of the 
 Dominant seventh. 
 
 133. STUDY H. S., §§152-155; also Key, pp. .'J2-.53, and 
 153, page 74. 
 
 COLLATERAL READING, §137, (3)-(4). 
 
 134. QUESTIONS. 
 
 (1) State which are "Principal" and which are 
 '"Secondary" chords of the seventh. 
 
 (2) What is the difference in construction between a 
 chord of the Dominant seventh and a chord of the sev- 
 enth upon the .second degree of the scale? 
 
Graded Lessons in Harmonif 111 
 
 135. XOTE. 
 
 It is not necessary in the following exercises to find and 
 describe the interval of the Minor seventh, which is present 
 in each chord, but each Augmented and Diminished interval 
 should be found and described, and the proper resolution indi- 
 cated. 
 
 WRITTEN EXERCISES. 
 
 Describe each dissonant interval and tell how it should 
 resolve in the following chords: D-FJ-A-C; Bb-D-F-Ab; 
 E-GJ-B-D. Proceed similarly with other chords of the 
 Dominant seventh, until you can easily find the dissonant 
 intervals. 
 
 KEYBOARD DRILL. 
 
 Take in turn the following chords ; while holding down 
 the keys, find and describe each dissonant interval : 
 G-B-D-F; F-A-C-Eb; A-C8-E-G; B-Dlt-F#-A. Continue 
 till the dissonant intervals are easily and quickly found. 
 
 The Principle of Tendencies. 
 
 136. STUDY H. S., §§152-155; alsc Kev, pp. 52-53 and 
 153, page 74. 
 
 COLLATERAL READING. Study carefully §137, (3). 
 
 Definition. The process of passing from a dissonant to 
 a consonant interval is called "resolving" the dissonant 
 interval. We can now speak of resolving the following 
 intervals. 
 
 WRITTEN EXERCISES. 
 
 (a) Write the interval of a Diminished fifth from 
 C and let it progress, as shown in H. S., Fig. 43, to the 
 nearest consonant interval, which will be a Major third. 
 Observe that each tone moves only a half-step to the next 
 tone. Observe also that in this progression the letter 
 always changes; for exiimple, C goes upward a half -step 
 to Db, not to C#. 
 
 Similarly write the Diminished fifth upon CS and 
 reJsolve it as above. Proceed similarly with the Dimin- 
 ished fifth upon each (chromatic) degree of the scale 
 and resolve it. 
 
112 Graded Lessons in Harmony 
 
 (b) Referring to Fig. 42 in H. S., for an illustration, 
 write the interval of an Augmented fourth upon each 
 (chromatic) degree of the scale and resolve it to the 
 nearest consonant interval, which will be a Minor sixth. 
 Observe that each voice moves only a half-step and that 
 the letter should change as in the resolution of the Dimin- 
 ished fifth. 
 
 KEYBOARD EXERCISES. 
 
 Repeat the foregoing written exercises in resolving the 
 Diminished fifth and Augmented fourth upon each chro- 
 matic degree of the scale. When doing this be sure to 
 name the notes as they are played, somewhat after this 
 fashion: "The Diminished fifth Ct-G resolves by con- 
 traction to D-F#, which is a Major third"; The Aug- 
 mented fourth C-FS resolves by expansion to B-G, which 
 is a Minor Sixth." 
 
 COLLATERAL READING. 
 
 137. (1) So many of the foundation principles of musical 
 structure and so much of the practical use of musical 
 material are involved in the chord of the Dominant sev- 
 enth and its derivative chords, that it may well be de- 
 scribed as the epitome of structural law. A knowledge 
 of these controlling principles opens the way to a simple 
 and comprehensive understanding of all musical structure 
 — a view of the subject that shows the symmetry and uni- 
 versality of Nature. 
 
 In a previous section the structure of the chord of the 
 seventh was discussed. It was there shown that the 
 chord is formed from the triad by the addition of another 
 tone, making a chord of four tones and consisting of alter- 
 nate letters. There are seven chords of the seventh in 
 each key, for, like the triads, one may be formed upon 
 each note of the scale. The constituent intervals of these 
 various chords of the seventh must vary according to the 
 scale tones which are used (for only scale tones may be 
 used if we would keep the chords strictly in the key), 
 resulting in various forms or kinds of seventh chords. 
 For example, the chord upon the first degree (of a Major 
 key) will be composed of a Major triad and a Major 
 seventh, making a very harsh chord, while the chord upon 
 the second degree will have a Minor triad and a ATinor 
 
Graded Lessons in Harmon 1/ 113 
 
 seventh, giving an entirely different character (but still 
 harsh). Of the chords of the seventh upon the seven 
 different scale tones, the one upon the fifth degree, or 
 Dominant, is found to possess qualities and properties 
 which distinguish it from all others. To properly study 
 the chord, let us reviev^r the principles from which the use 
 of the chord is developed. (See Collateral Reading in 
 previous lessons.) 
 
 (2) The Principle of Resolution. All chords are 
 divided into two great classes, indicating either a state of 
 rest or a state of seeking for rest. These classes are 
 known as consonant and dissonant, and the process of 
 passing from a dissonant to a consonant chord is called 
 "Resolution." It is a universal law of music that disso- 
 nant chords shall be "resolved." As all chords of the 
 seventh are dissonant, it will be seen that all must re- 
 solve, or proceed, to another chord which shall be conso- 
 nant. 
 
 (3) The Principle of Tendencies. In the structure of 
 music two kinds of tendencies are recognized: (a) Melo- 
 dic Tendencies, or the tendencies of certain tones of the 
 scale to proceed in definite directions, among which we 
 will remind the reader of the tendency of the seventh 
 degree, or Leading Tone, to progress upward to the 
 Tonic, and of the fourth of the scale to progress down- 
 ward to the third degree; and (b) Harmonic Tendencies, 
 or the tendencies of certain dissonant intervals to progress 
 in definite directions, of which the more important are the 
 tendency of Augmented intervals to resolve by further 
 expansion into a consonant interval, and the tendency of 
 a Diminished interval to resolve by further contraction. 
 
 To illustrate, the interval p is an Augmented fourth, which 
 
 B C 
 
 tends to resolve by further expansion, thus, p- ', while the 
 
 interval n is a Diminished fifth and resolves thus, q 
 
 (4) Application of these Principles to Chords of the 
 Seventh. Chords are composite, being made up of inter- 
 vals, and the intervals are in turn composed of scale tones. 
 Now observe one of the most important principles of 
 
114 Graded Lessons in Jlarmnnii 
 
 musical structure: when a chord is dissonant, it must be 
 resolved; and when a dissonant chord contains a tone 
 which has a strong tendency either melodic (i.e., as a 
 scale tone) or harmonic, the chord as a whole will be 
 strongly influenced or even controlled by the tendencies of 
 its constituent intervals and tones. 
 
 It should be observed that the tendencies in their 
 operation are largely confined to dissonant chords, for a 
 consonant chord never contains a dissonant interval, and 
 is therefore never influenced by harmonic tendencies (only 
 dissonant intervals have harmonic tendencies), and a 
 melodic tendency alone is not sufficiently strong to seri- 
 ously disturb the quality of rest in a consonant chord. 
 But when a dissonant chord has specific tendencies in its 
 constituent intervals or tones, the general inclination to 
 progress, occasioned by the dissonance, receives a power- 
 ful influence in some direction, or toward some particular 
 resolution. Sometimes the inherent tendencies of a chord 
 point in different directions, in which case the stronger 
 tendency rules, while in others all the tendencies agree to 
 force the chord in one given direction, restricting the 
 chord to one, and only one, natural resolution. 
 
 (5) Application to the Chord of the Dominant Sev- 
 enth. If in the light of the above-mentioned principles 
 we examine the various chords of the seventh in the key, 
 we will at once see why the chord upon the fifth degree 
 is so much more powerful than the other chords, through 
 its inherent tendencies, as to be called the Dominant or 
 ruling chord, for it forces its own individuality to the 
 front, pushing its way to the key center by insistently re- 
 solving to the Tonic triad. In the accompanying illustra- 
 tion, the roots of the chords upon the successive degrees 
 of the scale are shown by capital letters, and the tenden- 
 cies of the tone, by the lines at the side of the letters, 
 indicating the direction of the tendency. 
 
 b/ c d e f^ g a 
 
 g a b/ c d^ e f^ 
 
 e f\ g a b' c d A 
 
 C D E Fv G A B7 
 
 12 3 4 5 6 7 
 
Graded Lessons in Harmony 115 
 
 Observing the tendencies in this illustration, it will be 
 seen that the only chords having more than one tendency 
 are those upon the fifth and seventh degrees of the scale. 
 It will be shown later that the chord upon the seventh 
 degree is considered and treated as practically identical 
 with that upon the fifth degree; that is, as a form of 
 Dominant harmony. The chord upon the seventh degree 
 will therefore be ignored for the present, leaving the 
 chord upon the fifth degree as the one chord in which 
 several distinct and separate tendencies unite in demand- 
 ing a specific resolution of the chord. 
 
 The melodic tendencies are for the seventh of the 
 scale, B, to progress upward to C, and for the fourth 
 of the scale, F, to progress downward to E. The har- 
 monic tendencies are that the Diminished fifth, B-F, 
 shall resolve by contraction to C-E. It should be particu- 
 larly noted that in this case the same letters, B and F, 
 are involved in both the melodic and harmonic tendencies, 
 or, in other words, that each tendency reinforces the 
 others in demanding the same resolution. It is not a 
 mere coincidence that this should occur in this chord, for 
 it will be shown that this point is the principle which pro- 
 claims that the chords of the Dominant seventh, the 
 Dominant Minor ninth, the Diminished seventh and the 
 three forms of the Augmented sixth chords, as well as 
 the wonderful group of "Attendant Chords," are merely 
 different forms of one and the same chord thought, with 
 similar origin, similar treatment, and similar resolution. 
 It is further most remarkable, and sufficient proof of the 
 truth of the theory, that in every position and inversion of 
 Dominant harmony, and in every one of the above-men- 
 tioned forms, the tendencies are infallible in their opera- 
 tion, no exceptions being found under any conditions. In 
 the accompanying illustration is shown the resolution of 
 the Dominant seventh chord in various forms to its Tonic 
 triad. The tendencies are here shown by the oblique 
 lines. 
 
 ^e f^ b^ 
 
 d ^e g g 
 
 b***^ ^c d^5« 
 
 '^e 
 
116 Graded Lessons in Harmony 
 
 Those letters which have no lines, since they are not 
 tendency notes, may be called neutral tones, and are free 
 to progress either upward or downward to a place in the 
 chord of resolution, or to retain the same note, as may be 
 found desirable. 
 
Graded Lessons in Harmony 117 
 
 LESSON 22. 
 
 CHORDS OF THE SEVENTH (Cont.) 
 The Principle of Resolution. 
 
 138. In past lessons we have learned that chords are com- 
 posed of intervals and that intervals give quality to the 
 chords. We learned further that chords composed exclu- 
 sively of consonant intervals are consonant and require 
 no resolution ; while chords containing even one dissonant 
 interval must be classed as dissonant chords, requiring to 
 be resolved. We have learned als6 that dissonant inter- 
 vals have a natural tendency toward some particular reso- 
 lution, described under the head of "Harmonic Ten- 
 dencies." 
 
 It is only a logical deduction from the above to the 
 statement that if the dissonant interval or intervals in a 
 chord are resolved according to their natural tendencies, 
 the chord will be resolved in the most natural manner. 
 Let us apply this to the resolution of the chord of the 
 Dominant seventh by studying carefully H. S., §§155-159, 
 and Key, 157-159, including all the keyboard and written 
 exercises given. 
 
 Re-Statement of the Foregoing as a Principle. 
 
 139. Dependent chords (all chords of the seventh are de- 
 pendent chords), contrary to the methods universally 
 taught, are not treated in a haphazard or chance way, but 
 follow well defined and perfectly natural principles, which 
 are practically universal in their application. This treat- 
 ment is the direct outcome of the natural qualities of the 
 chord tones themselves. By ''qualities" is meant certain 
 tendencies which are inherent in various scale tones. 
 These tendencies are less pronounced in consonant or inde- 
 pendent chords, but are developed or brought into activity 
 by the presence of dissonance. 
 
llf< Graded Lessons in- Ilarmoni/ 
 
 Resolution of Inversions of the Chords of the 
 Seventh. 
 
 STUDY /-/. S., §173, and Collateral Reading, §142. 
 EXERCISES : H. S., §173. 
 KEYBOARD EXERCISES. 
 
 (a) Take the chord of the Dominant seventh on the 
 root G, place it in turn in all positions and inversions, and 
 resolve each as shown in H. S., §§172-173. 
 
 (b) Take in turn every other Dominant seventh chord 
 and treat as above. 
 
 140. EAR-TRAINING. 
 
 Try to contrast triads with chords of the seventh, 
 noting the incomplete effect of the latter and the restful 
 quality of the former. When working with the different 
 inversions and positions of the chords of the seventh, 
 listen to the dissonant element of the Augmented fourth 
 or Diminished fifth and try to feel the direction in which 
 these voices tend to progress. This will help to deter- 
 mine the inversion or position. 
 
 Practical Application of the Chords of the Dominant 
 Seventh. 
 
 141. Having learned to construct the chords of the Domi- 
 nant seventh in all keys and to resolve them, we should 
 now learn to put our knowledge into practical use as 
 follows. 
 
 Cadences. 
 STUDY H. S., §190. 
 
 WRITTEN EXERCISES. 
 
 (a) Write the cadences in six Major and six Minor 
 keys as shown in (a) H. S., Fig. 60. 
 
 N.B. If found at all difficult, the above should be done 
 in twelve Major and Minor keys. 
 
 (b) Form a perfect cadence in which the Leading 
 Tone of the scale is in the Soprano of the first (or Domi- 
 nant seventh) chord. 
 
 yoTE. After writing one or two examples of exercises 
 (b) read H. S., §164. Perform this exercise in six Major and 
 six Minor keys not using the same keys as in exercises (a) 
 unless exercise (a) was written in all keys. 
 
Graded Lessons in Ilarmoni/ 119 
 
 (c) Write examples of imperfect cadences, not neces- 
 sarily like (b) in Fig. 60, H. S., but make as many differ- 
 ent forms as you can. 
 
 (d) Write plagal cadences as illustrated in (c), H. S., 
 Fig. 60, in three Major and three Minor keys. Place the 
 chord in as many positions as possible. Observe that the 
 "amens" sung at the close of hymn tunes are usually only 
 plagal cadences. 
 
 KEYBOARD EXERCISES. 
 
 Repeat the above exercises in every Major and Minor 
 key, in as many different positions and inversions as 
 possible. 
 
 Note. The third and seventh of the Dominant seventh 
 chord are called "tendency notes" or "active notes," the pro- 
 gressions of which are fixed. The other two notes (first and 
 fifth of the Dominant seventh chord) have no tendencies — 
 therefore we call them "neutral," or inactive tones — and they 
 have no fixed progression, but may progress either upward or 
 downward, or may remain quiet, whichever will produce the 
 best efifect. If the fifth were to go upward in the resolution, 
 it would double the third of the chord ; since it is better to 
 double the Root of a chord rather than the third, the fifth 
 usually progresses downward in the resolution. 
 
 COLLATERAL READING. 
 
 142. (1) In summing up the matter, we find that the chord 
 of the Dominant seventh has an almost irresistible in- 
 clination to resolve to the Tonic of the key, not because 
 one is the Dominant and the other the Tonic, but because 
 the Dominant chord contains within itself melodic and 
 harmonic tendencies which unite to compel the chord to 
 progress in that direction. We are now better enabled to 
 see the full meaning of the statement that a "chord is com- 
 posite, being made up of intervals," and to realize that 
 the character and qualities of the intervals go far toward 
 determining the quality and treatment of the chord. 
 
 (2) It would be a pleasant digression, at this point, 
 to show how the standard theorists of the past in their 
 teachings and writings, have unconsciously followed the 
 principle of tendencies without being able to formulate the 
 subject. Practically all the rules of part-writing are 
 founded on the cooperation or the opposition of these ten- 
 dencies and other simple influences ; the opposition of these 
 
]2() Graded Lessons in JJarmonjf 
 
 tendencies explains in a wonderfully simple manner, the 
 numerous so-called exceptions to the rules of harmony, 
 which may be shown not to be exceptions or imperfections 
 in any sense of the word. Further, the study of tenden- 
 cies, harmonic and melodic, will reveal why certain pro- 
 gressions and certain melodies are sometimes awkward 
 and unsatisfactory when they cannot be called incorrect. 
 In a word, the study of the subject from the point of view 
 here described will take one to the very heart of music, 
 putting reason and principle in the place of instinct. Dr. 
 Jadassohn used to say, "If you will work very hard for 
 many years, you will eventually feel why one note must 
 pass up and another down. I cannot tell you in words." 
 The doctor felt but did not know the inner principles of 
 tendencies, which are able' to explain the subtlest shadings 
 of meanings in music. In this subject there is material 
 for the most serious study by any musician, sufficient to 
 occupy many months, and rich in the reward for earnest 
 thought. 
 
