Cornell University Library MT 7.011 1886 Text book of musical elements. 3 1924 021 800 945 BOUGHT WITH THE INCOME FROM THE p - SAGE ENDOWMENT FUND THE GIFT OF Henrg W. Sage 1S91 /mm JPSIC ^m... Cornell University Library The original of this book is in the Cornell University Library. There are no known copyright restrictions in the United States on the use of the text. http://www.archive.org/details/cu31924021800945 TEXT BOOK OP MUSICAL ELEMENTS TEXT BOOK OF MUSICAL ELEMENTS GEO. QAKEY (Mds.Bao. Cantab.) Author of " Text Book of Counterpoint " and " Text Booh of Earmony," Teacher of Harmony and Counterpoint at the City of London College and the Tonic Sol-fa College. FIFTH EDITION. ILonDon : J. CTJKWEtf & SONS, 8 & 9 WAKWICK LAOT!, E.C. In Cloth, Is. 6rf. / Paper, Is. LONDON J. CUEWEN & SONS, MUSIC PRINTERS, FLAISTOW, B. PREFACE. 1 V HB information given in this book should be in the possession uf all practical musicians; it is a pre-requisite to higher studies in musical art, and is essential to a just and intelligent rendering of music, be the performer vocalist or instrumentalist. The lack of theoretical knowledge which is exhibited by so many amateur performers in their inability to explain or to write correctly the simplest musical passage is now recognised by the various musical institutions and other examining bodies. Theoretical knowledge forms the chief subject of all preliminary examinations, and is a requirement in most examinations that are ostensibly confined to testing practical skill. To assist persons preparing for these examinations is one of the objects that the author has had in view in writing the following pages, and it is hoped that the questions and exercises which follow the text of the work will be specially useful for that purpose. The present work differs from others of the same class prin- cipally in its plan and arrangement. The several topics are in the progressive order that the author considers best adapted to convey an entire knowledge of the subject to an ordinary student. The chief elements and the fundamental structure of notation are dealt with first, the minutiae of ornament, variation, and contraction VI PREFACE. being reserved for after and separate consideration in chapters specially devoted to them. Prominence is given to all the details of notation as it is written to-day rather than to those ancient methods of writing music which are often referred to in similar works. Such references have more place in a history of music, and are rarely, in the author's experience, a help to those who are endeavouring to master the elements of music. The various details of notation diffused throughout the work, with those which have special mention in the chapter embracing points of writing, will, it is hoped, help those who wish to write accurately and clearly. The chapter on the elements of harmony introduces a subject not generally included in a work of this class. The best teachers of the pianoforte find it advantageous that their pupils should not only possess a thorough knowledge of what is usually comprehended in the term " musical elements," but that they should also have some knowledge of the rudiments of the art that deals with the construction of music. The hope of the author is that the concluding chapter will not only meet the wants of those who seek to acquire a purely rudimentary knowledge of the art, but that it may stimulate some to make a more comprehensive study of the subject of harmony in its entirety. Upton, B. September 16th, 1886. CONTENTS. CHAPTER I. CHAPTER II. CHAPTER III. CHAPTER IV. CHAPTER V. CHAPTER VI. Preliminary Definitions Tune Notation of Tune ... Notation of Time ... Accent and Measure... Time Signatures CHAPTER VII. The Major Scale and Key Signatures CHAPTER VIH. The Minor Scales and Key Signatures CHAPTER IX. Accidentals and Chromatic Scale CHAPTER X. Enharmonic Change CHAPTER XI. Time Modifications CHAPTER XII. Tune Modifications CHAPTER XIII. CHAPTER XIV. CHAPTER XV. CHAPTER XVI. Miscellaneous Intervals The Elements of Harmony QUESTIONS AND EXERCISES 1 ... 2-3 ...4-10 11-13 14-19 20-22 23-29 80-32 83-37 88-39 40-47 48-52 53-56 57-62 63-68 69-77 78-95 TEXT BOOK OF MUSICAL ELEMENTS CHAPTER I. PRELIMINARY DEFINITIONS. 1. Music is produced by the combination of sound and rhythm. 2. Sound is the result to the ear of vibrations of the air. 3. Rhythm describes a series of percussions in more or less regular order. 4. Musical Sound is the result of vibrations of the air that are regular or periodic in order, and sufficiently rapid to produce continuity of effect. 5. Pitch is the term used to express the difference between musical sounds that result from the variation of the number of vibrations of the air in a given time. The greater the number of vibrations the higher the sound ; the lesser the number the lower the sound. 6. Intensity is a term applied to sounds in referring to the difference in the force or strength of them. The difference depends on the extent of the vibrations of the air; the larger and more extended the vibrations the louder will be the sound. 7. Duration in relation to sound is the time that the vibrations of the air continue at the rate that causes the sound. 8. Time chiefly comprehends the variety in the duration of sounds as compared with one another. 9. Tune chiefly comprehends the variety in the pitch of sounds as compared with one another. It CHAPTER II. TUNE. 10. The definition of Tune in the previous paragraph is of Tune in the abstract as distinguished from Time in the abstract. Tune in the concrete not only includes Time, but other elements ■which it is necessary to consider separately. 11. Different sounds may be grouped together in a satisfactory manner in two ways. The sounds may be grouped for production successively, in which case the result is Melody ; or they may be grouped for production simultaneously, in 'which case the result is Harmony. 12. Melody alone or melody and harmony combined may be comprehended in the word Tune. But Tune in either sense is dependent upon a certain relation of the sounds to one of them that is regarded as the basis of the others. 13. Prom a given sound a succession of seven others in more or less regular order combine to form what is termed a Scale, from scala, a ladder. See Fig. 1. 14. The sounds numbered 1 to 7 are those which from their being quite distinct and different from each other form the series of the scale proper. But the eighth sound gives complete- ness, and this series of eight sounds is called a Complete Scale. The highest sound of the complete scale is at once the eighth or octave of it and the first of another scale that might be raised above it. Conversely the lowest sound of a scale is at once the first of it and the eighth or octave of the scale immediately below. 15. The several sounds that make up the scale, it will be per^ ceived by Fig. 1, are not all at equal distances from each other. Those which have the greater distances between them are said to be a Tone apart, as from 1 to 2. Those which have the smaller distances between them are said to. be a Semitone apart, as from 3 to 4. TUNE. 16. Of the semitones in the scale there are but two; it is chiefly composed of Tones. Hence the term Diatonic Scale (from the Greek words signifying "through" and "tone") is applied to distinguish it from another which will in due course be mentioned. 17. There is more than one form of the Diatonic Scale. But that in which the order of tones and semitones succeed as in Fig. 1, viz., with the semitones between the third and fourth and seventh and eighth sounds, is termed the Major Scale. 18. The Major Scale is also said to be made up of two similar groups of four sounds! Bach group includes two tones and a semi- tone, the semitone in each being at the top. See Fig. 1. These groups of four sounds are called Tetrachords. The Tetrachords in the Major Scale are themselves separated by a tone. 19. The sound upon which the scale is built and which governs all the rest is called the key-tone or Tonic. Each of the other sounds of the scale have names that are more or less characteristic of their importance. The fifth sound, which is the sound upon which the second tetrachord is built, is called the Dom- inant. The third sound, lying midway between these two, is called the Mediant. The fourth sound holds a similar position below the upper tone that the Dominant does to the lower Tonic, and is called the St/bdominant. The sixth sound.lying mid- way between the upper Tonic and the Sub- dominant, is called the Submediant. The second sound, from being the tone immediately aboye the Tonic is called the Supertonio. The seventh sound, from its similar position below the Tonic, is called by some the Sttbtonic, and by others the Sitbsemitone, bui it is more generally known as the Leading Note, from its tendency to lead to the Tonic. The sixth of the scale holds also a similar relation to the Dominant that the second does to the Tonic, and is sometimes called the Super- dominant. The table at the side gives in order the names that are in general 8th Tonic. 7th Leading Note. 6th Submediant. 5th Dominant. 4th Subdominant. 3rd Mediant. 2nd Supertonic. 1st Tonic. CHAPTER III. NOTATION OF TUNE. 20. Musical sounds are written upon a series of parallel lines and in the spaces between them, in characters that vary in shape according to the length of the sounds. 21. A group of five lines is the number now in use, and such a group is called a Staye or Staff. Fig. 2. 5 4 The lines and spaces are counted from below, as shewn. Relative differences of pitch are shewn by placing the characters referred to higher or lower upon the staff. 22. The staff of five lines, though more convenient than either the staff of the lesser or the staff of the greater number that was formerly in use, is inadequate to express all the sounds within the range of an ordinary voice or instrument. Short lines are therefore added as occasion requires above or below the staff. Fig. 3. These short lines are called Legek Lines. 23. Two staves in particular are in general use, upon which by the aid of leger lines it is possible to express all the sounds within the range of the human voice, or all those within the ordinary range of instruments. • 24. To distinguish one staff from another a character is placed at the beginning called, from tne word key, a Clef. NOTATION OF TUNE. 25. The clef that is used for the staff that represents the higher series of sounds is -written thus i Fig. 4. 9 and the clef that is used for the staff that represents the lower series of sounds is written thus Pig. 5. 5fe = _ ^== 26. The first-named or higher clef is called the Treble clef, and the staff upon which it is placed receives the name of the Treble staff. The second-named or lower clef is called the Bass clef, and the staff upon which it is placed receives the name of the Bass staff. 27. The clefs, besides distinguishing the staff, serve also to fix the pitch name of one of the sounds on the staff, and to give the clue to the rest of the sounds. 28. The differences of sounds as to their pitch, apart from any question of scalewise order, are called after the first seven letters of the alphabet, the letters ABCDEI6 being used for seven successive sounds in ascending order and the names being repeated for each successive series. 29. The treble clef is said to stand upon the second line of the staff (its curves cross that line more often than any other), and the clef itself is a corruption of the letter Q-. Hence the treble clef is called the G clef, and gives the pitch-name of G- to the second line of its staff. 30. The bass clef stands upon the fourth line of its staff, and the clef itself in the first form of it given in Kg. 5 is a corruption of the letter F. Hence the bass clef is called the F clef, and gives the pitch-name of F to the fourth line of its staff. 31. Adjacent sounds are placed upon a line and in its next space above or below, or vice versa, in a space and upon its next line above or below. The next higher sound to that which is represented by the Q clef would stand in the second space, which, as the first of another alphabetical series, would be called A. The next lower sound to that represented by the Q- clef would stand in the first space, which, as the next of the alphabetical series back- 6 TEXT BOOK OF MUSICAL ELEMENTS. wards would be called F. Proceeding with tie sounds each way from the clef sound it will be seen that the sounds of the lines and spaces of the treble staff will be these Fig. 6. m 32. Taking the bass staff and proceeding each way from the F of the fourth line that is determined by the olef it will be seen that the sounds of the lines and spaces will be these Fig. 7. mi 33. Placing now the staff for the higher sounds above that for the lower sounds, as they are used in the writing of music for the pianoforte, harmonium, &c., Fig. 8. t m- it will be evident by the gap in the alphabetical series that there are other sounds between the two staves. If one more sound be added above the bass staff and one more below the treble staff, the two will meet in on a leger line that is at once the first leger linn above the bass staff and the first leger line below the treble staff. Fig. 9. i i/ D - -0- A-B 34. The standing between the two staves is called Middle C. NOTATION OF TUNE, 35. Any sound higher than that on the first leger line above the bass stafl will obviously be in the domain of the treble staff, and any sound lower than that on the first leger line below the treble stafl will similarly be in the domain of the bass staff. Kg. 10. -o-JX. i£: t IS -O "IT — m~ " A " "°" -T- 36. Music for the higher voices of women rarely goes below the first leger line of the treble staff, and music for the lower voices of men rarely goes above the first leger line above the bass staff, i.e., the middle in each case. But for the lower voices of women, when the music descends into the region of the bass stafl, a second leger line below the treble staff would be necessary, and for the higher voices of men, when the music ascends into the region of the treble stafl, two and three leger lines above the bass staff would more often be necessary. 37. To avoid the multiplicity of leger lines in these cases two other staves are in occasional use. The first takes its three lowest lines from the bass stafl and its fifth line from the first of the treble stafl, the fourth line being the leger line of middle 0. Kg. 11. m m 38. Another stafl is formed by taking for the lower lines two from the bass staff, and for the higher lines two from the treble staff, its middle line being the line of middle 0. Pig. 12. m 8 TEXT BOOK OF MUSICAL ELEMENTS. 39. To distinguish, these staves from the others a clef is used which is supposed to be a corruption of the letter C, made thus m This clef always represents the pitch of middle C. It therefore is placed on the fourth line of the staff described in § 37 and on the third line of the staff described in § 38. 40. The C clef placed on the fourth line of a staff £ is called the Tenor clef, and the staff receives the name of the Tenor staff. This staff is used for the higher voices of men and for the higher range of certain instruments as the violoncello and bassoon. 41. The C clef placed on the third line of a staff £ is called the Alto clef, and the staff receives the name of the Alto staff. This stafi is used for the lower voices of women and for the viola and some other instruments, but is less used for voices than the Tenor staff, except in the voice parts of German editions <>f full scores of classical compositions. 42. A stafi is also used having the line of middle C for its first line and the other four lines from the treble staff. The C clef on the first line distinguishes this staff and gives to it the name of the Soprano staff. It is used for the higher voices of women instead of the Treble staff in the German editions just referred to. 43. Still more rarely a staff is used having for its first line the fifth of the bass staff, the line of middle for its second, and for the rest the first three of the treble stafi. The C clef comes on the second line of the stafi and gives to it the name of the Second Soprano staff. Its use is almost entirely confined to the German editions referred to in previous sections. 44. The relative positions of all the foregoing staves to each other is shewn in the following diagram, which represents a stafi of eleven lines. Fig. 13. Alto. 2nd Soprano. 1st Soprano. Treble. I mmmmmn Bass. Tenor. NOTATION OF TUNE. The group of eleven lines is sometimes called the Gkeat Stave or the Grand Staff, but it is not in use as a separate staff. 45. It has been seen that the only sounds that are directly represented in pitch are the clef sounds— treble G, bass P, and middle C. The others are determined from" these by the aid of the staves. 46. The particular pitch of notes needs sometimes to be referred to apart from their relation to any staff. The difference, for instance, between E of the third space of the bass staff and the E of the first line of the treble staff may need to be distinguished. 47. The differences in pitch between notes of the same alphabetical letter are named according to the series of notes from one C to the B above. Thus the series of notes extending from the C on the second leger line below the bass staff to the B on the second line is called the Great Octave ; the series extending from in the second space of the bass staff to the B above the staff is called the Small Octave ; the series extending from middle to the B of the third line of the treble staff is called the Once- marked Octave; and the series extending from C of the third space of the treble clef to the B above the first leger line is called the Twice-marked Octavo. The letters are printed and marked as shewn in the diagram at the side. 48. Most of the C sounds have also special names. Middle C, as has already been shewn, is distinguished as such. The in the treble staff is called treble C or Standard 0. The C above that on # I I 60 o 10 TEXT BOOK OF MUSICAL ELEMENTS. the second leger Hue above the treble staff is called in alt. The C in the second space of the bass staff is called Tenor C, being the lowest note of the Yiola. 49. It has been stated that the pitch is determined by the number of vibrations of the air in a given time. The exact differences of pitch are reckoned from one sound which is chosen as a standard. The treble has been chosen as a pitch sound for a standard as being suitable for vocal purposes. The lowest sound distinguishable by the human ear is one that is produced by sixteen vibrations of the air in a second. This corresponds to the C that is two octaves below the of the great octave. The sound an octave above this lowest sound gives 32 vibrations in » second. Bach octave doubles the number of vibrations, so that the number of vibrations in a second of treble C is 512. This is called the Philosophical Standard, and is only a little higher than that used in the time of Handel. This standard, though based on a scientific foundation, has not prevailed, and the pitch has gradually risen till it is now a full semitone higher than Handel's tuning fork of the year 1740. The high and unsettled state of the pitch in this and other countries has brought about a movement for adopting a uniform standard. The pitch that has been officially adopted by all the principal governments of continental Europe, and which seems most likely to be adopted for a uniform standard, is reckoned from A in the second space of the treble staff — the pitch sound from which musical instruments are tuned. This A is produced by 435 vibrations in a second, and is known as the French Standard Pitch or Diapason normal. This gives for treble C 517£ vibrations. 11 CHAPTER IV. NOTATION OF TIME. 50. The relative durations of sounds are expressed in characters called Notes, differing in shape or form. By the position on the staff the note represents the pitch of the sound, and by the form or , shape of the note the relative length of the sound. 51. There are in common use at least six forms of notes. These, with the names by which they are known, are as follows — a The Semibreve, or "Whole Note. 1° I The Minim, or Half -note. I* I The Crotchet, or Quarter-note. r I* The Quaver, or Eighth note. £ fe The Semiquaver, or Sixteenth note. £ 5 ^ e Demisemiquaver, or Thirty-second note. The proportional names shew the relative values that each bears to the whole note and to each other. 52. The semibreve may be described in form as a round white note ; the minim as a white note with a stem ; the crotchet as a black note with a stem : the quaver, semiquaver, and demisemi- quaver as a crotchet with one, two, and three hooks respectively. The stems of notes may be turned up or down according to circum- stances. "When the head of the note is below the middle line of the staff the stem is turned up on the right hand side of it, and when the head of the note is above the middle line the stem is turned down on the left hand side of it. 53. Occasionally a note is still used that is twice the length of the semibreve, written thus ||o]|, called a Breve from its original use in ancient music, when it was a short note. 54. Still rarer than the last a note is used of half the length of the demisemiquaver, having four hooks, thus k 5 and called a 8emidemisemiquaver. 12 TEXT BOOK OF MUSICAL ELEMENTS. 