 This exposition of what is believed to be the most 
 important single feature of musical theory is necessarily 
 brief and lacking in detail, but the interested student will 
 be able experimentally to test the principles involved 
 through the following exercises, or by reference to H. S. 
 
 (3) Exercises, (a) Form chords of the Dominant 
 seventh in all keys, both at the keyboard and in writing ; 
 trace out the tendency notes and intervals and resolve. 
 
 (b) Repeat in all positions and inversions. 
 
 143. QUESTIONS. 
 
 When you have thoroughly studied Lessons 19-22, write 
 answers to all the questions in Key, pp. 81, 83-86. Also 
 rewrite answers to those on pp. 91-92. This will reveal 
 the weak spots. 
 
 144. ANSWER TO QUESTION 21, Key, p. 83. 
 
 This point is a development of the order of sharps or 
 flats in a signature. If we remember that in a signature 
 or scale the sharps or flats always enter in a prescribed 
 order, and that the presence of the second sharp or flat 
 always presupposes (in fact, requires) the presence of the 
 first, we can find a simple and conclusive way of deter- 
 mining the key from this chord alone. 
 
Graded Lessons in Harmony 121 
 
 Let us take any chord of the Dominant seventh, for 
 example, G-B-D-F. Now the first sharp to appear in a 
 key is Ft, but as we here have F, it shows that the key. to 
 which this chord belongs has not even one sharp (since, if 
 it had any sharps whatever, F could not be natural). 
 Further, since in the order of flats Bb is the first, the fact 
 that we here have B^l shows that this chord belongs to a 
 key which has not even one flat. 
 
 Now what key has not even one flat or sharp? The 
 answer is C, and this chord, G-B-D-F, therefore belongs 
 to the key of C alone. 
 
 Illustration. E-G#-B-D. The GS shows that this 
 chord belongs to a key having at least three sharps, since 
 G# in a signature implies the presence of F# and CS. The 
 D*! shows that the key could not have four sharps, since 
 D would be that fourth sharp. Now what key has three 
 sharps but not four? Ans. A. 
 
 You will observe that the "sharpest" note (leading 
 tone) and the "flattest" note (fourth of the scale) are 
 the significant notes. 
 
 Read H. S., §§29, 250. 
 
 NOTE ON QUESTION 36, Key, p. 84. 
 
 I think of Augmented and Diminished intervals as the 
 "extreme" forms of dissonance, and I think of Major and 
 Minor intervals (when dissonant at all) as "milder" 
 forms. The above is like thinking of Soprano and Bass 
 as the "outer" parts and the Tenor and Alto as "inner" 
 parts. This will appeal to the thinking musician, if he 
 considers the perfect interval as the one most closely ap- 
 proximating the scientifically estimated interval, while the 
 Major form is a trifle larger than what science would 
 require and the Minor a trifle smaller. 
 
 ^-Augmented 
 
 Shown in tabulated form it /Yp.^jwt n,» ^»„f», 
 would be somewhat like this; U(Mini 
 
 ^Diminished 
 
 With the above for a preliminary, which the student 
 may forget if it does not appeal to him (I can make no 
 further explanation, since the point is only a theory or 
 phantasy of my own), we may make this statement : 
 
122 Graded Lessons in Haimoiii/ 
 
 In the resolution ,of dissonances, it will be found that 
 in the "extreme" forms both tones progress; while in the 
 "milder" or "moderate" forms it is sufficient if only one 
 tone progresses. Applying this to the resolution of the 
 Dominant seventh chord, it will be noted that in the inter- 
 val of the Dim. fifth or Aug. fourth both tones must pro- 
 gress, while in the same chord the interval of the Minor 
 seventh requires that only one tone progress. 
 
 Think this over — you may be interested. 
 
 ANSWER TO QUESTION 11, Key, p. 92. 
 First inversion. 
 
 ANSWER TO QUESTION 12, Key, p. 92. 
 
 In every inversion there will be consecutive figures or 
 notes upon successive degrees ; the upper one of these two 
 is always the root. 
 
Graded Lessons in Ilarmonji 
 
 123 
 
 LESSON 23. 
 
 CHORD OF THE SEVENTH (Cont.) 
 
 The Closing Formula, 
 
 145. This is a most useful drill for every student, as it can 
 at first be given in exceedingly simple form and afterward 
 elaborated until it becomes very efifective for improvisation. 
 
 STUDY H. S., §191 ; also Key, 191. 
 Illustrations of a closing formula. 
 
 Fig. 5. 
 (a) 
 
 (*) 
 
 l£ 
 
 ^ 
 
 -zs"- 
 
 -fr 
 
 IV 
 
 vt 
 
 
 .M 
 
 ^ 
 
 -^ ^ 
 
 -^ 
 
 
 / o .- 
 
 -^ 
 
 
 
 fZi 
 
 / 
 
 <?' 
 
 s 
 
 
 
 ^ ■ 
 
 Tl 
 
 ^ r- 
 
 
 22 
 
 g 
 
 
 \~ 
 
 I «> 
 
 
 
 
 
 tJ 
 
 
 
 
 
 
 
 
 
 
 
 PJ- 
 
 
 
 
 
 KL^ <i 
 
 
 
 
 
 
 
 
 
 
 Vt 
 
 The student should 
 write and play all 
 these forms in their 
 three positions. 
 
 WRITTEN EXERCISES. 
 
 Write in four Major keys the closing formula as shown 
 in Fig. 5; (a) above, (Advanced students may also per- 
 form the exercises in the Minor keys.) 
 
 KEYBOARD EXERCISES. 
 
 Following the same form, play the closing formula in 
 every Major key. 
 
124 
 
 Graded Lessons in Harmony 
 
 \ FEW EXAMPLES OF CLOSING FORMULA 
 WITH INVERSIONS. 
 Fig, 6. A 
 
 $ 
 
 ^= 
 
 f-^ 
 
 ai 
 
 ■-^- 
 
 ^- 
 
 ^=^- 
 
 JOL. 
 
 This is not a complete 
 ending, since it is not a 
 "perfect cadence." 
 
 I IV Is Vt 
 
 It might be completed by 
 the addition of another closing 
 formula. 
 
 Three parts with Pa.ssing \otes. 
 .Fig. 7, 
 
 IV Vt I 
 
 146. Try to form examples in the same or other keys, 
 more or less after the above order. If you find difficulty, 
 try to transpose these into other keys. This will give 
 some help. 
 
 Note. The chords may be introduced in any order, simply 
 remembering to use Vi just before the final Tonic chord. 
 
 Important Note. In playing the closing formula, it is 
 essential that the final chord should fall upon a strong beat, 
 usually the first beat of the measure, and the next preceding 
 chord — the Dominant seventh — should appear upon (or at 
 least continue through) the last beat of the preceding measure. 
 
Graded Lessons in Harmony 125 
 
 147. WRITTEN EXERCISES. 
 
 Following illustration (b), Fig. 5 above, write the 
 closing formula in four Major keys. (Advanced students 
 will do the same in the Minor keys.) (N.B. Do not use 
 the same keys as in the previous written exercise.) 
 
 KEYBOARD EXERCISES. 
 
 Following the above form, play the closing formula in 
 all Major keys. 
 
 148. WRITTEN EXERCISES. 
 
 Following the illustration (c), Fig. 5, write the closing 
 formula in four Major keys. (Advanced students will do 
 the same in the Minor keys.) 
 
 KEYBOARD EXERCISES. 
 
 Following the above form, play the closing formula 
 in all Major keys. 
 
 149. KEYBOARD EXERCISES. 
 
 The student should play both the cadences and the 
 various forms of the closing formula in the form of 
 "Bounding" and "Rocking" chords. An illustration of the 
 "Bounding" chords, and also of the "Rocking" chords as 
 played by the student should be written out complete in 
 one key as part of this lesson. 
 
 150. QUESTIONS 1-17, Key, pp. 114-115. 
 
126 Graded Lessons in Harmony 
 
 LESSON 24. 
 
 PART-WRITING— DOM. SEVENTH CHORD. 
 
 The Principles of Part-Writing. 
 
 151. In previous lessons on part-writing, repeated allusion 
 has been made to the principles described in H. S., §§161- 
 169; and Key, pp. 64-67. 
 
 STUDY with great care H. S., §§161-169, and Key, 
 pp. 64-67. Do not leave it till every point has been 
 thoroughly considered. This matter should be frequently 
 read over and kept in mind while doing the work in part- 
 writing. Beyond this it is difficult to give any further 
 specific rules for guidance in the study of part-writing; 
 in the last analysis it will be found that tact and musical 
 feeling are of far greater importance than these com- 
 paratively elementary rules. 
 
 EXERCISES IN PART-WRITING. 
 
 H. S., §160 and §170, 3 ex. Do not write more till 
 you can write these correctly without help from the Key. 
 
 COLLATERAL READING. 
 
 152. (1) Statement. It should be observed that the qual- 
 ity of dissonance is the first element of the principle of 
 resolution. The unrest of the interval is shown in the 
 incompleteness of the chord, forcing it to progress to a 
 consonant chord. 
 
 (2) Statement. As the presence of the dissonance 
 is the force which causes the chord to progress,' so the 
 specific quality of the interval determines what that move- 
 ment shall be, or, in other words, determines the resolution. 
 This fact is believed to be the most vital element in the 
 study of theory, the one with the widest application, aind 
 unfortunately, the one most neglected. It is shown in 
 the following; 
 
Graded Lessons in Harmony 127 
 
 PRINCIPLE OF HARMONIC TENDENCIES. 
 
 (3) Statement. The most prominent quality of a dis- 
 sonant interval, after its quality of dissonance, is the 
 unrest or incomplete effect, and the tendency, through 
 this unrest, to progress in certain definite directions. 
 
 (4) Statement. As compared with the normal form, 
 the. Augmented form is an expression of a size abnor- 
 mally large, and has a natural tendency toward further 
 expansion into some other and larger interval, rather than 
 to retreat to its normal form. (See H. S., §154). Simi- 
 larly, the Diminished interval is an expression of abnor- 
 mal smallness, and tends toward development by contrac- 
 tion into another and smaller interval. Formally stated : 
 (1) Augmented intervals tend toward further expansion; 
 and (2) Diminished intervals tend toward further con- 
 traction. E.g., the Augmented fourth, F-B (play it), 
 tends to expand to E-C; while the Diminished fifth, B-F 
 (play it), tends to contract to C-E. The demand for ex- 
 pansion or contraction does not necessarily exact a move- 
 ment of both tones of the interval, though it frequently 
 does. See H. S., §68. (N.B. It will be well to do again 
 the additional exercises in Key, p. 17.) 
 
 (5) Statement. In addition to the tendencies of Aug- 
 mented and Diminished intervals shown in the preceding 
 statement, there are also tendencies oa the part of the 
 dissonant Major and Minor intervals. (The only disso- 
 nant Major and Minor intervals are the seconds and 
 sevenths.) Of these the Major, representing the larger 
 form, tends to resolve by further expansion, while the 
 Minor, or smaller form tends toward further contraction. 
 For example, play the Minor seventh, C-Bb, when it will 
 be seen to tend toward the interval C-A or Db-Bb, resolv- 
 ing by contraction. Now play the Major second Bb-C, 
 when it will be seen to tend toward A-C or Bb-Db, resolv- 
 ing by expansion. 
 
 (6) Deduction. A very simple and natural deduction 
 may be drawn from (4) -(5) above, which assists_ in 
 placing the subject before us in a logical and practical 
 form. Observing the table in §66, (1), it will be noted 
 that while Major and Minor are correlative as are also 
 Augmented and Diminished, the Perfect stands by itself, 
 in the apparent center between Major and Minor. 
 Further, the Perfect interval is the one interval which 
 
128 Graded Lessons in Harmony 
 
 is never dissonant, and therefore is not subject to the law 
 of harmonic tendencies. It is but a simple deduction 
 from these facts to consider the Perfect as the central 
 form, dividing the two larger intervals, Major and Aug- 
 mented, from the two smaller intervals, the Minor and 
 Diminished. Further, observe that those dissonant inter- 
 vals which are larger than Perfect resolve by expansion, 
 while those which are smaller than Perfect resolve by 
 further contraction. Formally stated, the principle of 
 harmonic tendencies is as follows. (1) All dissonant 
 intervals are subject to the laws of harmonic tendencies, 
 tending either toward expansion or contraction in their 
 resolution. (2) Of these dissonant intervals, the Major 
 and Augmented forms have a natural tendency toward 
 resolution by further expansion, while the Minor and 
 Diminished intervals tend toward resolution by further 
 contraction. Remember that only dissonant intervals 
 possess harmonic tendencies. Further, these tendencies 
 are found to be inherent in the intervals themselves, like 
 the melodic tendencies of scale tones, and not artificially 
 added. Examples of various dissonant intervals are given 
 below, with dashes affixed, indicating the natural progres- 
 sions of the tones composing the intervals, whether 
 upward, horizontal or downward, in progression to conso- 
 nant intervals : 
 
 -e B-^ E — e 
 
 or 
 F^ F f . 
 
 e 
 
 Dim. 5th Aug. 4lh Maj. 7th Min. 2nd 
 
 (7) Observation. Note that in the extreme forms — ■ 
 Diminished and Augmented — both notes of the interval 
 progress, while in the less extreme forms — Major and 
 Minor — it is sufficient if one note progresses while the 
 other remains stationary. 
 
 (8) Exercises, (a) Form examples of all the disso- 
 nant intervals mentioned in §66, (1), indicating the normal 
 progression of each tone, as shown in (4)-(5) above. 
 
Graded Lessons in Harmoni/ 129 
 
 (b) Examine the following chords, finding the dis- 
 sonant intervals and indicating the proper progression of 
 each tone: G-B-D-F; A-C«-E-G; B-D-F-Ab; G#-B-D-F. 
 
 (c) Examine similarly dissonant chords in printed 
 
130 Graded Lessons in Harmony 
 
 LESSON 25. 
 
 PART-WRITING— DOMINANT SEVENTH 
 
 CHORD (Cont.) 
 
 Special Directions, Hints, Etc. 
 
 153. You have now had sufficient experience in part- 
 writing to realize that it is not a matter of absolute and in- 
 flexible rules which always operate in the same way, but 
 you now begin to find that what is good in one place may 
 not be desirable or even correct in another. You also are 
 wishing to learn by what authority your teacher objects to 
 a progression at one time while allowing it at another. I 
 beg you to believe that it is not a mere whim or a desire 
 to use the red pen. Dr. Jadassohn used to say that these 
 things cannot be taught, but if the student lived lon^ 
 enough, practiced part-writing regularly, and had a musi- 
 cal disposition, he might ultimately learn to feel that 
 which could not be expressed in words. Now I am in- 
 clined to take issue with him, to a certain extent at least, 
 for I believe the earnest student can learn to know defi- 
 nitely when a progression is acceptable and when it is not 
 suited to the occasion. 
 
 PART-WRITING is a matter of judgment, of recon- 
 ciling apparently opposing rules; but the judgment should 
 rest upon a consideration of the nature of the material 
 employed and the objects to be attained. It may be said 
 in passing that many of the older rules of part-writing 
 appear to have been formulated with reference to onl)- 
 the most conventional progressions ; and when other con- 
 ditions arise, it will be found that these rules (which 
 are mostly prohibitions) fail to apply. Further, it may be 
 said that many rules (such as the one regarding the re- 
 tention of a "common note" in the same voice) are de- 
 signed merely to guide the first attempts of the student, 
 the rules being reduced to the rank of suggestions without 
 obligation when the student is more experienced ; or they 
 may be considered as crutches, to be laid aside at the 
 proper time. For these reasons the student, as he ad- 
 
Graded Lessons in Harmony 131 
 
 vances, should not be surprised to see progressions per- 
 mitted or demanded, which at first were forbidden. 
 
 The basis for correct judgment is found, first, in the 
 nature of the material employed. By this is meant that 
 there are (a) individual qualities inherent in the different 
 degrees of the scale out of which grows the principle of 
 Melodic Tendencies; and (b) the result of combining 
 tones into intervals, out of which grows the principle of 
 Harmonic Tendencies; and (c) the Suggestive Oualities, 
 various items outlined in H. S., §161, (4)-(8). 
 
 To illustrate the thought in (a) and (b) above, it will 
 suffice to say that a hidden fifth would be wrong if so 
 placed in the scale that the melodic tendency of some 
 important note would be violated, while a similar progress 
 in another part of the scale, where the tendencies were 
 not violated would be permitted. 
 