55. When notes having hooks occur in succession they are frequently grouped together by bands which take the place of hooks. Notes of equal value may be so grouped, thus Fig. 15. m : m . or of different values thus Fig. 16. 56. Any single note is of the proportionate value of one half the note of the next higher in value, as seen by the proportional names of the notes in § 51. But other proportionate values have to be provided for. This is mostly accomplished by dots. A dot placed after a note adds one half to the original value of it. Thus a dotted minim ^ . is equal to three-fourths of the semibreve, or to three orotchets ; a dotted crotchet J . is equal to three-fourths of a minim, or to three quavers, and so on. The dot is placed close to the note to which it belongs. If the note is on a line the dot is placed in the space above unless the next note is on a lower degree of the staff, when the dot may be placed in the space below. See Fig. 35, p. 19. 57. The value of a note may be further increased by the addition of a second dot. The second dot adds half the value of the first, so that the two together add three-fourths to the original value of the note. Thus a minim followed by two dots (^ . . is equal to the combined value of a minim, crotchet, and quaver (I ! r), or to seven quavers ; a crotchet followed by two dots J . . is equal to a crotchet, quaver, and semiquaver ( I . R) combined, or to seven semiquavers, and so on. 58. The same duration values that are accomplished by adding dots after a note, as well as other proportionate values, can be effected by two or more notes joined together and made practically one by a Tie or Bind - — ^, used thus — Fig. 17. 59. As the sounds of music are in measured time and are represented by notes so the cessations of sound or silences in music are equally regular, and are represented by characters called Bests. NOTATION OF TIME. 13 Each note has its corresponding rest and is named after the note which it equals in length, as a semibreve rest or whole-note rest, minim rest, &c. The following shows the rest for each note, and the position each respectively occupies upon the staff. Kg. 18. d J J— 3 §^ 3=3= 60. It will be seen that there is very little difference between the semibreve and minim rests, but the longer rest depends from the line — usually the fourth line — and the shorter (minim) rest stands on the line — usually the third line. There is as little difference in the crotchet and quaver rests, but the crotchet rest turns its head to the right and the quaver rest turns its head to the left. 61. In consequence of the similarity of these crotchet and quaver rests a new form has been invented for the crotchet rest, which is now of almost universal use. It is made thus J 62. As the original value of a note is increased by adding dots the value of rests can be increased in like manner and in the same proportion. Thus |* • is equal to T T Except, however, in com- pound measures, to be presently described, the dotted rests ire little used. I 4 / CHAPTER V. AOOBNT AND MEASURE. 63. The elements of Tune thus far noticed are the variety in the sounds as regards the difference in pitch, and the variety as regards the duration of the sounds. Another element now to he noticed is the variety in the force or intensity (§ 6) of the sounds. 64. A sound that is more emphasised than its immediate neigh- hour is said to hear Accent. 65. The grouping of sounds as to their pitch may he the same in one melody as in another, and the duration value of the sounds may he the same in each, hut the tune will vary according to which of tho sounds are accented. Thus in the following group of sounds Pig. 19. 13 5 7 =\ 1 =^ Z I X accents may be placed on the first and succeeding odd numbered notes as marked, or accents may he placed thus Fig. 20. 1 3- on the second and succeeding even numbered notes, which gives quite a different tune from the other. 66. The regular recurrence of accented sounds is a primary element of the rhythm of music. 67. The order of the recurrence of the accented sounds deter- mines the division of the music into measures. 68. The principal accented sound is shewn by a line drawn before it across the staff This line is called a Bab. 69. The space between one bar and the next, or that which is contained between them is called a Measitre. 70. There are several kinds of measures, the variation between them consisting principally in the number of equal parts in which the measure is said' to be divisible, as two, three, or four, &c. These unit divisions of the measure are called Beats or Pulses. The ACCENT AND MEASURE. \a number of beats or pulses in a measure, in conjunction with tbe order of the recurrence of accent, produces various species of Time. 71. When the measure is divisible into two pulses the time is called Duple. In this there is but one accented pulse in the measure, viz., the first pulse as indicated by the bar. The examples in § 65 are both in Duple time, the accent on every other sound dividing the music into measures of two pulses or beats each, though in the one example the music begins with an accented pulse, and in the other with an unaccented pulse. The two examples would be thus barred ?ig. 21. i s *—3r Fig. 22. m *=?- * 72. In the first of these examples the first measure is complete. In all cases in which the music begins with a complete measure the first bar comes at the accent of the second measure— the bar that should mark the first accent is omitted, being understood. On the other hand, a bar is used at the end of the line when the measure is complete. A bar in this case can be considered as marking accent only in respect to the first note in the following line, where the bar is again omitted as in the cases in which the music commences with a complete measure. (See Kg. 30.) In the second example the first measure is incomplete ; it is only half a measure. In all cases in which the music begins with an incomplete measure the music or the main section of it will end with an incomplete measure, to balance the incompleteness of the first. 73. Two lines side by side, called a Double Bar, are used to mark the close of a musical composition, or for the close of a principal movement or division of it. See an example in Pig. 30. 74. In the examples in § 71 the crotchet is used as the unit of the measure, but any other note could be used for the unit of the measure, and the music would be practically the same. Thus the first example might be written in either of the two following ways — 16 TEXT BOOK OF MUSICAL ELEMENTS. Fig. 23. A- b=*=g ^-hs*-^: d cJ -&—" Fig. 24. i 1^=^ ?s==p: £^ 75. When the measure is divisible into three pulses the time is called Triple. In this, as in Duple time, there is but one accented pulse, the other two pulses being both unaccented. The National Anthem is written in this triple time. The first two measures, with the crotchet used for the unit, would stand thus Fig. 25. m -1 3=*: But the same music could be expressed with the minim or quaver, or any other note for the unit. Using the minim, the music would be thus written Fig. 26. i r-> r* P £ 76. When the measure is divisible into four pulses the time is called Quadruple or, Com to on. This measure is almost equivalent to the union of two duple measures. There are two accented pulses— the first, which may be called the primary accent, and the third, which may be called the secondary accent. The second and fourth pulses are unaccented. The following is an example of this measure with the minim, crotchet, and quaver severally used foi the unit Fig. 27. I 5=S= -*=— (= £E 4= ACCENT AND MEASURE. 17 Fig. 28. I T- W =e± s=^= Fig. 29. I W- » • =g 77. In the foregoing examples of the different measures it is seen that the measures within the same example are not all made up in the same way, but the value is the same in each measure. The value may be made up of rests as well as of notes. Bach pulse, too, may be subdivided by notes or rests of less value than the unit of the measure. In the following excerpt from an air by Dr. Boyce the value of four crotchets is in each measure made up in a different way. • Fig. 30. 2EQESE* xtw-r tg=m &=* V * ' * y - V 78. When a pulse is subdivided a secondary accent is produced. Thus if there be two notes within the pulse, as in the following example Fig. 31. I e there will be an accent on the first note of the divided pulse almost equal to the secondary accent of the quadruple measure. 79. All the measures just noticed are termed simple — as simple duple, simple triple, simple quadruple — when necessary to dis-' tinguish them from the forms which are next to be described. When the measures are simple the music is said to be in Simple Time. 18 TEXT BOOK OF MUSICAL ELEMENTS. 80. In the simple forms of the measures the subdivision of the pulses is usually by notes or rests of the value of halves, or quarters, or eighths of the pulse. 81. Another form of the measures is that in which each pulse or beat is subdivisible into three. The measures in this form denote Compound Time. 82. None of the notes used for the unit of simple measures admit of equal subdivision by three. To allow of such a sub- division the note representing the undivided pulse of a compound measure is always a dotted note. 83. The compound form of duple time has, therefore, in each measure two dotted notes, as two dotted crotchets or their equiva- lents, i.e., the value of a dotted crotchet, which may be made up by quavers, grouped when possible, or of a crotchet and a quaver ; or the measure may be expressed with two dotted minims or their equivalents in subdivisions of notes of less value, i.e., in crotchets or minims and crotchets. The following is an example of compound duple time with the dotted crotchet for the full pulse of the measure. Fig. 32. ''Over the water to Charlie," Jacobite Song. 84. The compound form of triple time has three dotted notes in each measure, as dotted crotchets or their equivalents in quavers, or crotchets and quavers; or the measure may be expressed by three dotted minims or their equivalents. The following is an example of compound triple time with the dotted crotchet for the full pulse of the measure. Fig. 33. I ►35*^33* jfcfce £±r*£ Th-h 6*-=*3* =P- 85. The compound form of quadruple or common time has four dotted notes in each measure, as dotted crotchets or their equivalents; or the measure may be expressed by four dotted minims or their equivalents. The following is an example of compound quadruple time with tfca iatfcd crotchet for the full pulse of the measure. ACCENT AND MEASURE. 19 Fig. 34. " Pastoral Symphony," Messiah. I *=£ 3RFF 1 4 ** * W=f i 86. In all these compound measures where the pulse is divided there is a secondary accent on the first note of the pulse as explained for the subdivision of the pulse in simple time in § 78. 87. Each of the triple divisions in these compound measures may be again subdivided. These lesser divisions are usually in equal halves, and the first half is often made the extension by that much of the previous note that divides the pulse into three. See the following example. Fig. 35. Old English Song. 88. In performance of music by a number of executants the principal divisions of the measures are marked by a conductor with a baton, who, as it is termed, "beats the time." That is, he marks the time at each beat or pulse. 89. The method of beating duple time is, down — up ; of triple time, down — left — up, or with some conductors, down — right— up; and of quadruple time down — left — right — up. 90. The beating is the same whether the form be simple or compound, unless — in the latter especially — the music moves slowly and the pulses are often and minutely divided, when it is customary to indicate the principal subdivisions of the pulses by smaller move- ments of the baton. The methods vary with the different kinds of time as well as with the different fancies of the conductor. JW CHAPTER VI. TIME SIGNATUKES. 91. The kind of measure and the kind and number of notes Mnployed in it are usually expressed at the commencement of a musical composition by a sign called a Time Signatuke. 92. The Time Signatures mostly consist of figures ■written in the form of fractions one above another. The lower figure has reference to the whole note or semibreve. The upper figure gives the number of notes in the measure of the kind represented by the lower figure. As in a semibreve there are two minims the numeral 2 represents a minim. Therefore \ means two minims in a measure. As in a semibreve there are four crotchets the numeral 4 repre- sents a crotchet. Therefore | means three crotchets in a measure. And so on. 93. . It has been seen that in a measure of duple time there are two principal divisions, that in a measure of triple time there are three principal divisions, and that in a measure of quadruple time there are four principal divisions. In the time signatures of these the upper figure is 2, 3, and 4 respectively. But the lower figure of the signature differs according to the kind of note used for the unit, as shewn in sections 74-76. 94.' The upper figure in a signature of compound time is a multiple by three of the upper figure of the corresponding simple time signature as (2 X 3 =) 6, (3 X 3 =) 9, and (4X3=) 12 respectively. The lower figure denotes, as before, the kind of note as regards proportional value to the semibreve, but instead of its representing, as in simple time, the pulse of the measure, it represents the note of the smaller (triple) divisions which usually occur within the pulse. Thus in \ a signature of simple triple time the 4 repre- sents the pulse or beat, but in §, a signature of compound duple time which contains the same quantity as the other, the lower figure 8 represents the notes by which the principal pulses or beats are (or supposed to be) -subdivided. TIME SIGNATURES. 31 95. Both' in simple time signatures and compound time signa- tures the lower figure represents what is technically called the unit of the measure. 96. In common or quadruple time the signature, instead of being expressed in figures, is often represented by a Q, 97. In simple duple time when the unit is a minim the signature is sometimes represented by a barred Q, thus (J) instead of by §. This is called Alia breve or Alia capella time. 98. Again, in common or quadruple time when the unit is a minim the signature is also occasionally represented by (ft especially in church music. This had some meaning in former times, when the breve was reckoned as the whole note, but to use (ft now for a quadruple measure instead of f is most confusing, and the practice is exceedingly reprehensible.* 99. The following is a table of the signatures in present usn. Fig. 36. Simple. Compound. e»i J J 4 czi . J. Pi 2 i i § 1 1 p 4 A A 8 A. «. § JV 6 ;> 16 A. 1* 4. 3 I 1 1 2 A A A IA. J. j. CD 3 1 1 i 9 | 1 i •S' 4 A A 4 8 M. M. ^. § > r» h A 1* h f» CO 8 m. m. m. 16 *.. ^. #. ° r 2 J J J J ¥ J. i id. A. ed. •d, c«| J J j J S J. I J. J. s 4 p> p» h i* 12 N 16 J. r» i* h c 8 m M 4 *\ *. *. 4. • The author agrees with the late Dr. Hullah, -who said it was greatly to be desired that all these characters were banished from the Time Table, and that the signatures were confined to numbers. 22 TEXT BOOK OF MUSICAL ELEMENTS. 100. The time signature is placed on the staff immediately after the clef, thus "2 f\ or immediately after the sign or signs that constitute the key signature (to be described in next chapter) thus jfc& z ¥==: or 'f j^t^" £&=: W— 8-— 101. The time signature is not repeated, but if in the course of the music the measure is changed it is indicated by a now time signature. 23 CHAPTER VII. THE MAJOB SCALES AND KEY SIGNATURES. 102. It has been seen in Chap. II, § 13 to 17, what is the construction of a major scale, and that the successive sounds thereof are not all equidistant. It has also been seen in Chap. IV that musical sounds are, notwithstanding, written upon a series of equidistant parallel lines and the spaces between them. It is obvious, then, that the staff cannot accurately represent the different distances of the sounds found in the scale ; the semitones between the third and fourth and between the seventh and eighth (§ 17) shew as much distance between them on the staff as the tones. 103. A similar want of correspond- ence in appearance with the actual difference of distance of one sound from another is observable in a piano- forte key-board (see fig. 37) where the white notes or digitals- are all equi- distant but the sound-distances between E and P and between B and C are but half the distances of the others. 104. The places of the smaller distances on the staff are, then, assigned by the alphabetical pitch names ; the semitones occur between E and P and between B and C ■D* ffl a o [T| , f n £ $ w ' 'J W E-t fn o 9 < ffl 1 W fc r^ .a> """*"" fc o- e "g 1 o —I 24 TEXT BOOK OF MUSICAL ELEMENTS, 105. If any C be taken for the first of a scale it will be found that the tones and semitones occur in the order named in § 17 that form a major scale. Such a scale would be called, after the pitch note upon which it is raised, the scale of 0. This scale is also called the Standard Scale. 106. Other major scales are formed, not only upon each of the pitch notes represented by the other six letters of the alphabet, but also upon artificial alterations of these notes. 107. Other semitones are created between the tones of the standard scale by raising the lower sound of two that are a tone apart, or by lowering the upper sound of the two. 108. To raise a sound, as F, by a semitone, this character J, called a sharp, is used before the note thus fell and the note is then called F sharp, or sharpened F. < 109. To lower a sound, as B, by a semitone, this character 1>, called a flat, is used before the note thus 2 ~}>~m and the note is then called B flat? or flattened B. *T 1 10. It has been seen in § 18 that the major scale is made up of two tetrachords each of which is crowned by a semitone. If a scale be raised on G- it will be seen that the first or lower tetrachord corresponds to the second or upper tetrachord of C $ Fig. 38. | Scale founded on G. =^=^==^ TZr a & r^ _ | CS <§S -3 c «l^ cs ^i 1 CO "<^ •a o CO 28 TEXT BOOK OF MUSIOAL ELEMENTS. signature alternately a fourth below and a fifth above up to the fourth sharp, -when the next is again a fourth below the previous one instead of a fifth above. 116. The last written sharp of a signature is always the seventh or leading-note of the scale, so that the next note above of the alphabetical series will give the pitch note of the scale represented. 117. Another series of scales is formed by taking the lower tetrachord of the standard scale as the upper of a new scale of F, and proceeding downwards, thus Fig.j42. | Sca le of 0. | Scale formed oa F, I Here it will be seen that in the lower part of the scale being formed the sounds do not produce a tetrachord. The proper order of tones and semitones is obtained by lowering the B by a \>, which gives a semitone for the tetrachord and leaves a whole tone between the two tetrachords (§ 18). Fig. 43. ZS2: i =zfe 118. The lower tetrachord of this scale of F would in its turn form the upper tetrachord of a scale of BP, and a series of scales with flats could be formed in like manner; each new scale standing in the relation of a fourth above the previous one, or what is practically the same thing, a fifth below, and each requiring an additional flat for the lower tetrachord, as seen in the table of Fig. 44, on previous page. 119. All but one of the scales with flats are seen to be formed upon notes that are in the first instance lowered by a flat, and illustrate what was said in § 106. 120. "When music is written in any of the foregoing scales, the flats, as in the scales with sharps, are placed altogether on the staff after the clef, as a key signature, and they affect all the notes of the same alphabetical name throughout the music THE MAJOR SCALE AND KEY SIGNATUSES. 29 121. The following are the signatures in the treble staff of the several keys with flats. Fig. 45. F Bt» Ei> Ai> ^m pto p^ ^ fog^fc n GH7 A Of 122. The alphabetical order of the flats in the scales is, as in the signatures with sharps, the same as the order of the scales themselves. Each flat is a fourth above the previous one, but for the sake of symmetry the flats are on the treble and bass staves placed in the signature alternately a fourth above and a fifth below. 123. In all the signatures with flats after F the last written flat but one is the pitch note of the scale, represented. 30 CHAPTER VIII. THE MINOR SCALES AND KEY SIGNATURES. 124. It was said in § 17 that there was more than one form of diatonic scale. Formerly there were many other forms than the one that has been already described, but the only other form now in use is that of which the following, having A for its first and final notes, forms the model. Fig. 46. $ IE21 Eg^== 4fc2_ This form is called the Altered Diatonic Minor Scale. 130. In descending melody the order of tones and semitones of the original minor scale is mostly maintained, thus — Kg. 49. i =Z2i 131. As this scale of A minor in its original form has no altered notes no sharps are required for a signature. The clef sign alone, as in the case of C major (§114) is sufficient. The sharps necessary to raise the seventh and sixth are introduced against those respective notes of the scale as they may be required in the course of the music. 