 STUDY. 
 
 The student will now study again H. S., §§161-109 ; 
 also Key, pp. 64-67, noting particularly that this recon- 
 ciling of opposing influences is much like the exercise of 
 tact in every-day life ; it is much easier to use tact than to 
 force our way, regardless of others. So remember that 
 the early rules of part-writing are much like the rules of 
 childhood, to be replaced later by maturer judgment. 
 
 EXERCISES -IN PART-WRITING. 
 
 Write the remaining exercises from the given Basses 
 in H. S., §170. 
 
 COLLATERAL READING. 
 
 15-1. THE FUNCTION OF THE EAR IX THEORY. 
 
 Perception of Music Through Hearing. 
 
 (1) It is a very limited method which confines the 
 study to part-writing. The power to construct and use 
 chords at the keyboard, and to recognize the structure of 
 music from hearing it, are among the most useful and 
 enjoyable features of Theory study. More of cultivation 
 and musicianship for teacher and student may be attained 
 by a short course along these lines than by years of 
 part-writing. It is difficult to give detailed directions 
 
132 Graded Lessons in Harmont/ 
 
 in a limited space for proper training in the art of listen- 
 ing intelligently. The study should be pursued upon the 
 basis of relationship (see Collateral Reading, §12, [1].) 
 and one may profitably follow several lines, as for 
 example : 
 
 (a) Learning to listen accurately and intelligently to 
 the tones produced in playing. In this respect the violin- 
 ist and singer have an advantage over the pianist, for they 
 must critically form each tone, whereas the pianist, having 
 the tones "ready-made," is not obliged to concentrate his 
 attention upon this point. He must therefore be educated 
 to do so, not only in his daily study, but also in listening 
 to the performances of others. 
 
 (b) Learning to write from dictation by means of a 
 carefully graded course in musical dictation. This should 
 cover the power to distinguish between whole and half- 
 steps, the scales, intervals, chords of all kinds, resolutions, 
 connections, melody, rhythm, modulation and the orna- 
 ments of music. Detailed directions may be found in 
 H. S. A most practical form of dictation and ear-train- 
 ing may be given in class or club work by having the 
 members follow with the fingers upon a dumb keyboard, 
 or printed representation of the keyboard, the scale notes, 
 intervals and chords sounded upon an instrument by the 
 leader. In addition to the mental pictures formed from 
 hearing, the ability to produce is thus gained by having 
 the fingers in that position upon the keys in which the 
 effect was originally produced. This association of cause 
 and effect is of the highest value. The use of such a 
 representation of the keyboard in the classroom, by 
 which a larger number may also have the same training 
 and actual drill as the individual student at the keyboard, 
 is one of the latest advances in Theory teaching. 
 
 (c) Trying to think and sing certain intervals; e.g., 
 sounding C upon the keyboard, try to think how far to 
 the tone F and test by reference to the keyboard. Later 
 extend this to include all possible intervals. 
 
 (d) Trying to think how unfamiliar passages of 
 printed music would sound ; in other words, mentally read- 
 ing music. 
 
 (e) Trying to achieve absolute pitch. Discover the 
 pitch of voices, bells and whistles ; also, think a given 
 pitch, sing it, and then prove by reference to the piano. 
 
Graded Lessons in Harmoni/ 133 
 
 For example, as you read this, fix in your mind and voice 
 the pitch of the tone G, as nearly as you can, and prove 
 it at the instrument; similarly, try to find the key of 
 selections heard in the concert-room. 
 
 (f) Constantly noting the effect of Major and 
 Minor in keys, chords, intervals and melodies. 
 
 (2) At first, in listening, as in early experiences with 
 a foreign language, only single stray bits will be recog- 
 nized, like a cadence in melody or harmony, or a charac- 
 teristic rhythmic feature. Continued striving will in- 
 crease the capacity, until the ability may be achieved to 
 recognize successive chords, to follow a melody, to trace 
 modulations, and to have an understanding of musical 
 form; or even, with the talented few, to mentally picture 
 the appearance of a composition as it looks on the score. 
 
134 Graded Lessons in Harmony 
 
 LESSON 26. 
 
 PART-WRITING— DOMINANT SEVENTH 
 CHORD (Cont.) 
 
 155. SPECIAL NOTE. 
 
 Further rules are not necessary in taking up the study of 
 part-writing with inversions. Remember the principles of 
 Tendencies and Individuality of Scale Tones, and the natural 
 or conventional progressions of single tones and chords. 
 
 Students frequently misunderstand the figuring of Basses. 
 Read everything written up to this point about figuring of the 
 chords, and also H. S., §199. 
 
 PART-WRITING : H. S., §173. 
 
 156. EAR-TRAINING. 
 
 For several lessons past we have done nothing new 
 with ear-training. It is presumed that the student has 
 been working quietly alone, reaching toward greater facil- 
 ity in recognizing the individual tones of the chord, and in 
 recognizing position and inversion, possibly also in recog- 
 nizing, or in making a beginning in recognizing the 
 degree of the scale upon which a given chord is placed. 
 Specific direction is scarcely necessary for this work, and 
 if a student has not already tried to do this it should now 
 be undertaken without further delay. 
 
 Next we should try to distinguish Dominant seventh 
 chords from triads, chiefly by the absence or the presence 
 of repose, elsewhere described as dissonance or conso- 
 nance. 
 
 l.-)7. QUESTIONS. 
 
 Answer again questions 14-29, Key, pp. ~l-7-2. 
 
 158. NOTES ON ADVANCED PART-WRITING. 
 
 As you go into more difficult work, you will find it 
 more frequently necessary to double the Third, occasion- 
 ally to carry the Leading Tone downward and to violate 
 other tendencies, for the following reasons: 
 
Graded Lessons in- Harmon// 135 
 
 (1) The musicians who wrote the exercises did not 
 definitely understand the tendencies as a principle. Dr. 
 Jadassohn, for example, felt the tendencies but did not 
 systematize them. 
 
 (2) In general, these tendencies are not always para- 
 mount. They are always to be held in mind and observed 
 when there is a choice; but when by observing them we 
 run into awkward progressions or consecutives, or even 
 if the work cannot be made as smooth as otherwise, we 
 should not consider tendencies in the least. In a word, 
 they are to be observed only when nothing is to be lost ; 
 therefore do not hesitate to violate a tendency or double 
 the Third of a chord when you think any improvement 
 can be gained thereby which will outweigh the disadvan- 
 tage of violating the tendency. 
 
136 
 
 Graded Lessons in Harmony 
 
 LESSON 27. 
 
 CADENCES: ELABORATED 
 MELODICALLY. 
 
 Improvisation. 
 
 159. Note. The above high-sounding title means simply that 
 we are to form cadences with melodic passing notes instead of 
 going directly from the Dominant seventh to the Tonic chord. 
 We can elaborate the progressions in the several examples 
 given below. 
 
 KEYBOARD EXERCISES. 
 
 (a) Following the example given in Fig. 8 (a) below, 
 play the cadence in every Major and Minor key. 
 
 (b) Similarly play the cadences in all keys, following 
 in tone the examples shown in Fig. 8 (b) and (c). 
 
 Special Note. The student^ should now read H. S., §§315- 
 322. 
 
 Note. The student should write three examples in each of 
 the above mentioned forms as part of the lesson, to show that 
 he is doing the work correctly. He may also try to originate 
 other forms, more or less similar to the examples shown below 
 and may write illustrations of them. It is also well to look 
 for examples of cadences in printed music, observing the 
 habits of different composers in this respect, or comparing 
 different styles of music. 
 
 Fig. 8. 
 
 (a) 
 
 m 
 
 f 
 
 e^ 
 
 -I- 
 
 /*rf. 
 
 # M. 
 
I 
 
 (4) 
 
 Graded Lessons in Harmony 
 
 137 
 
 — I- 
 
 _<2_ 
 
 =1= 
 
 m 
 
 
 Fed. 
 
 -zi— 
 
 Fed. 
 
 g 
 
138 Graded Lessons in Harmony 
 
 LESSON 28. 
 
 HARMONIZING THE SCALE. 
 
 160. NOTE. 
 
 So much difficulty has been experienced by beginners in 
 harmonizing the scale that the study in this line has been 
 delayed till now instead of following the order of H. S. 
 
 The student should realize that any note may belong to 
 three different triads, since it may be the Root of one triad, 
 the Third of another and the Fifth of another. For example, 
 the note C is found in the triad of C-E-G, of A-C-E and of 
 F-A-C. 
 
 It should also be remembered that we cannot harmonize the 
 scale by any promiscuous series of chords which contain suc- 
 cessive tones to be harmonized, but that a certain natural 
 succession of chords is required. It is very difficult to say 
 what constitutes a natural or conventional series of chords. 
 In one way it appears a little like the feeling of gravitation 
 toward the key center. Please read carefully H. S., §§340, 
 341 ; also Key, pp. 180-183. The student is also recommended 
 to learn the opening paragraphs of a most valuable little work 
 by Dr. Cutler, "Harmonic Analysis," published by Ditson. 
 
 EXERCISES. 
 
 Fill out the inner voices in exercises 1, 2, 3, 4, H. S., 
 §135 (a), afterward referring to Key as usual. Next 
 complete exercises 5, 6, 7, 8 of the same section; then 
 do the exercises (b), (c), (d) and (f), omitting (e) 
 unless you are experienced in work of this character. 
 
Graded Lessons in llarmonij 139 
 
 LESSON 29. 
 
 SECONDARY CHORDS OF THE SEVENTH. 
 PART-WRITING. 
 
 161. STATEMENT. 
 
 There is a natural tendency inherent in music, causing 
 a common chord to progress to the chord whose root is a 
 fifth below or a fourth above. This seems to be a 
 natural characteristic of music, and defies rational ex- 
 planation. (The writer believes this to be the conven- 
 tional result of constantly hearing the cadencing close of 
 Dominant to Tonic; but he can hardly pursue the 
 thought here.) When the seventh is added to the com- 
 mon chord, making a dissonance, this tendency to pro- 
 gress to the fifth below or the fourth above becomes more 
 marked, and in the case of the Dominant seventh chord 
 it is even more marked still. Mr. Cutler, in his Harmonic 
 Analysis, says that following this thought, the chord upon 
 III progresses naturally to that upon VI, VI to II, and 
 V to I. He says further, that the nearer this progres- 
 sion approaches to Tonic harmony the more gratifying 
 and reposeful the effect, which is another way of saying 
 the natural tendencies have been satisfied. 
 
 For the above reason we may expect the secondary 
 chords of the seventh to follow, in a general way, the 
 treatment of the chord of the Dominant seventh. It 
 should be remembered, however, that as the tendencies in 
 the secondary seventh chords are either absent entirely, 
 or are less in agreement with each other, the net result, 
 or tendency to progress to the chord a fourth higher or 
 a. fifth lower, is much less pronounced. In fact, these 
 same tendencies, which were so unvarying in the case of 
 the Dominant seventh chord, may even make it very easy 
 for the secondary chords of the seventh to progress in 
 an irregular manner ; so do not expect the secondary sev- 
 enth chords to be as well behaved as those of the Domi- 
 nant seventh. Do not forget that the Dominant seventh 
 
140 Graded Lessons in Harmony 
 
 is the one chord which is like Nature's Chord, and 
 that it has qualities and properties possessed by no others. 
 
 STUDY H. S., §176-1?'8. 
 
 WRITTEN EXERCISES. 
 
 Write the scale of G Major. Upon each degree write 
 the chord of the seventh, using only scale tones — no acci- 
 dentals. Now describe the first or Tonic seventh chord, 
 by naming and describing each and every interval, not 
 only from the root but from the other notes as well, stat- 
 ing in which interval or intervals the chord differs from 
 the chord of the Dominant seventh built upon the same 
 root. Proceed similarly with each secondary seventh 
 chord. 
 
 KEYBOARD DRILL. Key, p. 93. 
 
 162. RESOLUTIONS. 
 
 Statement. As just stated, the resolution of th^se 
 chords, while often following that of the Dominant sev- 
 enth chord, is in no way obligatory, since the tendencies 
 do not incline in the same way in all the chords. In fact, 
 the resolution of these chords is more like the progression 
 of the triads, and might well be called "progression"' 
 instead of resolution. This brings us to the consideration 
 of the point that in music there are two ways of moving 
 from chord to chord: (1) by simple progression; that is, 
 moving from chord to chord as in connecting triads, either 
 with or without the common note (see H. S., §102 et seq.) ; 
 (2) by resolution, in which the tendency notes point the 
 way. (See H. S., §152 et scq.) In the first case the pro- 
 gression of the chord is more or less free, as there is 
 usually a choice of possible chords to follow ; in the latter 
 case the progression is not free, but is practically forced 
 to one particular chord by the operation of the tendencies. 
 In the secondary seventh chords there are tendencies, of 
 course, but as in very few cases do the tendencies of any 
 two notes agree, there is no real and positive force opera- 
 ting in any one direction. The fact that there is a dis- 
 sonance forces us to the conclusion that some chord must 
 follow, but ivMch chord is not so clearly shown, for the 
 tendencies do not unite upon any one. Being therefore 
 more free, the secondary seventh chords may be treated 
 
Graded Lessons in Harmony 141 
 
 more like common chords or triads, and may be allowed 
 to progress to any chord of the key, provided that for- 
 bidden progressions like consecutive fifths, etc., are not 
 formed, and that the effect is good (if it sounds well it 
 will probably not be wrong, though of course what sounds 
 well to the beginner might not always be the choice of the 
 experienced musician). 
 
 COLLATERAL READING. 
 
 Read H. S.. §§187-188. This will give a little further 
 light upon the subject. 
 
 WRITTEN EXERCISES. 
 
 Form in turn each secondary seventh chord (the chord 
 upon each degree of the scale except the fifth) in the key 
 of C Maj., and resolve each one to as many different com- 
 mon chords in the key as appear to you to sound well, 
 taking care to avoid forbidden progressions. 
 
 KEYBOARD EXERCISES. 
 
 Proceed as above, using in turn every other Major key. 
 (Advanced students may do the same with the six Minor 
 keys also.) 
 
 PART-WRITING, H. S., §184, fifth ex. only. 
 
142 Graded Lessons in Harmony 
 
 LESSON 30. 
 
 SECONDARY SEVENTH CHORDS— 
 PART-WRITING (Cont.) 
 
 163. Commence with the sixth exercise, H. S., §184, 
 complete the exercises in that section and in §186. 
 
 Analytical and Comparative Reviews. 
 
 164. Note, While we are working steadily forward in part- 
 writing, it is not practicable to develop further new principles, 
 but it is most earnestly suggested that this is the proper time 
 to make a thorough review of all the matter studied up to this 
 point. As you read, try to realize the symmetry and com- 
 pleteness of the laws of music : that they are the laws of 
 nature expressed in this our chosen form. Try also to realize 
 that the same laws are expressed in architecture, in oratorx-, 
 in painting, sculpture and in every department of life. 
 
 STUDY with great care H. S., §201, and Key. 201, p. 
 110. Think out as carefully as you can the relationship 
 of each principle of the science of musical structure, and 
 its application in the work so far as you have studied. 
 
 STUDY also H. S., §§202-203. 
 
 Complete your review with this lesson, as with the 
 next lesson we shall undertake further work in ear- 
 training. 
 
Graded Lessons in Harmony 143 
 
 LESSON 31. 
 
 SECONDARY SEVENTH CHORDS IN 
 MINOR-PART-WRITING (Cont.) 
 
 165. STUDY H. S., §187 and write the exercises there 
 outlined. 
 
 WRITTEN EXERCISES. 
 
 Write the chord of the seventh upon the seventh de- 
 gree of every Major scale, and resolve to the Tonic chord. 
 Write upon two staves, and in four parts. 
 
 KEYBOARD EXERCISES. 
 
 Repeat the above at the keyboard, using two hands. 
 
 PART-WRITING EXERCISES. 
 
 H. S., §§188, 189. (Compare with Key.) 
 
 Ear-training: Dominant Seventh Chords. 
 