132. The presence of the character necessary to raise the seventh of the minor scale, which is the note chiefly altered, is that by which a melody in the minor scale is most readily distinguished from one in the major scale. 133. The notes of this scale of A minor, in its original form, being all found in the major scale of C, the minor scale of A is said to be the relative minor of the major scale of C, and, per contra, the major scale of is said to be the relative major of the minor scale of A. 32 TEXT BOOK OF MUSICAL ELEMENTS. 134. The minor scale begins on the sixth of the relative major, and the major scale begins on the third of the relative minor. 135. As in the altered diatonic form of the minor scale (Fig. 48) the upper tetraohord is precisely the same as in the scale of A major (Pig. 40) the scale of A minor is also said to be related to that major scale as the Minok op the same Tonic. 136. Every major scale has its relative minor scale, similarly formed and subject to the same variations as the scale of A minor. 137. Each minor scale is called after the pitch of its first note, and may be said to be related not only to the major scale of the third above, but (as shewn in § 135) to the major scale of the same pitch note as its first or tonic. 138. The relative minor and major scales being formed mainly of the same notes there is no difference in the signatures. 139. All the signatures of the major scales given in Eig. 41 and Pig. 45, represent also the signatures of the relative minor scales, thus — Fig. 50. Signatures of Minor scales with Sharps. H^ te nil I y dfc£ Oft m- Gtf x£ D# tJ 3fe 2fcfc D Signatures of Minor scales with Flats. Q F fc£ m pm pm pk= •J ' n y f=4=? 147. Occasionally — in major keys with flats especially — a note is required to be lowered from its normal pitch a whole tone. This is effected by placing two flats before the note, thus — Kg. 56. I »H? L rJ — & :fc* -r^r there being no separate character in use for a double flat. 148. All the foregoing characters, sharps, flats, and naturals, when used in the course of the music are known by the generic name of Accidentals. 149. The double sharp and dou ble flat can only be used as accidentals. They are never found in a signature. ACCIDENTALS AND CHROMATIC SCALE. 35 150. An accidental affects all the notes within the measure of the same alphabetical name as that against which it is was first used, unless it be contradioted by another accidental to restore the note according to the signature. 151. If the last note in a measure is an altered note and the first note of the next measure is of the same alphabetic name, the accidental in the previous measure affects also the note or notes in this succeeding measure. But the practice is to repeat the acci- dental in this case for greater clearness. 152. Although an accidental does not, except in the case just stated, extend its effect beyond the -measure in which it occurs, if is customary, if the note that has been altered occurs in the following measure, to restore the sign of the note according to the signature, thus — Kg. 57. 5 '*=£=% 3fc * 153. The use of the restoring sign in each of these cases is as a caution. Hence Catjtionaet Accidental is the term applied to the sign in such circumstances. The use of the cautionary acci- dental in any other part than that in which the first accidental appeared is generally productive of confusion. 154. To restore a note that was originally sharp (in the signature) and has been made doubly sharp (by x) it is customary to use a t] and ft, thus — Kg. 58. 1^ 3t X T- 155. To restore a note that was originally flat and has been made doubly flat, it is customary to use a q and t>, thus — Kg. 59. 1 Mp Efe $=*= 665t X % ± *: 156. The use of the Q in both the foregoing cases is by many musicians held to be, and it undoubtedly is, unnecessary. There are but few, however, that at present have the courage to omit the t| in such circumstances. 36 TEXT BOOK OF MUSICAL ELEMENTS. 157. When a note that is flat in the signature needs to be' raised to a sharp of the same name no previous b is required before the $. See the # D in the third measure of the following — Ex. 60. i * P^ From Gounod's Mora et Vita. -I- *P ** ^ J- 1 * F± ■t- 158. And when a note that is sharp in the signature needs to be lowered to a flat of the same name no previous t] is required before the !?. See the > D and t> in the following — I Fig. 61. From Mackenzie's Jason. ^ £— i l l y i ^ Spc £ 159. Another use of the natural remains to be noticed. This is when for a new movement in the so-called open key of C major or of A minor the original or previous signature has been one having flats or sharps. In such a case naturals will be necessary to counteract the signs of the former signature, thus — Fig. 62. i From Gounod's Mora et Vita. S^S its ^\i"£i I 9 I lu - ce at @& Ky - ri - e ! ft I* s s ££: Efc =*=t W^ ^-/fz irV 160. When a new signature is required that expresses a change from a signature with sharps to one with flats, or, vice versa, from one with flats to one with sharps, or a change is required to a signature with a less number of sharps or a less number of flats respectively than that of the previous signature, it is still the custom with some authors and publishers to replace the sharps or flats not wanted with naturals, thus — ACCIDENTALS AND OSEOMATTO SCALE. 87 Mg. 63. fggi fe^fflfc j^gig pm. The naturals are not, however, necessary, and certainly do not increase the perspicuity of the new signature. 161 . Between any two sounds that are a tone apart a semitone can be introduced as shewn in § 107. A succession of sounds embracing an octave and proceeding by semitones is termed a Chromatic Scale. 162. The chromatic scale has no separate use like the major and minor scales, but is simply an ornamentation, or, as its name implies, a coloured form of an ordinary scale. 163. The chromatic scale has its interposed semitones variously written. But the modern form, which is considered the most theoretically correct, is as follows — , Kg. 64. I \r-> jg j | -T5- o cy c p ^st-V-S ^ k* Po rj A* 1 in which every new semitone is the flattened note of the one above, except that lying between the fourth and fifth notes of the original scale, which is universally written as the sharpened note of the one below. This form of the scale is convenient for explaining harmonies that comprise these altered notes, and the form is called by some writers the Harmonic Chromatic Scale. 164. The chromatic scale is, however, in practice, often written in ascending with every introduced semitone as the sharpened note of the one below, and in descending with every introduced semitone (excepting that named in previous paragraph) as the flattened note of the one above, thus — Fig. 65. ^saafe* ^ 3*^*^** w» #Ptt=2^» £2 ^- This is called the Arbitrary Chromatic Scale. 38 CHAPTER X. ENHARMONIC CHANGE. 165. It has been seen that a double sharp raises a sound by a whole tone and a double fiat lowers a sound by a whole tone. So that, practically, a note thus altered that originally has its next scale note a whole tone above or below, as the case may be, is raised or lowered to the pitch of that next scale note above or below. Thus \> b A is equal to G, and x E is equal to G. Where the semi- tones occur in the standard scale a single sharp or flat raises or lowers the sound to the pitch of the next note in the scale. Thus, (E equals F, and tJC equals B. 166. An alteration of the names of notes that are identical in pitch, such as just described, is termed an Enharmonic Change. 167. Every note in pitch is capable of a triple representation, except that lying between G and A, which can only be represented in two forms, as J G or \> A. Thus E can be represented as x D or 9 E, G as xE or \>\> A, and so on. 168. By comparing the scales with sharps and the scales with flats (Eigs. 40 and 44) it will be seen that the three with the greatest number of sharps are identical with the three with the greatest number of flats; the scale of B is identical with the scale of C!?, &c. In these scales which are identical the one is the enharmonic of the other. 169. When in a key with a number of flats in the signature a brief change takes place to another key that would require several double flats to express it, the composer usually writes the notes in a key with sharps that is the enharmonic equivalent to the one with flats. Thus in Eig. 60, of § 157, the last two measures are written in the notation of the key of E, as the equivalent of what is really the key of F7. 170. Similarly in a key with a number of sharps in the signa- ture a change to another key that would require a number of double sharps to express it is written in a key with flats of the enharmonic equivalent. Thus in the following passage — ENHARMONIC CHANGE. 39 Fig. 66. From the Duet and Chorus "Hero of Hellas," in Mackenzie' b Jason. « » * J g £=* *jf S S^^^ll 1 afi n JbJ i n ^frbJr.-fii i r* pt ab 5 $i£ 1 p^ r > , c ^ i ^r tW: the notation of A!? is used from the second measure onwards as the enharmonic of the key of G#. 171. Sometimes a passage is simultaneously expressed in two differently written keys, the one the enharmonic of the other, in different parts of the score. This is usual when it is convenient to write in the notation of one key for the voices and in that of the other for the instruments. In the following passage the voice parts are in the notation of the key of BM?, and the instrumental part in the notation of the key of A. Fig. 67. From Gounod's Mors et Vita. 40 CHAPTER XI. TIME MODIFICATIONS. 172. Silence for a whole measure in any kind of time but \ is expressed by a semibreve rest. Fig. 68. pM ^m p^ j^ 173. In the \ time the silence of the whole measure is expressed by a rest corresponding to the breve (§ 53) thus 2 E: I£2E 174. In the separate parts for voices or instruments where a uumber of measures' silence is required it is expressed either by writing the number of measures over the semibreve rest, thus Pig. 69. IE i m or the quantity is made out in rests to the value, in which not only the breve rest is utilized, counting as two measures, but an extended form of it, as used in old music for the next higher note in value, called the Long, thus which counts as four measures. These are combined as follows Pig. 70. 3 ijb^l fe=j i 175. It is often optional to write a continuous sound in the way shewn in § 57, with dots, or as shewn in § 58, with a tie. But if a TIME M0DJFWATI0N8. 41 continuous sound extends over two measures it must be written with tied notes, thus — Pig. 71. _ m *=? 1 ^3- -&- * though formerly such passages were written thus — Fig. 72. .f^EgE $ =p=P= :f ± I 176. In the foregoing examples, and in these — Fig. 73. I =1= ^ & -4- T SFS=5"= ^= m which the sound commenced on the unaccented division is continued over the accented division, is illustrated the effect called Syncopation. The natural accent is thus anticipated, and the commencement of the sound receives a stress equal to an ordinary accent. 