 166. It is presumed that the student has made some prog- 
 ress in distinguishing the chord of the Dominant seventh 
 from Major or Minor triads. Assuming this to be the 
 case, we will now try to recognize the various positions of 
 the chord of the Dominant seventh. The process is some- 
 what as follows : Taking as the basis for comparison the 
 individual quality of scale tones described in Lesson 2, it 
 becomes quite simple to distinguish the position of the 
 chord of the seventh, and also the position of the Tonic 
 triad to which it resolves. (Consider the Dominant seventh 
 chord in the following illustrations to be that of G-B-D-F 
 and the Tonic chord to which it resolves, C-E-G.) When 
 the chord of the seventh is in the position of the third 
 for example (B at the top), the Leading Tone of the scale 
 is felt to be prominent, and it will resolve or progress 
 upward a half-step and give a decided feeling of finality 
 when it reaches the Tonic C. Again, if the Dominant 
 
144 Graded Lessons in Harmony 
 
 chord is in the position of the fifth (D at the top), we 
 will feel a downward tendency in the upper note, D, and 
 a sense of finality or completeness when it goes downward 
 to the Tonic, C. If, on the contrary, D progresses up to 
 E in the Tonic chord, the incompleteness will be quite 
 apparent. Again, if the Dominant seventh chord be in 
 the position of the seventh (F at the top), the tendency 
 to go down will be apparent, but the result will not be final 
 as it will progress down to the third of the Tonic chord. 
 Again, if the Dominant chord be in the position of the 
 octave (G at the top), it will not move, but will keep the 
 same letter in the resolution. This leaves a sort of "float- 
 ing" feeling as contrasted with the calm incompleteness 
 of the position of the third of the final chord and the 
 definite close when the final chord is in the position of the 
 octave. 
 
 Work out the above thoroughly at the keyboard, listen- 
 ing and comparing the different positions as described, 
 then if necessary write out these different positions and 
 ask a friend to play them in miscellaneous order while 
 you are to judge of results. In all the above, if the bass 
 is used it should invariably be in the direct form. You 
 will find this much less difficult than you anticipate. The 
 author has been delighted to find so simple and compre- 
 hensive a way of presenting this subject. 
 
 1()7. QUESTIONS 1-27, Key, pp. Ill, 113-114. 
 
 168. EXERCISES IX HAR^^IOXIZING THE SCALE. 
 
 (a) H. S., §171; 
 
 (b) H. S., §175. ( See Illus., Key, pp. 184-185.) 
 
Graded Lessons in Harmont/ 145 
 
 LESSON 32. 
 
 SECONDARY SEVENTH CHORDS— 
 PART-WRITING (Cont.) 
 
 169. PART-WRITING: EXERCISES WITH NON- 
 
 CADENCING RESOLUTIONS. 
 
 After studying H. S., §§192-195, and Key, 188, 197, p. 
 109, proceed with the part-writing exercises in H. 6"., §196. 
 
 Ear-training: Dominant Seventh Chords. 
 
 170. TO DISTINGUISH THE DIFFERENT INVER- 
 SIONS of the chord of the Dominant seventh and its 
 resolution, use the same course of reasoning for the Bass 
 as was applied to the upper voice in the last lesson on 
 Ear-training. It is more difficult than the preceding, for 
 the reason that it is more difficult to distinguish the bass 
 note and to separate it from the other notes of the chord. 
 Those students who have been most faithful in the pre- 
 vious prescribed drill in singing the inner notes (or differ- 
 ent notes) of the triads, will be best prepared for this 
 drill. I would suggest that before undertaking the dis- 
 covery of the inversions by ear it will be most desirable 
 to give careful drill to singing the lowest tones in various 
 inversions of the chords of the Dominant seventh, with 
 or without the assistance of a friend at the piano. 
 
146 Graded Lessons in Harmony 
 
 LESSON 33. 
 
 SECONDARY SEVENTH CHORDS— 
 PART-WRITING (Cont.) 
 
 171. STUDY Key, 200, p. 104. 
 PART-WRITING. H. S., §200 (afterward refer to Key). 
 
 Analytical and Comparative Review. 
 
 172. Study carefully H. S., §201, and Key, 201, pp. 110-111. 
 Try to realize how the various terms, such as Major, 
 Minor, Augmented, Diminished, Principle, Signature, Ten- 
 dency, etc., have a systematic application, and how the 
 principles involved follow like a thread throughout the 
 whole subject. It is this universal application to founda- 
 tion principles which makes this study so simple, so scien- 
 tific and so satisfying. 
 
Graded Lessons in Ilarmoni/ 147 
 
 LESSON 34. 
 
 INTRODUCTION TO MODULATION. 
 
 (NOTE. The following lesson is designeu to give 
 facility in handling chords and in developing the con- 
 sciousness of related keys, rather than to be a systematic 
 presentation of the subject of modulation.) 
 
 173. Definition. Modulation is the connection of two 
 different keys, or the process of passing from one key to 
 another. 
 
 PROCESS. There are a large number of ways by 
 which modulation can be effected. In a later lesson a defi- 
 nite means of modulating from any key to any other will 
 be given. In this lesson it is desired to show how easily 
 we may progress from one key to the key of its Dominant 
 or Sub-dominant. It will be remembered that the Domi- 
 nant and Sub-dominant are the nearest related keys of 
 any given key; therefore the progression to either of these 
 keys occurs more frequently than to any others. A modu- 
 lation may be effected very easily where the two keys 
 have a chord in common ; that is, a chord which is the 
 same in both keys. In such a case, this common chord 
 may be approached as if it belonged to the first or old 
 key, and may progress as if it belonged to the new key, 
 or key to which we modulate. 
 
 Modulation to the Dominant. 
 
 To illustrate, let us modulate from the key of C to the 
 key of G. We find upon observation that the chord of C is 
 the first degree in the key of C and the fourth degree in thg 
 key of G. Therefore, although when first heard, the chord 
 of C suggests, or may be said to belong to, the key of C, 
 it may be followed by the chords in the key of G, since 
 it also belongs to that key. A simple way of modulating 
 would be, therefore, to make use of the Closing Formula, 
 as may be illustrated in the following: (O. K. stands for 
 Old Key, or the key from which we modulate, and N. K. 
 for New Key, or key to which we modulate.) 
 
 FORMULA: (aj O. K. f I 
 
 N. K. 1 IV, I„ V, I. 
 
148 
 
 Graded Lessons in Harmony 
 
 Illustrated in notes it would be as follows in the three 
 positions : 
 
 Fig. 9. 
 
 /^r 
 
 
 
 
 ^ 
 
 
 
 
 /L f^ =- 
 
 
 
 
 \^ 
 
 ^ 
 
 
 
 rTT ^ 
 
 
 
 
 
 K 
 
 Lf ^ 
 
 
 y-l' ^ 
 
 
 If -^ 
 
 
 
 
 B'^ 
 
 
 \o ° 
 
 O 
 
 +^-^- 
 
 -^ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 pj. 
 
 
 
 
 
 
 
 
 IvS' ri 
 
 
 
 
 
 
 
 
 \-^ 
 
 
 
 
 
 
 
 ^ 
 
 KeyofC j I 
 
 " "g(iv 
 
 Vt 
 
 [iV 
 
 \ 
 
 -zr 
 
 ^^es: 
 
 KeyofC (I 
 " "G\IV IB Vt I 
 
 WRITTEN EXERCISES. 
 
 Following the examples in Fig. 9, write examples of 
 modulations to the Dominant in any four keys, showing 
 the modulations in all three positions in each key. 
 
 KEYBOARD EXERCISES. 
 
 (a) Taking in turn every Major key, modulate to the 
 key of the Dominant. Much care should be taken with 
 this exercise ; note whether it is easy to find the chords, 
 and with what speed you can perform the modulations in 
 all keys. 
 
 (b) Advanced students will repeat the above in all 
 Minor keys. 
 
 Modulation to the Sub-Dominant. 
 
 174. ILLUSTRATION. 
 
 To modulate to the key of F from the key of C. This 
 modulation is also effected by means of a common chord ; 
 for the chord of C, which is the first degree of the key of 
 
Graded Lessons in Tlannonij 
 
 149 
 
 C, is also the chord upon the fifth degree or Dominant in 
 the key of F. We can therefore perform this modulation 
 by simply adding the Dominant seventh of the new key, 
 creating a cadence in that new key as shown in the illus- 
 tration below. It should be said of the modulations both 
 to the Dominant and Sub-dominant, that in order to make 
 the modulation correct the rhythmic arrangements of the 
 chords should be as described in H. S., §190. 
 
 Fig. 10. 
 
 I-F 
 
 
 
 
 
 
 
 a 
 
 1 tn 
 
 — & — 1 
 
 2 
 
 
 
 
 
 V<s^ 
 
 
 S 
 
 ■k«S2 
 
 
 P 
 
 \ -" 
 
 
 
 
 
 z? 
 
 
 
 
 *,•>• 
 
 7 . 
 
 ^ 
 
 % 
 
 e> 
 
 
 
 
 
 
 
 ] 
 
 r -g- 
 
 ^ 
 
 :i: 
 
 
 
 -<5>- 
 
 
 
 
 \!m\ 
 
 
 
 
 
 
 
 
 
 PJ. 
 
 
 
 
 
 
 
 
 
 CL^ <3 
 
 ir3 
 
 
 rj 
 
 a 
 
 
 *r3 
 
 /z^ 
 
 
 
 
 
 
 
 
 
 
 
 KeyofC I I 
 " "FlV 
 
 u 
 
 Vt 
 
 Vt 
 
 Vi I 
 
 WRITTEN EXERCISES. 
 
 Modulate from the Tonic to the Sub-dominant in three 
 positions, in any four Major keys. 
 
 KEYBOARD EXERCISES. 
 
 (a) Take in turn every Major key; modulate to the 
 key of the Sub-dominant as shown in Fig. 10. Note in 
 detail the ease or difficulty of the operation. 
 
 (b) Advanced students will repeat the above in all 
 Minor keys. 
 
 Modulation to the Relative Minor. 
 
 175. In the preceding modulations the connection was ef- 
 fected by means of a chord common to both keys, followed 
 by some form of the closing formula. Modulation to the 
 relative Minor may be effected similarly, since the Tonic 
 chord in the key of the relative Minor is identical with 
 that upon the sixth degree of the key from which we 
 modulate. 
 
 PROCESS. As the Tonic chord of the relative Minor 
 has a note in common with the old Tonic, we may pass 
 directly to the new Tonic triad ; but this is not sufficient 
 to "establish" the new key. This should be followed, 
 
150 
 
 Graded Lessons in Harmony 
 
 therefore, either by the new Dominant seventh chord, 
 which resolves to the new Tonic, as illustrated at (a) 
 below, or by a larger portion of the closing formula, as 
 shown at (b). 
 
 NoTF.. There are other and smoother ways of modulating 
 to the relative Minor, but at present we are striving for the 
 most simple means and will therefore be satisfied even if the 
 efifcct is not the most artistic possible. 
 
 Fig. 11. 
 
 
 
 
 or (*) 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 ^G 
 
 
 
 
 
 
 ^■S 
 
 
 
 'i-r' 8 
 
 
 S2Ui- 
 
 
 
 
 -'4 
 
 --%- 
 
 %«■ 
 
 i^ 
 
 
 tT -g- 
 
 -S- 
 
 
 -i- 
 
 ""' 
 
 -S- 
 
 
 
 
 
 
 
 
 
 
 
 
 
 pj. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 1 
 
 
 , 
 
 ^ 
 
 
 O 
 
 
 
 
 
 
 KeyofC)! VI 
 
 ■■ "A I 
 
 Vt 
 
 VI 
 I 
 
 Is 
 
 4 
 
 -<S- 
 
 ^^'RITTEN EXERCISES. 
 
 hrom the same four keys modulate to the key of the 
 relative Minor, adding the closing formula as before. 
 Each of these modulations should be done in two or more 
 positions and inversions : to do the same thing in several 
 positions and inversions stimulates the inventive ability 
 and you will find this helpful. 
 
 KEYBOARD EXERCISES. 
 
 Taking in turn every Major key, modulate to the key 
 of the relative Minor. In every case try several inver- 
 sions and several positions, and observe which is the best 
 effect. 
 
 Special .Vote. In all work in Modulation special pains 
 should be taken to observe the rules of part-writing. The 
 point in which pupils are most likely to violate good taste are : 
 (a) Non-observance of Tendencies (this has been discussed 
 elsewhere) ; and (b) Failure to treat inverted basses (basses 
 of inverted chords) as melodies and to lead them stepwise 
 instead of skipping as in the ordinary Bass (direct form). 
 
 Remark. If ynu find l)y comparing your work with the 
 AVv, that you liavo violated tendencies, wrongly treated the 
 
Graded Lessons in Ilarmoni/ ].S1 
 
 inverted bass or forced the character of the progressions, 
 you will need a little review of the points mentioned, rather 
 than the study of the complicated forms of modulation which 
 of themselves are sufficiently difficult after one has learned 
 the trick of handling voices properly. 
 
 STUDY again Lessons- 13 and 20. Review with this all 
 the notes on part-writing to be found in the Key. Also study 
 over the matter of tendencies and do what you can about 
 applying the points. 
 
 176. RELATIVE SHARPNESS OF SCALE TONES. 
 
 There is a wonderful application of the principle of 
 "relative sharpness" described in H. S., §29. The prin- 
 ciple is this : Comparing the relative sharpness of the dif- 
 ferent notes of the scale of C, it will be found that the 
 letter B is the sharpest note, represented by five sharps. 
 Now B is the Leading Tone in the scale of C. The next 
 sharpest note is E, with four sharps ; the next sharpest is 
 A, with three sharps. Then comes D, with two sharps, 
 G, with one sharp, and C, with no sharps, and finally F, 
 with one flat, or "minus one" sharp. 
 
 For the sake of illustration, these different letters in 
 their rank of decreasing number of sharps might be com- 
 pared to the officers in a regiment of soldiers. The com- 
 mand is held by the highest officer, represented by five 
 sharps, or B. If this highest officer is removed, E will 
 become the highest remaining officer, as it is the next in 
 order. If E is removed. A, with three sharps, takes com- 
 mand, and so on down through the series, D, G, C and F. 
 
 Applying this to the scale, let us destroy the rank of 
 B by changing it to Bb, which leaves E as the sharpest 
 note. E is therefore the Leading Tone of the scale, and 
 the scale containing Bb is seen to be the scale of F, of 
 which E is the Leading Tone. If we now lower E to Eb, 
 the next sharpest note is seen to be A, which is the Lead- 
 ing Tone in the key of Bb. Lowering A in turn, we find 
 D, the next sharpest note, to be the Leading Tone in the 
 key of Eb, which key has been developed by flatting the 
 three previous letters as described. Continuing in turn, 
 we find that the keys of Ab, Db and Gb are successively 
 developed. 
 
 It should be seen that the list of keys successively pro- 
 duced above is nothing else than the descending circle of 
 keys. Through this it may be observed that the key of C 
 
152 Graded Lessons in Hormont/ 
 
 epitomizes key relationships in a still more wonderful 
 manner than that described in the statement that the 
 Dominant and the Sub-dominant keys are represented in 
 the tetrachord relationship, and also in a more wonderful 
 manner than that described in §40. 
 
 WRITTEN EXERCISE. 
 
 Repeat the process, demonstrating each step, in the 
 keys of D, E and Bb Major. 
 
 READ H. S.. §§29, 250; also Key. p. 119. 
 
Graded Lessons in Harmon;/ 1S3 
 
 LESSON 35. 
 
 ATTENDANT CHORDS. 1. 
 
 Preparation for Modulation and Analysis. 
 
 177. NOTE. 
 
 The subject of Attendant Chords is one of the most won- 
 derful and beautiful features of these lessons. It is also won- 
 derfully simple although almost universal in its application, 
 for it is a remarkable and logical carrying out of the simple 
 principles of relationship, viz., the relation of Dominant and 
 Tonic. Remember that in this you are not studying some- 
 thing entirely new and strange, but only a wider application 
 of something you already know, 
 
 STUDY H. S., §§265-267. 
 
 WRITTEN EXERCISES. 
 
 (a) To what triad does the chord of the seventh on 
 G resolve? Write the chord of the Dominant seventh 
 upon two staves in direct form and position of the sev- 
 enth, and resolve it. 
 
 (b) Fill out the Dominant seventh chord upon every 
 (chromatic) degree and resolve each to the proper triad, 
 having regard to variety in position and inversion in the 
 various chords. 
 
 (c) (As illustrated in H. S., §267.) What is the root 
 of the Dominant seventh chord which shall resolve to 
 the triad of A Major? Write it and resolve. 
 
 Similarly, name the roots of the Dominant seventh 
 chord resolved to the triads of Db, At, Bi, Ab, Et. Write 
 them and resolve to both Major and Minor triads. 
 
 KEYBOARD EXERCISES. 
 
 Repeat all of the above exercises, forming each chord 
 at the keyboard as promptly as possible, and resolving the 
 same. Resolve them also to Minor triads. 
 
154 Graded Lessons in Ilarmonij 
 
 178. STUDY AND THINK ABOUT H. S., §§269-270. 
 
 N.B. Remember that these two paragraphs contain 
 the essence of one of the greatest principles of music. 
 Read to the end of the chapter, then return to these two 
 sections and think them over carefully again. 
 
 STUDY Chapter XII, Key. pp. 142-145. 
 
 WRITTEN EXERCISES. 
 
 Take the key of G; name the root of the [A] of the 
 Dominant. Write the signature of the key of G ; write the 
 above [A] chord and resolve it to the Dominant. 
 
 Repeat the above process with the chord leading to 
 Super-tonic. 
 
 Repeat the above process with the chord leading to 
 Mediant. 
 
 Repeat the above process with the chord leading to 
 Sub-dominant. 
 
 Repeat the above process with the chord leading to 
 Sub-mediant. 
 
 KF.YBOARD EXERCISES. 
 
 Repeat the above in all Major keys and carefully note 
 your success — whether you find it confusing to keep two 
 chords in mind in addition to the key, whether you have 
 difficulty in instantly forming the required chords and re- 
 solving them, and whether you find it difiicult to do the 
 above in various positions and inversions. 
 
 179. WRITTEN EXERCISES: H. S., §274, (a). 
 
 KEYBOARD EXERCISES: H. S., §274, (b). 
 
 Read H. S., §275. 
 
 Think of the tremendous bearing of this principle upon 
 music, and begin right now to find examples in the music 
 which comes under your eye in your daily life. See, 
 further, how this enlargement of the boundaries of the 
 key and the richness in material resulting from this prac- 
 tice exemplify the freedom and richness of modern life 
 and the intellectual and spiritual growth of our time. 
 
 180. QUESTIONS 1-13, Key, pp. ]45-14r,. 
 
Graded Lessons in Harmony 155 
 
 LESSON 36. 
 
 MODULATION (Cont.) 
 
 Use of Attendant Chords. 
 
 181. OBSERVATIOX. 
 
 The method to be here developed might be called a uni- 
 versal method, since by its use it becomes possible to connect 
 any two keys, and this by one and the same method. 
 
 STUDY H. S., §§276-280. Read Key, 276, p. 147. 
 
 REMARKS. 
 
 (a) The question may arise, why use any [A] chord at 
 all when there is a common note. It would not be a modu- 
 lation to connect the chord of C Major witli the chord of 
 Ab Major — that would be a jump into the new key and not 
 a modulation. To make a modulation you must at some point 
 or other form a cadence, that is, a Dominant seventh chord 
 followed by the Tonic in the new key. Therefore, if you can 
 get into the new key and form a cadence at the same time, 
 a more natural feeling is given than when you jump from one 
 key to the other by means of a common note without any [A] 
 chords whatever. 
 
 (b) I never like to use the [A] of the first chord in 
 practical work, without the [A] of the second chord for 
 the reason that it tends to return to the old key; so when it 
 must be used it is better to put in the second [A] chord as 
 well since the latter progresses naturally to the new key. 
 
 (c) The [A] chord of the new key is really essential if 
 either one is to be used. The [A] chord of the old key is 
 really onh' used to connect the old Tonic with the new fA] 
 chord. 
 
 Special Note. Remember that in finding any desired [A] 
 chord we need only to ask ourselves what would be the Domi- 
 nant if the (given) triad were the Tonic of a key. Attendant 
 chords are in their essence Dominant chords, but as they are 
 only transitory, they do not perform the office of a Dominant. 
 
 WRITTEN EXERCISES : H. S., §281, (a). 
 
 N.B. If it takes you too long to write out the modulation 
 it shows that your methods are not quite complete and that 
 
156 Graded Lessons in Ilarmoni/ 
 
 you must learn to think in the proper way. If you would 
 simply write the two chords you desire to connect upon a 
 sheet of paper, placing the two chords about four inches apart 
 and then write between them their respective fA] chords, the 
 common notes would come to light inside of two minutes. 
 Of course, to do this you must get your [A] chords absolutely 
 correct. 
 
 WRITTEN EXERCISES: H. S., §282, (a). 
 
 182. STUDY H. S., §283-284. 
 
 KEYBOARD EXERCISES. 
 
 Return to H. S., §§281-282 and try every exercise there 
 given in as many different inversions and positions as 
 possible, deciding which form is smoothest and most 
 musical. 
 
 WRITTEN EXERCISES. 
 
 After deciding upon the best form above, write it out 
 in full. 
 
 Special Note. Please stop at this point and do not try to 
 make a complete modulation yet. Before proceeding we must 
 see that our tools are in order. ■ 
 
 Treatment of Bass in Inverted Chords. 
 
 183. When a Bass is in an inversion rather than in the 
 direct form, it is presumed to be so for some melodic 
 reason ; that is, so that the Bass when taken alone will 
 sound more or less like a melody. Now as in writing a 
 melody you would prefer a smooth progression to a series 
 of meaningless skips; or as you would not choose an 
 awkward melody note for the sake of filling up the chord, 
 but would instead arrange the chord to suit the melody ; 
 so in the Bass progression, when once you take an inver- 
 sion, you should treat the Bass like a melody and allow 
 it to progress either step-wise or chord- wise (in its own 
 chord). Further, when a Bass is inverted and allowed 
 to progress step-wise, you will find that the harmonic 
 and melodic tendencies come into great prominence and 
 must be considered in order to produce a good effect. For 
 example, the Bass of the chord (see Fig. 12) should 
 progress as at (b), not as at (a). The Bass note, G, 
 
Graded Lessons in Harmon 
 
 II 
 
 157 
 
 being an inversion, should not skip to a new chord, but 
 should progress step-wise. Try the two examples and the 
 difference in effect will appeal to you. 
 
 In modulation and improvising, if you take an inver- 
 sion and find it does not progress smoothly, it is better 
 to discard the inversion and try direct forms ; but remem- 
 ber that the use of these inversions, and the smooth pro- 
 gressions of the individual voices produced thereby, are 
 a mark of skill in chord treatment. The practice, though 
 at first difficult, is most excellent and should be continued 
 for a long time, both in writing and at the piano. 
 
 Fig. 12. 
 
 (a) poor 
 
 
 (*) good 
 
 * 
 
 3iE 
 
 184. Before taking up the modulations through the At- 
 tendant chords, it will be necessary to gain facility in 
 passing from a common chord to that inversion of the 
 Attendant chord, which will permit of the smoothest 
 progression in every voice. The following special exer- 
 cises will aid in this work : 
 
 (1) At the keyboard, play the chord of C in direct 
 form and position of the fifth. Now pass to the nearest 
 forrn of its [A] chord, and then back to the C chord. Now 
 try if some other near inversion will not answer better, 
 or nearly as well. 
 
 In doing this exercise it is best to consider the Bass 
 first, noting the nearest possible place in the new chord, 
 for upon this will depend the question of which note to 
 double. Attend first to the Bass, then to the Soprano, 
 and then fill in, trying to avoid doubling undesirable notes 
 — you know which. 
 
 (2) Repeat the above in writing. 
 
 (3) Take the chord of C in direct form and position 
 of the octave and pass to the nearest form of the [A] 
 chord and back, as before. Try another progression of 
 the Bass, if possible. 
 
158 Graded Lessons in Harmony 
 
 (4) Proceed as before, but take the position of the 
 third. 
 
 (5) Take the chord of C in the first inversion, and 
 try successively the three positions. 
 
 (6) Take the second inversion and proceed as before. 
 
 (7) Write out the complete process as above, with the 
 chord of C. 
 
 (8) Start with each Major and Minor triad in turn, 
 and do the same thing. This will require several hours, 
 and should be spread over several days. You need the 
 continued association with this problem to get the best 
 results. When ease has been secured in this process, 
 you can take up the real modulations far more successfully. 
 
 185. WRITTEN EXERCISES. 
 
 Harmonize some descending scales using [.\] chords, 
 after studying text and examples as given in A.V_r, p. 188. 
 
Graded Lessons in Harmony 159 
 
 LESSON 37. 
 
 CHORD ANALYSIS. 
 
 186. We now come to one of the most interesting and 
 profitable features of our study. To be able to analyze 
 the chords in a composition is to know that composition 
 more intimately, to play it more intelligently, and to enjoy 
 it more fully than is otherwise possible. If we know 
 which chord is the key center, and know the natural rela- 
 tions of other chords in the key to this central or Tonic 
 chord; if we know the individual character of the differ- 
 ent tones of the scale, and the differing tone colors of 
 musical effects produced by Major, Minor, Diminished 
 and Augmented forms ; if we know the conventional pro- 
 gression of chords in a key, leading or tending toward 
 the Tonic chord, and the effects and meanings of the 
 different kinds of cadences ; if we know the relations of 
 different keys to one another, and the meanings and uses 
 of consonance and dissonance, or the Resolution of the 
 Dominant principle : if we know these things, we shall be 
 able to read the composer's thought almost like an open 
 book. It is intended from this time forth to divide the 
 work between three branches: (1) Logical exposition of 
 the principles; (2) Construction and other drill; and (3) 
 Analysis. 
 
 The methods of chord analysis will be best seen by the 
 illustration and description of the hymn tune, "Old Hun- 
 dred." (Note. The student should write, at the places 
 designated by figures in small type, the Roman numerals 
 required to indicate (1) upon which degree of the scale 
 each chord is formed, and (2) whether Major or Minor, 
 by using the capital letters for Major triads and small 
 letters for Minor triads.) 
 
160 Graded Lessons in Harmonij 
 
 Analysis of the Hymn. 
 
 (In Notation Below. _) 
 
 From the signature and the chords (which do not 
 contradict the signature) we may know that this composi- 
 tion is in the key of G Major; therefore write "Key of G" 
 (the capital G to indicate the Major key) at X. The first 
 chord, consisting of the notes G-B-D-G, is seen to be the 
 chord of G, or first degree of the scale of G, since these 
 notes will form the intervals of 1, 3 and 5 from the root G. 
 (See Collateral Reading, §75, [2]; also §112 [3]). Ob- 
 serve that the doubling of one note, G, does not affect the 
 character of the triad. In analysis it is a rule to "strike 
 out all duplicates of notes, and to bring the notes within 
 their smallest possible compass," when finding the root of 
 a chord. This chord is a Major triad, and as its root is 
 G, the first degree, write a capital I over the small figure 
 1. This. chord is then the Tonic triad (or common 
 chord), on the first degree in the key of G. It may be 
 further described by saying that it is in the "Direct Form" 
 (that is, it is not inverted, since the root is in the Bass. 
 If this is not clear, the student should refer to H. S., p. 66 
 et seq.; and Key, Chapter IV), and in the "position of the 
 octave," since the Soprano or highest note is the root of 
 its octave. Observe that the term inversion (or Direct 
 Form) relates to the Bass or lowest note, while position 
 refers to the highest note, or Soprano. The second chord 
 is a repetition of the first chord, and may be similarly 
 designated, above the small figure 2, or a short horizontal 
 line may be used instead, to indicate that the previous 
 harmony is continued. 
 
 The third chord, by the process of excluding duplicates, 
 placing the notes as near together as possible, and apply- 
 ing the test to the intervals forming 1, 3 and 5, will be 
 seen to be the common chord or triad on the note D, 
 which is the fifth degree of the scale. This chord should 
 be designated by a capital V above the figure 3. Observe 
 that it is in the direct form (root in the Bass) and the 
 position of the Third, since the note which is a third 
 above the root (D) is in the Soprano. Notice that the 
 marking of a chord does not specify the position or inver- 
 sion, but only its actual root, or note upon which the chord 
 is built. 
 
 Proceeding similarly, mark the successive chords as 
 
Graded Lessons in Harmon i/ 161 
 
 follows : At 4, a small vi, as the chord is Minor ; at 5, a 
 small iii, as this chord is also Minor; at 6, a small vi 
 again; at 7, a capital V; at 8, a capital I. This completes 
 the first line of the words. The next two measures will 
 be quite simple, if it is remembered that a chord is not 
 affected by being spread out over several octaves, since 
 the notes are considered just as if they were within the 
 compass of one octave, or as close together as possible. 
 Observe this particularly at chords 14 and 15. 
 
 In the third line of the words, chord 18 is inverted. 
 This is proven by the fact that FJ could not be the real 
 root, since if that were the root the other notes would 
 have to be A and C, counting respectively a third and a 
 fifth above F#; but as the notes given are A and D 
 instead of A and C, some other note must be the actual 
 root. If we try first A and then D as a possible root, we 
 will find that the notes which are a third and a fifth 
 above D correspond with those here given, proving that 
 the root is D, although the lowest note is F8. Now the 
 Roman numeral should represent the real root, and not 
 the note which may happen to be lowest; therefore we 
 must mark this chord with a capital V, and not with a 
 VII, as might be supposed at first glance. Similarly, 
 chord 21 is an inversion of the Tonic triad, I, and must be 
 so marked ; and chord 23 is an inversion of the chord on 
 Ft, and must therefore be marked with a small vii. 
 (Note. This chord is a Diminished triad, and in addition 
 to the Minor sign (the small letters in its numeral), it 
 should have affixed the sign °, to show the Diminished 
 quality; viz., vii°.) 
 
 Chord 31, with the last quarter note in the Alto, 
 presents four different notes, a form at present beyond 
 us. We will therefore mark it by an interrogation point, 
 indicating that it is a subject for later study. 
 
 If desired, the position of each chord may be indicated 
 by the figures, 3, 5 and 8 placed over the treble staff, and 
 the direct form or inversions by the letter D, or first or 
 second placed under the bass staff, and below the Roman 
 numeral. 
 
162 Graded Lessons in Harmony 
 
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 187. EXERCISES. 
 
 Analyze a number of simple hymn tunes. Do not yet 
 attempt to analyze piano music, as the many passing- 
 notes and broken chords make it more complicated. 
 
Graded Lessons in Harmont/ 163 
 
 LESSON 38. 
 
 CHORD ANALYSIS (Cont.) 
 
 188. Below are several hymn tunes for analysis which 
 should be done as illustrated in Lesson 37. All chords 
 which are unfamiliar to the student should be marked with 
 a '■ ?", and in case they have not yet been studied, should 
 be left for later discussion. 
 
 In cases where the key is actually changed, either by 
 coming to a pause in the new key, or by continuing in the 
 same through several chords, the change of key should 
 be noted in each case, using a capital letter to distinguish 
 a Major key and a small letter for the Minor key. As 
 soon as the subject of Attendant chords has been thor- 
 oughly studied, each Attendant chord should be noted by 
 indicating its relation to its Tonic. 
 
 189. ANALYSIS OF PIANO MUSIC. 
 
 As we have not yet discussed the subjects of Suspen- 
 sion, Syncopation, and other varieties of structure, there 
 may be a rather large proportion of chords which are 
 not yet clear to the student. All such chords may be 
 marked as before with the "?" and left for future study. 
 
 190. PASSING-NOTES. 
 
 As these occur so frequently in piano music, the 
 student will carefully read H. S., §§315-320 before pro- 
 ceeding to further study of analysis. Passing-notes may 
 be marked with the initials P. N. The student should 
 carefully distinguish between passing-notes and those 
 melodic passages in which the notes are really parts of 
 the chords, such chord notes not being marked as passing- 
 notes. 
 
 191. MATERIAL FOR ANALYSIS. 
 
 For the first exercise in analysis, a very simple piano 
 composition may be chosen by the student, preferably one 
 
164 
 
 Graded Lessons in Harmony 
 
 of the classics, such as one movement from a sonatina, 
 Handel's "Largo," or a simple teaching piece if preferred. 
 The analysis should show: first, the main key and all the 
 subsidiary keys; second, the harmonic structure of every 
 passage ; third, passing-notes ; and fourth, any irregulari- 
 ties in the chord structure ( for example, any chords which 
 cannot be classified as coming from any known root). 
 The subject of form analysis will be touched upon later. 
 The preferred subjects for analysis for this lesson are 
 one or two movements from a Kuhlau or Clementi sona- 
 tina, or one movement from the simpler sonatas of Haydn 
 and Mozart. When movements are short, two or three 
 movements should be analyzed. 
 
 NOTE FOR THE TEACHER. 
 
 Examples of difficult chords which the student is unable 
 to understand should be put in the form of questions to be 
 answered. In every case the chord should be clearly written 
 out, together with the preceding and following chords, with 
 the signature and plenty of space for notes upon the same. 
 Until the student has completed the work up to and including 
 foreign chords, it is impractical to discuss these chords very 
 thoroughly. 
 
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166 Graded Lessons in Harmony 
 
 LESSON 39. 
 
 CHORD OF THE DOMINANT SEVENTH 
 AND NINTH. 
 
 (Also called the chord of the Dominant ninth and seventh, 
 or more simply the "Chord of the Ninth.") 
 
 192. .STUDY H. S., §§204-206 ; Key, 204. 
 
 KEYBOARD EXERCISES. 
 
 (a) Form the chord of the Dominant seventh in the 
 key of G ; add to this the Major ninth. 
 
 (b) Form similarly the chor.d of the Dominant sev- 
 enth and add the Major ninth in all other Major keys. 
 
 (c) Repeat the foregoing exercises in one process, 
 that is, strike the whole chord at once, without stopping 
 to form the chord of the seventh and then adding the 
 ninth. Continue this practice until facility is gained. 
 