177. While one sound begun on an unaccented pulse and extending over an accented pulse may be expressed, as in these cases of syncopation, by one note, the silence for such portions of the measure must in all cases be expressed by separate rests for each pulse division. Thus silence for that portion of the measure corresponding to the second note in the two previous examples would be written thus Fig. 74. not thus- SE ^£ fj^EE^E^ I S E=F 42 TEXT BOOK OF MUSICAL ELEMENTS. 178. In compound time a sound lasting the whole measure may be written in one note, thus t Fig. 75. ±1 instead But if a sound extends from one division over a portion only of a second division it must be expressed by tied notes of the kind used for the separate divisions, thus Fig. 76. I -fi- sa 3 -g-3-3- not I £H^ 5 p=^=^= 179. A pulse in simple time is sometimes divided as in compound time, into three. A figure 3 is placed over the notes comprised within the pulse, and the group is called a Triplet. Fig. 77. 3 ^3 5 -r- m. i 3E -P--6 180. When several successive pulses are in triplets the effect is that of compound time. In these cases often the first triplet only is marked with the 3, and the rest are understood, especially when the notes are quavers or notes of less value, and are grouped in threes or sixes. 181. A portion of a pulse may be divided into three Fig. 78. or two pulses may be equally divided into three Fig. 79. IsT-^. s ^LC_r. JtJtJ^ 182. A pulse in compound time is also sometimes divided as in simple time by two, when a figure 2 is placed over the notes com- prised within the pulse, and the group is called a Couplet. TIME MODIFICATIONS. 43 Fig. 80. !S*:ft From Mackenzie's Jason :*=£: «E& St ± l=t i=t 183. Other occasional alterations from the prevailing time occur especially in instrumental music, in variously grouped notes, the groups being not only of divisions according to compound or according to simple time, but also of an odd number of notes. In all these cases the figure corresponding to the numeral expressing the number of notes to be performed in an accommodated time within the pulse or portion of a pulse, is placed over or under the heads of the notes, and when the notes are quavers, or notes of less value, they are grouped by bands, as in the following examples. Fig. 81. Beethoven. s^bT Fig. 82 Mackenzie. 184. The notes in the last examples are not only grouped by bands but also by a curve, which character is called a Slur. The slur is not absolutely necessary for the grouping, but is generally used when there are a number of notes, and it is often used in the ordinary triplet group when the notes are crotchets or minims. 185. The principal use of the slur is to connect any two or more different sounds that are to be sung to one syllable, or that if per- formed by an instrument are to be played smoothly, with as little break between the notes as possible. In a passage with the notes slurred in couples thus Eig. 83. I cftJ S 44 TEXT BOOK OF MUSICAL ELEMENTS. the second of the two notes that are slurred is played slightly shorter than the first. When a whole passage is to be performed in this smooth connected style the word Legato is used instead of the slurs. 186. Disconnected sounds are marked by a dash i placed over » ! t I the notes, thus r * T T This is called Staccato. Thus marked the sounds are to be performed in a very sharp and detached style. • • • • Dots are used instead of dashes, thus ,• .• P .• when the notes are to be less detached. This is called Semi-staccato. When a whole passage of detached sounds occurs the word Staccato or Semi- staccato is written instead of the dashes or dots oyer each note. 187. Another variety of staccato is used in instrumental music, in which the sounds are very slightly detached. This is shewn by dot s ov er or u nder the notes, grouped by a slur, thus • • • • I i j i .• P ,* ,• • * * • In instruments of the violin class, where such passages mostly occur, the grouped notes are taken with one stroke of the bow. 1S8. An efiect the opposite of the staccato is sometimes required in which each note is to be sustained to its full time, and this sign - or this, which indicates an accent in addition, v is placed over the note, thus ^ or ^ When a whole passage is to be performed with each note of it sustained to its full value, the term Sostenuto is written instead of the sign - over each note. 189. A sound or a silence is arbitrarily prolonged to an indefinite time by placing over the note or rest this sign «\ , called a Pause, thus 2 ^ r j ' F j? \. C*~ ' f* Occasionally the pause is placed over a bar or even between two notes when there is no rest to initial the silence that is required. When the pause is to be very long the word lunga is written over it, or lunga pausa. 190. To indicate exactly the speed at which » musical com- position, or any main division or movement of it, is to be performed, reference is made at the beginning to an instrument called a Metronome, first invented by Malzel. This is an instrument on the principle of a clock, having a swinging pendulum with a movable regulator, or simply a swinging pendulum with an adjustable weight to shorten or lengthen the pendulum, and so quicken oi TIME MODIFICATIONS. 45 Blacken the rate of its swing. The pendulum is marked in various divisions by figures, and moves or swings as many times in a minute as the regulator is set to. Thus if set at 60 it will swing once every second of time. If the music is to move at the rate of a second of time for the pulse it would be marked thus M M. J = 60. The M M stands for Malzel's Metronome, but these letters are often omitted. The pulse in compound time being represented by a dotted note the metronome rate is expressed thus g£ . = 60, or J • = 60, unless a slow rate is required, when the rate for the note representing the triplet subdivision of the pulse would be given as the crotchet or quaver in the cases just instanced. The higher the figure at which the pendulum is set the quicker the rate, and the lower the figure the slower the rate. It will be found that ^ = 80 represents a pulse to three -quarters of a second of time, and J = 40 a pulse to a second and a half of time. 191. Before the invention of the metronome the pace could only be indicated in a geneial way by words such as those given in the list in § 221. These words indicate the style as much as the pace of the music, and an entire composition or the divisions of long com- positions, as the sonata and symphony, into separate movements are often designated by such terms as Andante, Adagio, Largo, &c. 192. If a movement is to be repeated dots are placed before the double bar thus i : zz: or ^ : zz which shew that the music is to be repeated from the beginning, or from a previous double bar if one has occurred. 193. To mark more clearly the place from which the repetition begins dots are often placed on tho right of the previous double or bar thus z 194. Repetitions are also expressed by the words D.O. or Da Capo, which means repeat from the beginning; or by D.S., Dal Segno, which means repeat from the sign ; the sign being written thus § . Sometimes the repetition, though practically from the beginning, is not from the first note. In this case the § marks the exact place and the words Da Capo al Segno are used for the repetition. After a repeat the conclusion is shewn by the word Fine, or by a pause over the double bar fj. 195. Sometimes in the repetition of a movement the conclusion varies somewhat, in time or in tune, or in both, from the first TEXT BOOK OF MUSICAL ELEMENTS. version of the movement. In such a case the altered conclusion is written after the other, and the two phrases are bracketed and marked 1st time and 2nd time, thus Kg. 84. I 1st time. 32Z 2nd time. 77" VH—tf The phrase marked 1st time is omitted in the repetition and that marked 2nd time is substituted. 196. When a short passage is to be repeated it is sometimes marked by writing the word it's (twice) over the notes embraced in the passage, thus Kg- 85. £7 - i^g^ 3 -I h r - > 197. The repetition of a group of notes is indicated by this sign ■*• or ^5 according as the group consists of quavers or semiquavers, as at a b, and in manuscript writing chordal groups such as at c are often abbreviated as at d. Kg. 86. b. :& 3- 2 :3==? I 3E Sz -*-*- 5^55^ n c - . „ d - p. i ii i ' ii -&■ — r 2 S=3=q=^-4-4-t* PVP: g^iagfe i l J |j \-^-\- W W W -W-A 201. Very rapid iteration of sounds or alternations of sounds are indicated in a similar manner by uniting the stems of the notes with two or three bands, and writing the word tremolo or tremolando over the passage. 48 CHAPTER XII. TUNE MODIFICATIONS. 202. To save the use of a number of leger lines above the treble staff, and to facilitate reading, a passage is often written within the ordinary range of the stave an octave lower than it is intended to be played, and 8va with dashes or dots placed over the passage, thus Fig. 90. 8va I 3 S $ 203. Con 8va or 8ves placed over a passage means that the notes as written are to be played with octaves above. 204. Ottawa bassa or 8va bassa placed under a passage on the bass staff means that it is to be played an octave lower than written. Occasionally an 8 is written under a single note in the bass staff which means that the note an octave below is ¥ also to be played with the written note. 205. Loco (in place) is a term used after an octave passage written in the convenient forms just described, to shew more clearly where the pitch of the notes as written is resumed. 206. Combinations of sounds instead of being played absolutely together are sometimes played successively, as on a harp. This TUNE MODIFICATIONS. +9 effect is called and expressed by writing the word arpeggio or arpeggiando over the several combinations, or by these signs \ I placed at the left hand side of the notes, thus — Fig. 91. 1= or Ie3e is played thus Sometimes the arpeggio notes are written in this last fashion instead of in the abbreviated form with the arpeggio sign. 207. The notes written in small type in the last example are also occasionally used without ties, the principalnotesbeing restruck after the arpeggio. Used in this way the small notes come under the general term of Orace Notes, of which there are several kinds that may be now described. 