 193. WRITTEN EXERCISES. 
 
 (a) Write the chord of the Dominant ninth in the 
 key of G Major. Describe in detail each and every disso- 
 nant interval, giving the specific name and the proper 
 resolution of each. (Note. A quick way to do this is to 
 write the letters of the interval, one over the other like 
 a chord, then show by a short line pointing upward, down- 
 ward or horizontally how each note resolves; and then 
 add the letter to which the resolution is made.) Write 
 each dissonant interval separately in this way. Then 
 write the chord as a whole and affix the proper line to 
 each letter showing in which direction each note resolves, 
 
 (b) Repeat the above in the keys of A, E, B, Eb, Ab 
 and Db Major. 
 
Graded Lessons in Harmovxi 167 
 
 KEYBOARD EXERCISE. 
 
 Play the chord of the Dominant ninth and seventh 
 in each and every Major key; while holding the chord, 
 search for each dissonant interval and observe how it 
 should resolve. Take time to do this work carefully and 
 thoughtfully as it has educational value. 
 
 DRILL. 
 
 Repeat every exercise of the Major keys in every 
 Minor key. • 
 
 Observe that the ninth, which in the Major key is a 
 Major ninth, will be a Minor ninth in the Minor key. 
 This will change the specific names of some of the disso- 
 nant intervals. Observe the changes carefully. 
 
 Give special attention to the keyboard work, noting 
 your difficulties for future attention. 
 
 Inversions of the Chord of the Dominant Ninth and 
 Seventh. 
 
 194. READ H. S., §208. 
 WRITTEN EXERCISES: Key, 208. 
 KEYBOARD DRILL: Key, 208. 
 
 Secondary Chords of the Seventh and Ninth. 
 
 195. READ H. S., §209. 
 WRITTEN EXERCISES: ifex 209. 
 KEYBOARD EXERCISES: Key, 209. 
 
 A Study in Preparation of Dissonances. 
 
 196. STUDY H. S., §181; also §§302-303. 
 
 WRITTEN EXERCISES. 
 
 (a) How would you prepare the chord D-F-A-C-E 
 in the key of C (that is, what chord would you place 
 before it) ? Try it at the keyboard and see if the effect is 
 pleasant. 
 
168 Graded Lessons in Harmony 
 
 (b) Similarly prepare and resolve other secondary 
 seventh and ninth chords. 
 
 197. QUESTIOXS 1-4, Key, p. 117. 
 
 198. EAR-TRAIXING. 
 
 It is perhaps less difficult to recognize chords of the 
 ninth and seventh, for the reason that they often sound 
 much like suspensions and are treated very similarly ; that 
 is, they are usually resolved by letting the highest note 
 proceed one degree downward. Since the ninth chord has 
 five different tones, it also has a very full sound. 
 
 If you have a friend who can form chords of the ninth 
 interspersed with triads and chords of the seventh (both 
 secondary and Dominant), it would be well to secure aid 
 at this point. If you have no such friend, write out a 
 series of disconnected triads, seventh chords and ninth 
 chords, and either ask a friend to play them (you could 
 mark the triads, seventh chords and ninth chords with 
 some distinguishing marks so that anyone could tell you 
 whether you hear correctly or not) or simply look at the 
 chords of the ninth, trying to imagine how they sound, 
 and then go to the keyboard and hear if they sound as 
 you think. 
 
 Of course you will take every opportunity to exercise 
 the faculty of ear-training when hearing music. 
 
Graded Lessons in Ilarmom/ 169 
 
 LESSON 40. 
 
 CHORD OF THE DIMINISHED SEVENTH. 
 
 199. STATEMENT. 
 
 In this system, the following chords are shown to be 
 nothing more than slightly varying forms of one and the 
 same harmony, viz.. Dominant harmony : 
 
 (1) The Dominant Seventh chord; 
 
 (2) The chord of the Dominant Major Ninth; 
 
 (3) The chord of the Dominant Minor Ninth; 
 
 (4) The chord of the Diminished Seventh ; 
 
 (5) The chord of the Augmented Six-five-three; 
 
 (6) The chord of the Augmented Six- four-three; 
 
 (7) The chord of the Augmented Six-three. 
 
 All these chords will be shown to have the same root, 
 the same dissonant intervals (varying slightly, of course, 
 with the increased number of notes), the same tendencies 
 and the same resolutions. In thus proving their similarity 
 the simplicity of the subject is shown in a more striking 
 way than ever before in the whole history of musical 
 theory. In the following lessons the student should not 
 look for new things or principles, but only for the wider 
 application of the principles developed in the study of the 
 chord of the Dominant seventh. 
 
 STUDY H. S., §§210, 188, 211. 
 WRITTEN EXERCISES : H. S., §212. 
 KEYBOARD EXERCISES : H. S., §212. 
 
 200. STUDY H. S., §213. 
 KEYBOARD EXERCISES : H. S., §214 
 
 201. STUDY H. S., §215. Key, 215. 
 ADDITIONAL EXERCISES : Key, 215. 
 
170 Graded Lessons in Harmon// 
 
 WRITTEN EXERCISES. 
 
 Complete the illustration which is commenced in H. S.. 
 p. 133, Fig. 68. 
 
 Inversions of the Chord of the Diminished Seventh. 
 
 202. STUDY H. S., §216. 
 
 WRITTEN EXERCISES: H. S., §216, (a). 
 KEYBOARD EXERCISES: H. S., §216, (a). 
 
 203. STUDY very carefully and repeatedly H. S., §§217- 
 218. 
 
 WRITTEN EXERCISES: H. S., §219, (b), (c), (d). 
 KEYBOARD EXERCISES: H. S., §219, (b), (c), 
 (d). 
 
 204. STUDY H. S., §219, (c). 
 
 WRITTEN EXERCISES: H. S., §219, (f). 
 KEYBOARD EXERCISES: H. S., §219, (g). 
 20.5. ADDITIONAL EXERCISES: Key, 219. 
 KEYBOARD DRILL : Key, 219. 
 EXERCISES : Key, 219. 
 
Graded Lessons in Harmony 171 
 
 LESSON 41. 
 
 CHORD OF THE DIMINISHED SEVENTH 
 (Cont.) 
 
 Study of Roots and Notation. 
 
 206. STATEMENT. 
 
 The exercise in Lesson 40, calling for the completion 
 of Fig. 68 of H. S., showed that although there are in 
 notation twelve different chords of the Diminished sev- 
 enth — or even more by enharmonic writing — there are upon 
 the keyboard only three different forms of the chord: 
 namely, those shown under 1, 2 and 3 of each section in 
 Fig. 68. It should now be observed that the difference in 
 these chords, that is, the difference between 1 under (W) 
 and 1 under (X) is really only different in notation. To 
 understand this more fully, this lesson will be devoted to 
 the study of roots and notation. 
 
 STUDY H. S., §§238-243, observing particularly the 
 definition of the word "fundamental." 
 
 WRITTEN EXERCISES: H. S., §240; work es- 
 pecially on the Diminished seventh chord. 
 
 207. WRITTEN EXERCISES. 
 
 (a) Take the chord B-D-F-Ab and re-write the chord 
 so that it shall belong to and resolve in the four different 
 keys to which it may directly belong. 
 
 (b) Take the chord C-Dlt-FS-A and re-write it so that 
 it shall belong to and resolve in the four different keys to 
 which it may belong. 
 
 (c) Proceed similarly with the chord of CS-E-G-Bb. 
 
 KEYBOARD EXERCISES. 
 
 Play the chord B-D-F-Ab, and by (mentally) changing 
 the notation, or what amounts to the same thing, by men- 
 tally changing the root, resolve it directly in the four 
 different ways above described. 
 
172 Graded Lessons in Ilarmonii 
 
 OBSERVATIONS. 
 
 Please work very slowly and carefully upon this lesson, 
 for it is one of the most important subjects in our whole 
 course. 
 
 208. STUDY H. S., §§244-248. 
 WRITTEN EXERCISES: H. S., §248. 
 STUDY H. S., §§249-251. 
 
 To Discover the Key in Which a Foreign 
 Fundamental Chord is Written. 
 
 209. STUDY H. S., §29 ; also §§18-22 of Hozv to Modu- 
 late; H. S., §252 ; and Key, 215. 
 
 WRITTEN EXERCISES : H. S., §253. 
 
 210. STUDY H. S., §§254-257. 
 
 211. NOTES AND OBSERVATIONS. 
 
 Referring to Lesson 2, the student should read care- 
 fully the observations made upon the "Office of the Half- 
 step." We are here to use a remarkable illustration of 
 the same subject. In the chord of the Diminished seventh 
 the notes lie at an equal distance apart (all Minor thirds), 
 and therefore the chord gives us nothing pointing directly 
 to any particular key; in fact it may belong directly to 
 any one of the four keys by simply changing its notation, 
 and in reality may pass almost directly into any one of 
 the twelve Major and twelve Minor keys, as will be de- 
 scribed later. Now please observe that if the missing 
 root of any Diminished seventh chord be restored, the 
 chord will no longer contain exclusively Minor triads, 
 for the root will produce, with the next tone above, the 
 interval of a Major third. Now remember that between 
 the Dominant and the Leading Tone in any Dominant 
 harmony the third is Major (this is accomplished in 
 Minor through the use of the accidental raising of the 
 seventh degree). In the case of the Diminished seventh 
 chord without its root, this Major third is missing, and 
 therefore the element of contrast with the series of Minor 
 thirds, found in the complete chord, is lacking. Now 
 
Graded Lessons in Harmony 173 
 
 observe further that the full chord from which the Dimin- 
 ished chord is derived is, of course, the Minor ninth 
 chord, and that the Minor ninth is naturally just a half- 
 step above the octave from the root; and note also that, 
 in the chord of the Diminished seventh, this Minor ninth 
 is present and the root is absent. Therefore if we were 
 to lower the Minor ninth a half-step, the result would 
 be actually to destroy the ninth and to substitute the root 
 for it (which in reality changes the chord of the Dimin- 
 ished seventh to that of the Dominant seventh) . Now 
 let us take the chord of the Diminished seventh, 
 B-D-F-Ab ; if we either mentally or actually lower any 
 one of these tones a half-step we really introduce the root 
 of the chord, and both the key and the resolution become 
 instantly clear. For example, if we lower B to Bb the 
 chord will belong to and resolve to Eb. If instead we lower 
 D to Db (it now becomes necessary to enharmonically 
 change B to Cb, to make alternate letters or thirds from 
 the root), Db now becomes the Dominant of the key Gb, 
 and the chord will resolve to Gb. Or if we lower F to E 
 (enharmonically change Ab to G# to keep alternate letters 
 from E), the chord is seen to belong to the key of A. Or 
 if we lower Ab to G, the chord belongs to the key of C. 
 
 KEYBOARD EXERCISES. 
 
 (a) Take the chord B-D-F-Ab : "think" the roots as 
 above described and resolve to each of the four keys in 
 turn. 
 
 (b) Proceed similarly with the two remaining forms 
 of the chord (C-Eb-Gb-Bbb and C#-E-G-Bb.) 
 
 WRITTEN EXERCISES. 
 
 Write all that you have done in the foregoing keyboard 
 exercises. 
 
 To Proceed from the Chord of the Diminished 
 
 Seventh to Any One of the Twelve Major 
 
 and Twelve Minor Keys. 
 
 212. STATEMENT. 
 
 You have just learned how the chord of the Diminished 
 seventh may resolve directly to any one of four different 
 keys. Now in resolving the chord, the triad to which it 
 resolves may be considered not only as the Tonic of the 
 
174 Graded Lessons in Harmony 
 
 key, but it may also be a Sub-dominant or a Dominantof 
 other keys. In fact it may belong to any key in which 
 that chord could be found. For example, B-D-F-Ab re- 
 solves directly to C-E-G; C-E-G is the Tonic of the key 
 of C, Dominant in the key of F and Sub-dominant in the 
 key of G. By applying your knowledge of the closing 
 formula you can therefore resolve the chord B-D-F-Ab 
 to the triad of C Major ; and you may either pause there 
 or continue in the closing formula to the chord of either 
 F or G as a Tonic. We now have a group of three keys 
 to which this first form of the chord may be resolved, 
 namely the keys of C, F and G. 
 
 Taking the next inversion of the same chord with one 
 letter enharmonically changed (D-F-Ab-Cb), you will 
 realize how this form resolves directly to the triad upon 
 Eb ; and the triad of Eb may belong to the key of either 
 Eb, Ab or Bb, as Tonic, Dominant or Sub-dominant, re- 
 spectively. Continuing in this way, it will be seen that 
 the chord of the Diminished seventh B-D-F-Ab may be 
 resolved to each one of the twelve Major and twelve 
 Minor keys. 
 
 WRITTEN EXERCISES. 
 
 (a) Resolve, as above, the chord of the Diminished 
 seventh B-D-F-Ab to each one of the twelve Major and 
 twelve Minor keys. 
 
 (b) Similarly resolve the chord C-Eb-Gb-A to each 
 of the twelve Major and twelve Minor keys. 
 
 (c) Resolve the chord of the Diminished seventh 
 CS-E-G-Bb to each of the twelve Major and twelve Minor 
 keys. 
 
Graded Lessons in Harmony 175 
 
 LESSON 42. 
 
 CHORD OF THE DIMINISHED SEVENTH 
 
 (Cont.) 
 
 213. NOTE TO THE TEACHER. 
 
 In this lesson it is advisable to discuss all difficulties. The 
 work is all a matter of principles, and by calling the student's 
 attention to the great principles, you may be enabled to find 
 his difficulties very easily. Make an extended analysis of the 
 Keyboard Drill and note what facility each one is gaining by 
 faithful practice. 
 
 PART-WRITING EXERCISES: H. S., §220. (Com- 
 pare with Key.) 
 
 214. QUESTIONS 1-15, Key, pp. 125-126. 
 
 215. HARMONIZING THE SCALE. 
 
 If not found too difficult, try to harmonize a few 
 scales in different keys, using any of the chords which 
 have been studied up to this point. See Key, p. 186, for 
 examples. (See H. S., §221.) 
 
176 Graded Lessons in Harmon>i 
 
 LESSON 43. 
 
 CHORDS OF THE AUGMENTED SIXTH. 
 
 We have now reached those very important but 
 largely misunderstood chords, those of the Augmented 
 sixth. If the student would take the trouble to read the 
 treatment of these chords by the older authors such as 
 Jadassohn, Richter, Paul and others, and then carefully 
 study the exposition here given, he would rejoice that he 
 lives in the present age. 
 
 The Augmented Six-three Chord. 
 
 216. The student is advised to read the demonstrations of 
 these chords with one hand upon the keyboard, playing 
 each form and illustration as given. 
 
 STUDY H. S., §§222-225. 
 
 EXERCISES: H. S., §225. 
 
 The Augmented Six-four-three Chord. 
 
 217. STUDY H. S., §226. 
 EXERCISES: H. S., §226, (a) and (b). 
 
 The Augmented Six-five-three Chord. 
 
 218. STUDY H. S., §227. 
 EXERCISES : H. S., §227. 
 
 219. STUDY H. S., §228. 
 
 Special Note. Review and compare very carefully chap- 
 ters S-10, as advised in H. S., §228. 
 
 220. PART-WRITING EXERCISES. 
 
 Three exercises only, H. S.. §232. (Compare with 
 
 Key.) 
 
Graded Lessons in Harmony 177 
 
 LESSON 44. 
 
 AUGMENTED SIXTH CHORDS (Cont.) 
 
 Note. The student is earnestly advised to study what is 
 said of the Augmented sixth chord in the author's How to 
 Modulate, where it is discussed more fully, and the reasons 
 for its former misunderstanding shown. 
 
 Having studied the Attendant chords, and having realized 
 that any Attendant chord may appear in as many forms as 
 there are forms of Dominant harmony (read carefully the 
 N.B., in H. S., end of §228), the pupil will now realize that 
 Attendant chords may also appear in the form of the Aug- 
 mented sixth chords. It is one of these Attendant chords in 
 the form of the Augmented sixth which confused the older 
 theorists as described below. 
 
 Chord of the Augmented Sixth Derived from the 
 Supertonic. 
 
 221. STUDY H. S., §§229-230. 
 EXERCISES : H. S., §231 (a), (b). 
 
 PART- WRITING EXERCISES : The last four exercises 
 in H. S., §232. 
 
 222. STUDY H. S., §233. 
 EXERCISES. 
 
 Form chords of the Augmented sixth upon the Super- 
 tonic, and resolve them to the Tonic six-four as described 
 above, and progress to the Dominant chord. 
 
 223. EXERCISES. 
 
 Harmonize the scale as required in H. S., §233. See 
 Key, p. 186 for example and read text. Study examples 
 as given in Key, p. 187. 
 