208. The Appoggiatura is a note that is placed before another as an auxiliary to a principal note, and is usually a degree above or below the principal note. It is written smaller than the principal note from which it takes its time. The appoggiatura is sometimes long and sometimes short. If long it usually takes half the time of the principal note, unless this is a dotted note, when it usually takes two-thirds, thus — Kg. 92. Written ggl g^ fe g^= y Played. iiip iHi ilgs ijm But in modern music this long form of the appoggiatura is seldom used, the notes being written in full. The short form of the appoggiatura is written in a note of shorter value than the half of the principal note, and takes just the time represented by the value, thus — 80 TEXT BOOK OF MUSICAL ELEMENTS. Fig. 93. Written. Played. $^& 209. The Acciaccatura is a shorter form of the appoggiatura than the last, taking the smallest possible time from the principal note and is written as a quaver with a dash through the stem, thus — Fig. 94. I -kVeJ- ^ 210. The Beat is a term applied to a short appoggiatura or to an acciaccatura that is a semitone below the principal note as — Fig. 95. 7 3?E Btl 211. Two or three notes written in small characters sometimes precede a principal note, termed by some writers a compound appoggiatura. Thus — Fig. 96. t Jip: *£•£: £ The time for these extra notes is usually taken from the pulse or division that precedes the principal note. 212. The Turn is an ornament that embraces an upper auxiliary note to a principal note and a lower auxiliary note. There are two distinct forms of the Turn. In the Direct Turn, which has this TUNE MODIFICATIONS. 51 sign ~ written over the note, the upper auxiliary note comes first, the principal note next, then the lower auxiliary note, followed by the principal note again. Written thus : played 213. In the Inverted Turn which has this sign £ written over the note, the lower auxiliary note comes first, the principal note next, then the upper auxiliary note, followed by the principal note again. Written thus il 5 played 214. The time of the ornament varies with the length of the principal note and the rate of the movement. The ornament is sometimes at the beginning of the principal note, as in the foregoing examples, and sometimes at the end, as in the examples of Pig. 98, and sometimes, as in the following case of a dotted note, midway between the beginning and the end. In the turn over a dotted note in simple time the last note of the ornament is usually made the length of the dot, thus — Fig. 97. Written i 5 Played s 215. Usually the upper auxiliary note of the turn is a tone above the principal note and the lower auxiliary note a semitone below the principal note, unless the upper note is in the scale only a, semitone above the principal note, when the lower auxiliary is then commonly left a whole tone below. Sometimes the exact nature of the ornament is indicated by placing an accidental above or below the turn. Pig. 98. Written. i -7^- Played. tdrjrj M 5 #p^£ ■f=m-^ 5 3= tt 52 TEXT BOOK OF MUSICAL ELEMENTS. 216. The Shake or Trill, written tr, is the rapid alternation of a (principal) note with the note above. Usually the principal note comes first, and before the last recurrence of the principal note a note below is taken, making a turn for the finish, thus — Played. Fig. 99. Written. i 3= If the shake is to be made with any other note above the principal note than that indicated by a signature, a Jf, b, or t] is placed above the tr, as in the.case of the alteration mentioned for the turn. 217. The Mordent, written ■w, is like a single shake or trill, the principal note and the note above being taken very rapidly, followed by the principal note again, which occupies the greater portion of the time, written thus I played 218. In the Inverted Mordent, written ty, the note alternated with the principal note is a note below it, written thus played I s & 53 CHAPTER XIII. EXPRESSION. 219. The modifications of time and tune described in the previous chapters serve more or less to give in particular instances some expression to the music. But Expression in the full sense of the term comprehends not only many other modifications of time and tune of a general character that are effected by the use of technical terms, but also modifications of the intensity of sounds. By all these means light and shade are imparted to the musical picture that promote characteristic effects. 220. Different degrees of intensity are indicated by the following words from the Italian language or their abbreviations or signs — ^-Piano or p Soft. —Forte or / Loud. Mezzoforte or m/ Half loud. Mezzopiano or mp Half soft. —Fortissimo or ff Very loud. ^■Pianissimo or pp Very soft. --Crescendo, ores, or -=^^T Increasing. -Decrescendo, decres., ( ) . .Decreasing. •Diminuendo, dim., \ — — '" ] .Diminishing. Sforzando, 8/, > or /\ Eorcing. Forzato, fz. j i Forced. Sforzato, sf 1 ( Accented. Einforzando, rf, or Binf. Eeinf orcing. Morendo Dying away. Perdendosi Losing itself. -Dolce Soft. Forte piano oifp Loud, then soft. 54 TEXT BOOK OF MUSICAL ELEMENTS. 221. Different degrees of movement or pace are indicated by the following words from the Italian language. Those first named mostly apply to the whole composition, as said in § 191, but some- times they affect only a short phrase or section of the music In the progressive order that represents the slowest speed first, the terms are as follows — — Grave Grave, heavy. Adagissimo . . . .Very leisurely, slower than Adagio. ^Adagio Slow, leisurely. —Largo Large, grand, broad, slow. —Lento Slow. —Larghetto Diminutive of Largo, not so slow as Largo. —Andante Going at a moderate pace. Andantino Diminutive of Andante, going gently, not so slow as Andante. Moderato At a moderate pace. —Allegro Merry, lively. —Allegretto Bather merry, not so fast as Allegro. -Presto Quick. -^Prestissimo Very quick. 222. Other terms modifying or affecting the rate of movement are as follows : — Increasing the speed. — Accelerando Accelerated. Stringendo Pressing onwards. Decreasing the speed. Allargando Enlarging. Calando Decreasing. Lentando With increased slowness. — liallentando Becoming slower. Bitenuto, riten., rit Holding back the time. — Bitardando, ritard, rit. . .Betarding the time. Slentando A gradual diminution of the time. Afempo \ All used after some alteration of the Tempo primo or Tempo , time has been made, to show a return Come prima ) tothefirstorpreviousrateofmovement. A piacere )., , ,f 7 ., .. I At pleasure. Ad libitum ) L'istesso tempo In the same time ; i.e., the beats to be the same, whatever be the forms of the notes. EXPRESSION. 55 Tempo comodo . ... , ... In convenient time. Tempo giusto In exact time. Tempo ordinario In ordinary time. 223! The following are some of the terms used to indicate manner and style, &c. Affettuoso, or Affetuosamente . . Affectionately, or with feeling. Agilita With lightness. Agitato Agitated. Amoroso Lovingly. Animato, Animando Animated, animating. Appassionato, Con passione . . Passionately, with passion. Assai Sufficiently, very. Ben Well, e.g., Ben marcato. BriUante Brilliant. Cantabile In a singing style. Col canto With the singing part. Colla 'parte With the solo part. Colla voce With the voice part. Commodo Easy, without haste. Con aniina With soul. Con brio With vigour, with- spirit and full tone. Con energia With energy. Con espressione With expression. Conforza With force. Con fuoco With fire. Con moto Withmotion.withanimatedmovement. Conspirito With spirit. Con tenerezza With tenderness. Dolce With softness and delicacy. Dolente In a plaintive style. Espressivo, . Expressive, with expression. Qrazioso, con grazia Graceful, with grace. ■Legato Bound, in a smooth style. Leggiero Light. Ma But ; as Ma non rail. Maestoso, Con maesta Majestic, with majesty. Marcato Marked, marking. Mesto, Con dolore Sadly. Meno Less, as menc vivo, less lively. Mezzo Half. 56 TEXT BOOK OF MUSICAL ELEMENTS. Motto , Much, very.. Non tanto Not so much. Non troppo Not too much. Parlante Li a style of recitation. Pesante Heavy. Piu More; as Piu animato, more animated. Poco Little. — Poco a poco By degrees. Pomposo Pompous. Quasi Almost, as though. Becitativo Recitative, i.e., the delivery of the words as in a recitation, to musical phrases, with great freedom as to time. Risoluto Resolute. Scherzemdo Playing (playful). Segue It follows. Sempre Always ; as sempre pp. Smorzando Fading away. Soave Delicately, gently. ■ — Sostenuto Sustained. Tenuto • Held, sustained. Tranquillo Tranquil. — Vivace Lively, brisk. Vivo Lively. Volti Turn. Volti subito or v. s Turn quickly. 57 CHAPTER XIV. MISCELLANEOUS. Concerning Voices, Scores, and Points op Writing. 224. Music written for a single voice or instrument is termed a Solo, for two voices or instruments a Duo or Duet, for three voices or instruments a Trio, for four voices or instruments a Quartet, for five a Quintet, for six a Sestet, for seven a Septet, for eight an Ottetto, Music written for a mass of voices is called Choral Music. 225. In music that is written to be performed, some portions by- single voices to a part and some portions by a number of voices to a part, the words Soli (plural of Solo) and Ghorus are respectively employed. The word Tutti is also employed instead of Chorus. Sometimes there are portions for performance by a select number of voices to a part, when the word Semi-chorus is used. 226. There are in full anthems portions corresponding to the semi-chorus in other compositions, that in cathedrals and churches are alternately taken by the two divisions of the choir that sit respectively on the side of the dean and the cantor. The words Decani and Cantoris are used in this case for the semi-chorus sections, and the word Full is used when the two divisions of the choir unite. 227. In vocal music the part for the higher voices of women and children is called the Soprano or Treble, that for the lower voices of women and children the Contralto, that for the higher voices of men the Tenor, and that for the lower voices of men the Bass. 228. Bach of these parts is sometimes divided into first and second, as First and Second Soprano, First and Second Tenor, &c. M TEXT BOOK OF MUSICAL ELEMENTS. 229. The ordinary compass of the various voices for choral music is as follows — Kg. 100. 5 £ Eg e? Bass. Tenor. Contralto. Soprano. The extreme notes are used sparingly. But in Soli music these are often exceeded. 230. Music written for performance by men and women is said to be for mixed voices, that for performance by men only, or by women only for equal voices. 231. The group of staves which represent the whole of the parts of a composition is called a /Score. According to the manner in which the different parts are represented the term is qualified as follows. 232. A Full score gives the parts for each instrument and each vocal part, if any, mostly on separate staves. 