 224. EXERCISES : H. S., §234. 
 SYNOPSIS. 
 
 Write synopsis of this chapter and also of the develop- 
 
178 Graded Lessons in Harmony 
 
 ment of the various chords from a fundamental tone, as 
 shown in H. S., §235. Try to do this without reference 
 to the book, after reading that synopsis through once. 
 Read Key, 235. 
 
 RECAPITULATION : H. S., §235. This is most im 
 portant for the student who .is able to think. 
 
 Special Note. Try and realize the contents of H. S., 
 §§236-237, and express your ideas regarding the same in 
 writing. Read Key, 23S-236, p. 131. 
 
 225. QUESTIONS 1-13, Key, pp. 132-133. 
 
Graded Lessons in Harmony 179 
 
 LESSON 45. 
 
 MODULATION (Cont.) 
 
 226. The modulations so far made were incomplete, 
 as they fail to give a complete feeling of rest in the new 
 key. This feeling of rest and finality is secured by the 
 addition of the Closing Formula already described, and 
 further illustrated in H. S., §289. 
 
 EXERCISES. 
 
 (1) Returning to the exercises in modulation, Lessons 
 34 and 36, complete each modulation there made by the 
 addition of the Closing Formula. This work should be 
 largely done at the keyboard. Three or four examples, 
 showing a variety of positions and inversions, should be 
 written as a part of this lesson. 
 
 (2) Modulate from each Major key to the key of its 
 relative Minor, adding the Closing Formula in each case. 
 Write at least six examples. 
 
 Note. The larger part of the work in modulation should 
 be done at the keyboard, trying each modulation in every pos- 
 sible position and inversion, comparing the different forms 
 until the best and smoothest progression is found. 
 
 NOTE TO TEACHERS. 
 
 Pupils should write out in notation questions concerning 
 troublesome points, leaving room for notes and corrections. 
 At this time ample drill is required upon each individual point ; 
 for this reason this lesson is limited in its extent. 
 
180 Graded Lessons in Harmony 
 
 LESSON 46. 
 
 MODULATION (Cont.) 
 
 227. By reading H. S., §§290-293, we find that each 
 triad excepting that upon the seventh degree may become 
 a door through which the new key may be introduced. 
 The chief door of approach (the front door, so to speak) 
 of the new key is the chord of the Dominant, since it 
 leads directly to the point of rest. We may also, as just 
 said, enter by other doors, using, if desired, one of the 
 triads of the Closing Formula ; but this method is less 
 direct, since we need to follow out the Closing Formula to 
 its end in order to fully fix the new key. However, when 
 we wish to hide a modulation so that it will not be too 
 apparent to the listener, one of these less direct chords is 
 often chosen as the means of -entering the new key. Care- 
 ful study of H. S., §§293 and 300, will teach us how to 
 introduce the new key through these different triads. 
 
 EXERCISES. 
 
 (1) Study H. S., §294. Construct the formula and 
 modulate from every key to every other through the chord 
 of the Dominant seventh to the new key. Try each 
 modulation in its various positions and inversions and 
 write out with the formula at least ten examples. In all 
 cases the Closing Formula should be included. 
 
 (2) Modulate from every key to every other, entering 
 the new key through its Sub-dominant triad, and continue 
 from this Sub-dominant through the chords of the Closing 
 Formula to the final Tonic. Write out the formula. 
 
 Example. Modulate from C to A through the new Sub- 
 dominant. That is, pass from the chord C to the chord of 
 D (Sub-dominant of A) just as if you were modulating to 
 the key of D ; but instead of stopping on D, use it as IV of 
 the new key, and continue to V-V7-I /;; the key of A. To 
 illustrate : 
 
Graded L 
 
 Fig, 13. 
 n 
 
 essons 
 
 in Harmony 
 
 V ' 
 
 /L 
 
 1 
 
 un " 
 
 
 
 n *t „ ^ 1 
 
 KJi) '-i 
 
 "^ 
 
 ns> 
 
 1 J, H ^ -. . . ^ 1 
 
 J -S- 
 
 I- 
 
 
 -|:f-— ^ 
 
 ^ F- 
 
 <m\' ■ 
 
 IPJ. 
 
 
 
 ^ 1 
 
 CS' ,r> 
 
 
 
 1 
 
 
 
 
 /^ 1 
 
 I 
 1 1 
 
 ^of 
 
 IV IV 
 
 '1 "^7 I , 
 
 O.K. 
 
 
 N. 
 
 K. 
 
 
 181 
 
 Repeat this in the other two positions. 
 
 (3) Modulate as above from every key to every other, 
 entering the new key through the triad upon the second 
 degree. 
 
 (4) Modulate as above, entering the new key through 
 the triad upon the sixth degree. 
 
 As it is possible to enter the new key through any one 
 of its different triads, so it is possible to leave the old 
 key by any one of- its triads; for example, instead of 
 starting directly from the old Tonic, we may first pass 
 to any other triad of the old key (excepting the one upon 
 the seventh degree), and starting from that point, by the 
 use of Attendant chords, enter the new key through any 
 one of its triads. It will thus be seen what an infinite 
 variety in modulation is opened to the composer ; and 
 further it will be seen that all these varieties can be 
 formulated and applied in any key. To the writer's 
 knowledge this is the first successful attempt to formulate 
 the principles of modulation and apply them on a large 
 scale. 
 
 (5) Modulate from each of six keys to other keys, 
 leaving the old key through the chord of the Sub-domi- 
 nant; next, leave the old key through the triad upon the 
 sixth degree ; then leave the old key through the other 
 triads in turn. Write out a few examples of these modu- 
 lations, giving the formula for modulation in each case, 
 and adding the Closing Formula. 
 
182 Graded Lessons in Harmony 
 
 LESSON 47. 
 
 MODULATION (Cont.) 
 
 228. As we have now studied the chord of the Dimin- 
 ished seventh and the Augmented sixth chords, we should 
 put this knowledge to practical use in modulation. It will 
 be recognized that as forms of Dominant harmony, the 
 chord of the Diminished seventh or any of the chords 
 of the Augmented sixth may be freely used instead of the 
 Dominant seventh chord, wherever an Attendant chord 
 is required. This gives us a still larger scope of material 
 and progression than was available when confining our- 
 selves to the chord of the Dominant seventh alone. 
 
 EXERCISES. 
 
 (1) After studying H. S., §300, modulate from every 
 key to every other key, using the chord of the Diminished 
 seventh instead of the Dominant seventh chord as At- 
 tendant chord. Write ten examples, giving the chords 
 variety of position. 
 
 (2) Modulate from every key to every other key, using 
 one of the chords of the Augmented sixth as an Attendant 
 chord. Write ten examples. 
 
 229. QUESTIONS 1-16, Key, pp. 147-148. 
 
 230. OTHER MEANS OF MODULATION. 
 
 Several other means of modulation are in common use ; 
 e.g., modulation by means of the common chord, without 
 the use of a Dominant seventh or Attendant chord ; or by 
 the use of the single common note which is used as a 
 connecting link between two unrelated triads. Both these 
 methods work only in a chance, haphazard way, and it 
 is impossible to formulate their use into a method of 
 procedure which will apply in every case, as we are able 
 to do with the Attendant chords. Other illustrations and 
 further discussion of artistic modulation may be found in 
 the writer's How to Modulate, to which the earnest student 
 is referred. 
 
Graded Lessons in Harmony 183 
 
 LESSON 48. 
 
 ALTERED CHORDS. 
 
 2J1. NOTE. 
 
 We have now discussed all of the Fundamental chords 
 and have found that, practically, there is but one Fundamental 
 chord, which appears in larger or smaller forms. It should 
 not be imagined, however, that composers confine themselves 
 to these chords alone, for they frequently use combinations 
 of notes which fail to agree in every particular with any 
 chord we have studied, and in some cases they may even use 
 combinations of notes not traceable to any particular root. 
 The treatment of these altered notes and of the chords in 
 which they are contained is considered in Chapter XI of 
 H. S. 
 
 STUDY H. S., §§238-239. 
 EXERCISES : H. S., §240. 
 
 232. STUDY H. S., §§241-252. 
 EXERCISES : H. S., §253. 
 
 233. STUDY H. S., §§254-257. 
 
 EXERCISES as required in H. S., §257. 
 
 PART-WRITING EXERCISES : the first five exer- 
 cises in H. S.J §258. (Use Key in usual way.) 
 
 234. QUESTIONS 1-7, Key, p. 140. 
 
184 Graded Lessons in Harmony 
 
 LESSON 49. 
 
 ALTERED CHORDS (Cont.) 
 
 235. PART-WRITING EXERCISES. 
 The last six exercises in H. S., §258. 
 
 236. STUDY H. S., §§259-262. 
 EXERCISES : H. S., §263. 
 
 Special Note. Read H. S., §265 very carefully. Try and 
 realize its tremendous meaning, and that the conclusion 
 reached is only the natural following out and application of 
 the principle of tendencies which was first studied at the 
 beginning of this work. 
 
 237. QUESTIONS. 
 
 (1) If a chord consists of three Minor thirds, one 
 above the other, what is the chord? 
 
 (2) What Altered chords are most commonly in use? 
 
 (3) How can you distinguish between Altered chords 
 and Foreign Fundamental chords? 
 
 (4) What is the tendency of Altered chords? 
 
 (5) What is the tendency of the Minor ninth in the 
 chord ? 
 
 (6) When a chord might be either a Fundamental 
 chord or an Altered chord, how can its classification be 
 determined? 
 
 (7) Should Altered tones be doubled? 
 
 (8) What do you understand by the Neapolitan Sixth 
 chord ? 
 
 QUESTIONS 8-20, Key. pp. 140-141. 
 
Graded Lessons in Harmony 
 
 185 
 
 LESSON 50. 
 
 PASSING-NOTES. 
 
 238. EXERCISES. 
 
 (1) Following the example given below, connect the 
 chord of C with the chord of F in three positions, using 
 diatonic Passing-notes in one or more voices. 
 
 Fig. 14. 
 
 Passing-note, 
 
 Chromatic Passing-note, 
 
 iE 
 
 i 
 
 -I 
 
 -M 
 
 ^ 
 
 --?- 
 
 -i 
 
 r 
 
 -II 
 
 ^^ 
 
 S^ 
 
 E 
 
 Passing-note. 
 
 (2) Repeat in various positions and inversions. 
 
 (3) Similarly connect the chord of C with the chord 
 of E Minor in various positions and inversions, using 
 diatonic Passing-notes in one or more voices. 
 
 (4) Continue the above drill, giving six more exam- 
 ples of triad connections, preferably using the simpler 
 triads. 
 
 (5) Connect the triad on C with the triad on G, em- 
 ploying chromatic Passing-notes in one voice. 
 
 (6) Repeat in various positions and inversions. 
 
 (7) Give six more examples of triad connections with 
 chromatic Passing-notes in one voice. 
 
186 Graded Lessons in Harmony 
 
 LESSON 51. 
 
 PASSING-NOTES (Cont.) 
 
 239. STUDY H. S., §§315-316. 
 EXERCISES. 
 
 (a) H. S., §317, (a) and (b). 
 
 (b) Try to make an original series of chords (like 
 Closing Formula, for example), and insert as many Pass- 
 ing-notes as possible in all voices. This exercise may be 
 done either by making the straight chords (without 
 Passing-notes) first, and then adding the Passing-notes; 
 or the Passing-notes may enter into the original thought. 
 The composer would work in the latter way. 
 
 240. READ Key, pp. 180-181. 
 EXERCISES. 
 
 Harmonize the scale as in H. S., §317. Write several 
 examples. (See Key, pp. 190-191.) 
 
 241. STUDY H. S., §§318-319. 
 EXERCISES. 
 
 (a) Construct an original example of Passing- 
 chords. 
 
 (b) Construct a short phrase with Chromatically 
 Altered notes. 
 
 242. STUDY H. S., §§320-322. 
 EXERCISES : H. S., §322. 
 
 243. STUDY H. S., §323. 
 
 EXERCISES. Construct original examples of In- 
 verted Pedal. 
 
 PART-WRITING EXERCISES: H. S., §324. (Com- 
 pare with Key.) 
 
 244. STUDY repeatedly H. S., §§325-327. 
 
 245. QUESTIONS 1-12, Key. pp. 163-164. 
 
 246. GENERAL RECAPITULATION: A't'v, pp. 164- 
 165. 
 
Graded Lessons in Harmony 187 
 
 LESSON 52. 
 
 SUSPENSIONS. 
 
 247. This study is the beginning of the consideration 
 of how variety of musical structure is secured. 
 STUDY H. S., §§301-304. 
 EXERCISES: H. S., §305, (a), (b) and (c). 
 PART-WRITING: //. 6"., §306. (Compare with Key.) 
 
188 Graded Lessons in Harmony 
 
 LESSON 53. 
 
 SUSPENSIONS (Cont.) 
 
 248. STUDY H. S., §307. 
 
 PART-WRITING EXERCISES: four exercises as 
 in H. S., §308. (Use Key as directed.) 
 
 249. STUDY H. S., §309. 
 EXERCISES: H. S., §311. 
 
Graded Lessons in Harmony 189 
 
 LESSON 54. 
 
 SUSPENSIONS (Cont.) 
 
 250. PART-WRITING EXERCISES: last five exercises, 
 H. S., §308. 
 
 251. STUDY H. S., §312. 
 EXERCISES : H. S., §313. 
 
 252. STUDY H. S., §314. 
 EXERCISES. 
 
 Try to find examples of Syncopation ; also of Retarda- 
 tion and Anticipation, in printed music. 
 
 253. QUESTIONS 1-11, Key. p. 159. 
 
190 Graded Lessons in Harmony 
 
 LESSON 55. 
 
 CHORD ANALYSIS (Cont.) 
 
 254. Having now studied the Attendant chords, the 
 chords of the Augmented sixth and the Altered chords, 
 the student is prepared to analyze a large portion of more 
 difficult chords. He has learned that the root of any 
 Fundamental chord may be discovered by means of the 
 principle of the "sharpest note." He has learned that this 
 "sharpest note" is a sure guide in the chords of the Domi- 
 nant seventh. Diminished seventh, Major and Minor 
 ninth, and the three forms of the Augmented sixth ; that 
 therefore, in any change of key the ruling foreign chord 
 (the one usually coming just before a cadence) is sure to 
 reveal the key, since almost unfailingly one of these forms 
 of the Dominant chord will appear. The student has also 
 learned to distinguish between Fundamental chords and 
 Altered chords. 
 
 EXERCISES. 
 
 The pupil will now analyze the whole of Mendelssohn's 
 "Spring- Song," taking as a guide, if he wishes, the illus- 
 tration in H. S., Fig. 80. He will also analyze selections 
 of his own from Beethoven, including the more difficult 
 portions. 
 
Graded Lessons in Harmony 191 
 
 LESSON 56. 
 
 MISCELLANEOUS. 
 
 255. STUDY carefully H. S., §328. 
 EXERCISES. 
 
 Make examples of Cross Relations, and correct them. 
 
 256. STUDY H. S., §329. 
 EXERCISES. 
 
 Make an example of the Tritone and correct it. 
 
 257. STUDY H. S., §330. 
 
 CONSTRUCT or find examples of right and wrong 
 use of the chord of six-four. 
 
 258. STUDY carefully H. S., §331, and apply the point in 
 all later studies of analysis. 
 
 259. STUDY H. S., §332. 
 EXERCISES. 
 
 Turn to past part-writing exercises and find all 
 sequential passages in the bass. 
 
 PART-WRITING EXERCISES : H. S., §332. (Fol- 
 low directions about using Key. ) 
 
 260. STUDY H. S., §333. 
 
 261. STUDY H. S., §334. 
 
 262. STUDY H. S., §335. 
 
 EXERCISES. 
 
 Advanced students should be able to read a little in 
 C clefs at least. Those intending to do orchestral work 
 will find it indispensable. The student is, therefore, ad- 
 vised to drill himself in this work, first by transposing 
 
192 Graded Lessons in Harmony 
 
 hymn tunes into the four clefs, Bass, Tenor, Alto and 
 Soprano, and by reading orchestral music in the same 
 clefs. Study H. S., §336. 
 
 263. STUDY H. S., §337. 
 
 264. STUDY H. S., §338. 
 EXERCISES: H. S., §338. 
 
 265. STUDY H. S., §339. 
 EXERCISES : H. S., §339. 
 
 266. QUESTIONS 1-11, Key, pp. 168-169. 
 
Graded Lessons in Harmony 193 
 
 LESSON 57. 
 
 HARMONIZING MELODIES. 
 
 267. SPECIAL NOTE. 
 
 This is a difficult and vitally important section, which must 
 have careful and detailed consideration. Do not be impatient, 
 therefore, in taking one point at a time, nor work rapidly 
 through the exercises, but give thoughtful and musicianly 
 attention to each little point. 
 
 STUDY H. S., §340. 
 
 STUDY Key, pp. 170, 180, 181 (text only). 
 
 EXERCISES: H. S., §340. Work three exercises. 
 (Compare with Key.) 
 
 268. PROCEED similarly with the rest of the exer- 
 cises, H. S., §340. Do not consult the Key till each group 
 is completed. 
 
 269. EXERCISES: Key, p. 176, Additional Exercises, 
 (a) only. 
 
 270. QUESTIONS. 
 
 (1) To how many chords (triads) in the key may a 
 given tone belong? 
 
 (2) To how many triads out of the key may a given 
 tone belong? 
 
 (3) In choosing the chords for harmonizing a melody, 
 do we think of anything beside the possible chords to 
 which each tone may belong? 
 
 (4) When you see a certain note in the melody, do 
 you unconsciously associate that tone with the triad of 
 the same name? (To illustrate, when you see G in the 
 melody do you feel that it will require the chord of G to 
 harmonize it?) 
 
 (5) Can you sing the melody (to be harmonized) 
 without playing it? 
 
194 Graded Lessons in Harmony 
 
 (6) Can you mentally sing the melody? 
 
 (7) When you mentally (or audibly) sing the melody, 
 can you mentally construct or imagine the chords to go 
 with the melody tones ? If not the whole, can you men- 
 tally construct shorter series of chords? 
 
 271. ANSWERS. 
 
 ANSWER TO QUESTION (2). 
 
 Almost an indefinite number; it may belong to: 
 
 3 Major triads in each Major key. 
 
 3 Minor triads in each Major key. 
 
 3 Diminished triads in each Major key. 
 
 2 Major triads in each Minor key. 
 
 2 Minor triads in each Minor key. 
 
 2 Diminished triads in each Minor key. 
 
 1 Augmented triad in each Minor key. 
 
 ANSWER TO QUESTION (3). 
 
 We shoiild also think of the natural succession of 
 chords and their gravitation toward the Closing Formula. 
 
 ANSWER TO QUESTION (4). 
 
 To allow a given note to suggest the chord of the 
 same name is a common habit which should be developed 
 as rapidly as possible into more musicianly ways. 
 
Graded Lessons in Harmony 195 
 
 LESSON 58. 
 
 HARMONIZING MELODIES (Cont.) 
 
 272. SPECIAL NOTE. 
 
 Make a. special note of each difficulty you encounter in 
 preparing this lesson. 
 
 STUDY Key, pp. 180, 181 (repeated from Lesson 57). 
 
 273. STUDY Key, pp. 182, 183. 
 
 EXERCISES: H. S., §§341, 342, (two exercises only). 
 
 274. EXERCISES: Key, p. 176, (b). 
 
 275. EXERCISES: Key, p. 176, (f). 
 
 276. Examine many hymn tunes with "choice of 
 chords" in mind, noting- what the composer did and how 
 you would have treated the given melody had you har- 
 monized it. 
 
 Think over and review the principles of key and chord 
 relations as developed in H. S., and the notes in the Key, 
 from the beginning of the books. 
 
 Review the subject of Cadences. 
 
 277. QUESTIONS. 
 
 (1) In mentally singing the melody, can you mentally 
 CONSTRUCT or imagine the cadences ? 
 
 (2) Can you perceive the divisions of the melody into 
 phrases ? 
 
 (3) When two harmonizations of a given tone are 
 possible, what should control or influence your choice? 
 
 (4) What is the general principle underlying the har- 
 monizing of melodies? 
 
 (5) Give as many notes and directions as you can 
 about the choice of chords, without referring again to 
 book or Key. (Write this answer after doing the exercises 
 in notation.) 
 
196 Graded Lessons in Harmony 
 
 278. ANSWERS. 
 
 ANSWER TO QUESTION (1). 
 
 This is one of the first points to develop as we study 
 this plan of evolving the harmony and melody together. 
 
 ANSWER TO QUESTION (2). 
 
 Each phrase, usually of even length, two or four meas- 
 ures, requires some kind of a cadence; this alone will 
 supply a good proportion of the required chords. 
 
 ANSWER TO QUESTION (3). 
 
 The progression or relations to the preceding and fol- 
 lowing chords. Also, but less strongly, the principle of 
 variety. 
 
 ANSWER TO QUESTION (4). 
 
 That of the natural sequence of chords suggested by 
 the Closing Formula ; this does not apply rigidly, nor in 
 the first chords of a phrase, but we work gradually toward 
 it for each cadence. 
 
 ANSWER TO QUESTION (5). 
 See Key, pp. 182, 183. 
 
Graded Lessons in Harmony 197 
 
 LESSON 59. 
 
 HARMONIZING MELODIES (Cont.) 
 
 279. REVIEW Inversions. 
 REVIEW Chord Connection. 
 
 REVIEW Principles of Part-writing {Key, pp. 30-53). 
 STUDY Key, pp. 182, 183 (review). 
 
 280. STUDY Key, pp. 186-190 {text only). 
 EXERCISES. 
 
 (1) H. S., §342 (finish). 
 
 (2) H. S., §343 (two examples). 
 
 (3) Key, p. 176, (c). 
 
 (4) Key, p. 176, (f). 
 
 (5) Key, p. 176, (g). 
 
 (6) Transpose the harmonization of the Creed into 
 two other keys (written). 
 
 (7) Transpose into all other keys at the keyboard. 
 
 (8) Harmonize the Creed upon a different tone. 
 (Your own harmonization.) 
 
 281. QUESTIONS. 
 
 (1) In harmonizing melodies, do you have any trouble 
 with the details of chord connection, part-writing, inver- 
 sions, etc.? Note any difficulties in full, and study sepa- 
 rately each point. 
 
 (2) Can you use the "Half Close" easily at the end 
 of any of the phrases? 
 
 (3) Where could it occur? 
 
 (4) How can you discover the places in the melody? 
 
 (5) Can you use [A] chords easily in harmonizing 
 melodies ? 
 
 (6) Is there any particular way of deciding about 
 the need of an [A] chord in harmonizing melodies? 
 
 (7) Have you any suggestions as to when inversions 
 may be used? 
 
198 Graded Lessons in Harmony 
 
 282. ANSWERS. 
 
 ANSWER TO QUESTION (3). 
 
 At the close of any phrase excepting the final one, 
 which should be on the Tonic. 
 
 ANSWER TO QUESTION (4). 
 
 When the end of a phrase, usually two or four meas- 
 ures, occurs upon a note not belonging to the Tonic 
 chord, the cadence cannot be an "Authentic" one, but may ' 
 be a Half Close, Deceptive, Modulatory, etc. If the mel- 
 ody note in question belongs to the Dominant chord of the 
 key, it may easily suggest a Half Close. 
 
 ANSWER TO QUESTION (6). 
 
 No other way than to try them; and when the use of 
 key chords alone fails to give the smoothest effect, we 
 should try them. Sometimes the cadences will suggest 
 them. 
 
 ANSWER TO QUESTION (7). 
 
 Often when harmonizing successive scale tones in the 
 melody, to prevent bad consecutives. The frequent use 
 of inversions is a mark of musicianship. 
 
Graded Lessons in Harmony 199 
 
 LESSON 60. 
 
 HARMONIZING MELODIES (Cont.) 
 
 283. STUDY H. S., §343. 
 EXERCISES. 
 
 As in H. S., §343, write three examples of Single 
 Chants and three examples of Double Chants. 
 
 284. STUDY H. S., §345. 
 EXERCISE. 
 
 Following the suggestions here given, write examples 
 of two short hymn tunes and of two short phrases written 
 in free form for the piano. Any of Mendelssohn's "Songs 
 without Words," Schumann's "Traumerei," or a slow 
 movement from a sonatina will serve as an illustration. 
 
 285. STUDY H. S., §§346-349. 
 
200 Graded Lessons in Harmony 
 
 LESSON 61. 
 
 ANALYSIS AND FORM. 
 
 286. As the study of analysis and form is a separate 
 branch, we merely touch upon the subject in H. S., in 
 order to awaken an interest in this most necessary and 
 interesting side of the work. 
 
 Study carefully and thoughtfully H. S., pp. 224-235. 
 
 EXERCISES, as suggested and outlined in H. S., 
 pp. 224-235. 
 
Graded Lessons in Harmony 201 
 
 The author has endeavored in this volume to lighten 
 the work of the busy teacher, by putting into graded 
 lesson form the contents of Harmony Simplified. If the 
 teacher, with its help, shall be enabled to present the sub- 
 ject of Harmony in a simple and practical form; if the 
 student shall be stimulated to an ever-increasing interest 
 in the subject, and to further study and practice along the 
 lines laid out; if the earnest seeker after a thorough 
 knowledge of Harmony shall gain a clearer vision of the 
 fundamental principles and of their relation to universal 
 laws; if modern Harmony study shall be simplified, broad- 
 ened and intensified, and musical standards raised con- 
 tinually higher: then the purpose of this volume will have 
 been attained. 
 
HARMONY SIMPLIFIED 
 
 By F. H. SHEPARD 
 
 Pages, vii and 242 
 
 Price, Cloth, $125 Net 
 
 For an author who has devoted the best thought and most 
 intense energy of a busy Hfe to the production of an educative 
 work, there can hardly be a greater and more profound satis- 
 faction than to see the fruit of his labors fully and gratefully 
 recognized by competent authorities, and studied with real 
 enthusiasm by teachers and pupils alike. The Shepard system 
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 comprehension), but is at the same time even more complete and 
 thoroughgoing than the older methods. It is, emphatically, 
 simple and direct. Thorough treatment of the Scales, Keys, 
 Signatures and Intervals prepares the pupil to grasp with ease 
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 from the outset; the principles underlying the forms of prepara- 
 tion and resolution are presented with exceptional clearness, 
 this highly important section being really original in treatment 
 and showing a distinct advance over former presentations. 
 
 No music-teacher who has the proper training of the young 
 at heart should fail to read this work with careful attention; its 
 suggestive value is of the highest order. The following "ap- 
 preciations" from prominent educators bring this point into 
 strong relief. 
 
 From Prof. H. C. MACDOUGAL, of WeUesley CoUege 
 "I have been looking at your 'Harmony Simplified,' and must own that 
 I am surprised at its uniform excellence. It is really a remarkable book when 
 one compares it with the old . . . treatises, which are dry in their literary 
 style, and impossible to understand without a teacher at the elbow. . . . 
 To come down to particulars: Scales and Intervals are much clearer than 
 I have ever seen them. . . Your small-type matter, 'synopses* and 
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 Your treatment of Chords of the Seventh, and the whole idea of Tendencies 
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 202 
 
work like yours when I began, I should have been spared many years of grop- 
 ing for light. . . . Nothing but sincere admiration for what must be 
 considered the leading work on the subject." 
 
 From A. K. VIRGIL 
 
 "I am more than pleased with the work. It is perfectly clear — truth is 
 always clear. You have followed educational principles as has never before, 
 to my knowledge, been done in any work on harmony. I am much interested 
 in what you do in the book, and particularly in the very sensible way you go 
 about it. You are unquestionably an educator." 
 
 From WILLIAM MASON 
 
 "A cursory examination has excited my interest and produced a most 
 favorable impression." 
 
 From HOMER A. NORRIS 
 (Author of "Practical Harmony on a French Basis") 
 
 "Your 'Harmony Simplified' has so much to recommend itself to me that I 
 am constrained to send you aline regarding it. ... I have about decided 
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 my own book being too difficult for children, or for use in connection with 
 lessons on the pianoforte." 
 
 From FREDERICK ELMER CHAPMAN 
 (Director of Music, Public Schools, Cambridge, Mass.) 
 
 "In introducing the subject of Harmony into the Cambridge High School 
 course I have used no book, but have taken my system from seven or eight 
 authorities, yours among the others. I have concluded that it may be best to 
 adopt your 'Harmony Simplified' for use with the students. ... I like 
 your book very much, and shall be glad to get your idea as to its use in just 
 the place I propose to use it." 
 [Note. — "Harmony Simplified" was adopted.] 
 
 .From "A TEACHER" 
 
 "I never expected to find, nor did I believe there was so much light on 
 this subject, as you have given me in this course." 
 
 From "AN AMATEUR" 
 
 "I presume to write you in order to thank you for all the good 'Harmony 
 Simplified' has done me, . . , Twice I had attempted to study harmony, 
 and twice was obliged to give it up in despair at its being too complicated. . . . 
 Your book was a revelation to me. ... I had the comfort of learning that 
 the subject is learnable — indeed, most beautifully simple. I wish to thank 
 you for the knowledge obtained and the great comfort derived." 
 
 203 
 
A KEY TO 
 
 "Harmony Simplified" 
 
 and a 
 
 CLASSROOM MANUAL 
 
 By F. H. SHEPARD 
 
 Pages, vi and 191 Price, Cloth, $1.25 Net 
 
 The remarkable success of Mr. Shepard's unique work, 
 "Harmony Simplified," has not merely demonstrated its right 
 to exist; the method has elicited the warmest encomiums of 
 prominent educators whose pupils have been aroused to genuine 
 enthusiasm over their harmony tasks, and the heartiest thanks 
 of students obliged to study without a teacher's guidance. 
 
 To complete the good work comes this "Key" — a veritable 
 golden key to the treasure-house of Harmony, for it is far from 
 being a mere compilation of "Answers to Questions" and "Solu- 
 tions of Exercises." It is a series of heart-to-heart talks between 
 teacher and pupil, the teacher drawing upon his fund of ripe 
 pedagogical experience to forestall — so it would seem — every 
 possible question or objection that might be raised by the most 
 inquisitive or opinionated seeker after harmonic truths. It is 
 the outcome of twelve years' further experience in the teaching 
 of classes and individual students in accordance with the princi- 
 ples of "Harmony Simplified." 
 
 In the Preface the author dedicates the book to those who 
 are seeking to know "the reasons why." It is designed, first, 
 as a Key to the exercises in "Harmony Simplified"; second, 
 as a guide and classroom assistant in teaching from that text 
 book; and third, as offering suggestive and supplementary ma- 
 terial for those using other text-books. Students using the 
 Manuals of Jadassohn or Richter will find many of the Part- 
 writing exercises solved in the "Key." To further aid the 
 student, the choice between various forms of chords is discussed, 
 showing why one form is preferred to another in the individual 
 case. 
 
 The questions and answers, appearing as Notes upon the 
 Part-writing, are suggestions as to how the teacher may pro- 
 ceed in the classroom. Nothing so establishes the student in 
 his work as to be obliged to tell why each progression is made. 
 Such definite work soon develops quick choice and rapid musical 
 writing. The "Topics for Discussion" at the close of various 
 chapters will be found of value in the classroom and for individual 
 investigation, while many of the four hundred questions ar* 
 suited for use in examinations. 
 
Should be Found in the Library of Every Musician 
 
 HOW TO MODULATE 
 
 By F. H. SHEPARD 
 
 A direct, concise and simple method of modulating 
 
 from any key to any other 
 
 FEATURES 
 
 It can be studied step by step. It does not have twelve dif- 
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 artistic Modulation, as shown and illustrated by examples from 
 Beethoven, covers entirely new ground and is much appreciated 
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 Endorsed by Leading Musical 
 
 Authorities 
 
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 Spark, Herr Gustav Schreck, Toronto Conservatory, etc., etc. 
 
 Price, $1.00 Net 
 
 Published by A. AGNES SHEPARD, Orange, N. J. 
 
 The Shepard Keyboard Diagram 
 and Chord Directory 
 
 A Practical Substitute for the Keyboard in Classes, Lectures, 
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 also, of course, for thorough class drill at every step of the study. With 
 the aid of this device a hundred may each practically have the 
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 Printed on Heavy Cardboard - Price 25c. Net 
 Published by A. AGNES SHEPARD, Orange, N. J. 
 
 205 
 
Piano Technique Simplified 
 
 Condensed and Systematized 
 for the 
 
 Beginner of 7 'WJ"" Adult Beginner 
 
 By A. AGNES SHEPARD 
 
 THE teacher will find in this book simple and interesting Tech- 
 nique systematically and logically given, to carry the veriest 
 beginner, step by step, through the first months of study. 
 Through the use of these exercises the pupil will develop a vitalized 
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 In addition to the Technique, there is a list of material suited to 
 the first lessons and a great deal more. 
 
 It is, as the title indicates, simple, condensed, and systematized. 
 
 Pric e , 75 c. 
 
 BOOKS II AND III IN PREPARATION 
 Published by A. AGNES SHEPARD, Orange, N. J. 
 
 MUSIC DOMINOES 
 
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 ARPEGGIOS for EVERYBODY 
 
 By A. AGNES SHEPARD 
 
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 PRICE, SOc. 
 
 Published by A. AGNES SHEPARD, Orange, N. J. 
 
 206 
 
 
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