233. A Vocal score gives each voice part on a separate staff. The treble staff is used not only for the soprano part but for the contralto. The treble staff is also fast superseding the tenor staff for the tenor part, notwithstanding that the treble staff represents the pitch at an octave higher than the natural pitch of the tenor voice. But this difference in the octave is not found to be of any practical inconvenience to the singer. 234. A Short score is a vocal score condensed into two staves, the soprano and contralto parts being written on the treble staff, and the tenor and bass parts on the bass staff. The stems of the notes for the higher parts in each staff, viz., of the soprano and tenor, are turned up, and those of the notes for the lower parts in each staff, viz., of the contralto and bass, are turned down. Fig. 62 is a specimen of short score. 235. A Pianoforte score condenses also the whole of the music into two staves, all the notes to be played by the right hand being written as one part on the treble staff, and all the notes to be played by the left hand as one part on the bass staff. In this score all the notes in each staff have the stems of the note in one direction. MISCELLANEOUS. 59 up or down as may be convenient, except when some of the notes are longer or shorter than the others, when the stems are turned in opposite directions as in short score. The following is a specimen of pianoforte score — Fig. 101. Meudelssojin. d S^ .1 !l..J. 3-H^th rr-R- ^^^-^ 1 fN^ ' m • * •■^f — 3 i i <■ f- (i»Vti n W W ' PJ- », h * M ' u 1* • I ■ -l 1* L 1* ^— If ' w I r ' i 1 ^— II ' 1 ' i a* 5^^^^"^ i ^ ' 1 -^ * Bl H « *3£ ^^f ^ — »- 3=?- -Mf- qP=?c =#^ r 236. A score for the Harmoniwm or for Organ without pedals is in the same form as a pianoforte score. The vocal score usually includes a score for one of these instruments. 237. All the staves forming a score are grouped on the left hand side by a brace or accolade. The score for the accompanying instrument, piano, harmonium, or organ, usually has a brace to itself. See examples of each in Fig. 67. The bars in the score for the instrument are often, as in most instrumental scores, carried through the score from one staff to another. 238. All notes that are to be sounded simultaneously are placed exactly over each other. See the example of Fig. 101, where in the last two measures longer notes are opposed to shorter ones and rests occur. 60 TEXT BOOK OF MUSICAL ELEMENTS. 239. When in short score two parts are in unison it is shewn by the stems being turned up on the right hand side for the upper part and down on the left hand side for the lower part. In the case of a semibreve a double note is written, one interlacing the other, as in the following example, or two notes are placed side by side as close as possible. Pig. 102. ft* I i P 3= 3= ^=z 240. In a combination of notes that includes two next each other in the scale one of these is placed outside the others on the same side as the stem is turned, thus — Eig. 103. m &3 241. When in short score two parts, or in pianoforte score two melodies on one staff, come upon unison or upon notes next each other in the scale with notes of different value, the note of shorter value is placed first. See the B's in the third measure in the bass staff and the Q- and A in the fifth measure in the treble staff of the following. Fig. 104. From the "Amen Chorus" in Handel's Messiah. I -A MISCELLANEOUS, 61 242. When two parts come upon a unison and one is a crotchet and the other is any note of the quaver family, one head serves for the two notes. See the B's in the second measure and the A's in the third measure of the treble staff in the foregoing example. 243. A minim head also serves for the head of a quaver in another part in such a figure of accompaniment as the following — Fig. 105. S^ I 3=±L £ * 244. In pianoforte score the right hand part when ranging much below the treble staff is often written, to save leger lines, on the bass staff with the stems of the notes turned up, or partly on one staff, partly on the other, as in the following example. Fig. 106. Mendelssohn. % CT £ i&a =] u EEIE^ TOfTSU *JU* $Hfc£ -*i — =i — p- i i- t The absence of rests in the treble stafE helps to draw attention to the fact that the right hand part is to be found in the bass staff. 245. Similarly when the left hand part ranges much above the bass staff it is written on the treble staff with the stems of the notes turned down, thus— Fig. 107. h" ^ i fe jSE£ ft: jl i Jf-L 1*=P- =t m 62 TEXT BOOK OF MUSIOAL ELEMENTS. 246. Another method of expressing passages that overlap the range of the staff is to change the clef for the nonce, i.e. , to use the bass clef for the right hand part or the treble clef for the left hand part, as in the following example — Fig. 108, 3Eii 3TTT iP^SP^P^ m #-!= It may be noticed in these cases that there is no occasion to give the key signature with the altered clef. 247. The prevailing key signature is repeated at the beginning of each score, but the time signature is indicated only at the beginning or when the measure is changed. 248. When a change of time signature (§ 101) or of key signature (§ 160) is impending at the commencement of a line it is customary to give warning of it by giving the new signature at the end of the previous line, after a double bar. 249. A change of clef occurring at the commencement of a line is similarly indicated in advance at the end of the previous line. 250. At the end of a line or at the bottom of a page this sign WL, called a direct, is sometimes used to indicate the note that is following in the next line. 251. Transposition is a term that is used to express the exact reproduction of a passage at a higher or a lower pitch. The term is also used to express a change of a passage from one staff to another at the same pitch. 63 CHAPTER XV. INTERVALS. 252. The subject of intervals is a connecting link between melody and harmony (§ 11). Intervals have already been referred to, though not designated as such, when treating of successive sounds. But to obtain even a rudimentary knowledge of the rules that govern the art of combining sounds to make harmony it is necessary to have a clear understanding of all possible intervals. 253. The distance between any two sounds is called an Interval. 254. The scale consists of a series of intervals, but, as said in § 15, the distances between the sounds are not all equal. The distance between any one sound and its immediate neighbour is broadly termed a degree or step. 255. The differences between the larger and smaller steps of the Ecale have already (§15) been described as Tone and Semitone. The Tone and Semitone are also among intervals termed Seconds, two degrees being embraced. The larger interval or Tone, as D E. is called a major second, and the smaller or Semitone, as E P, a minor second. 256. The intervals of sounds a wider distance apart are named in a similar manner, according to the number of degrees embraced, counting the first and the last. Thus the sounds C E embrace three degrees, and the interval is called a Third ; the sounds OP ~2 embrace four degrees, and the interval is called a Fourth, and so on. 64 TEXT BOOK OF MUSICAL ELEMENTS. 257. There are as many different intervals within the scale as there are degrees. This is shewn by the following table, starting from the first of the scale of 0. Fig. 109. I ~ ° rj Z IZ2I 2nd 3rd 4th 5th 6th 7th 8ve, 258. In the following table, starting from above — Pig. 110. 2nd 3rd 4th 5th 6th 7th 8re. I E5IEE3E ~ n rj rj s-j 73- *> a g ■ g ^_ 1 a similar set of intervals is produced, but some of them are smaller than the corresponding intervals in the previous table ; in technical language, a change of quality has taken place. Thus the 3rd, 6th and 7th are each less by a semitone than they are in the table of Fig. 109. These smaller varieties are all termed minor, and the others are termed major. 259. The 4th, 5th, and 8ve are the same in each of the tables ; no change of quality has taken place. These are all called perfect intervals. 260. A similar series of intervals to those in Figs. 109 and 110 can be produced starting with any other note of the scale than the first, and no other changes of quality result than these two. The 4th from F upward (or -from B downward) I IZ2I contains a semitone more than any other 4th, and it is termed a Pluperfect Fourth, or, from its containing three whole tones, a Tritone Fourth.* The 5th from B upwards (or from F down- — Q- — si — wards) contains a semitone less than any other 5th, 5? ■; — ^ — and it is termed an Imperfect Fifth. 261. The imperfect fifth and tritone fourth are found only once in the same major scale, but twice in a minor scale in its harmonic form. " This latter term is preferable alike to Pluperfect, which is auomalous, and to Augmented (as some writers describe it), which properly describes a chromatic interval. INTERVALS. 65 262. Every interval may be converted from one kind to another by raising the lower sound an octave, or vice versa by lowering the upper sound an octave. This is termed Inversion. The following shews both processes applied to the tables of Figs. 109 and 110. The ' black notes are those from which the intervals were there reckoned- Kg. 111. 7th 6th 5th 4th 3rd 2nd Unison 2nd 3rd 4th 5th 6th 7th 8ve. . ■ -**-?-m- -m- -m- -m- -»- -»- -es- -e^- -^- -f3- -t^- c >s , -ss- ^u.. _.«_C2 — i=: rj o ■*■ 1 ' • ■ -*^-»- -»- -m- -»- -»- -m- -&- -&- -&- -&>- -&■ c -&essi- 2nd 3rd 4th 6th 6th 7th 8ve 7th 6th 5th 4th 3rd 2ndUnison 263. The change (of kind) that will be produced by the inversion of an interval may be ascertained by subtracting from 9 the number of the interval to be inverted. Thus 9 — 5 = 4, a 5th becomes a 4th ; 9 — 3 = 6, a 3rd becomes a 6th. 264. A change of quality also occurs by inversion, i.e., major intervals become minor intervals, and vice versa, and the imperfect fifth becomes a pluperfect fourth and vice versa. But the perfect intervals remain unchanged in quality. It will be seen that the inversion of the octave produces unison. This is an interval only in name. 265. Intervals within an octave are called Simple Intervals. Those that exceed the octave are called Compound Intervals. 266. Generally an interval is named after its simple form even if it be extended by one or more octaves. But a 9th (which is really a 2nd with an 8ve added to it) is usually so named, after its compound form. 267. The designation of any compound form of a simple interval may be found by adding the number 7 to the number of the simple interval for each octave. Thus a 3rd with one octave added to it becomes (3 + 7 =) a 10th ; an 8ve with an 8ve added to it becomes (8 + 7 =) a 15th. 268. All intervals formed by any two notes of the same major scale are termed Diatonic Intervals. 269. The semitones found in a diatonic major scale between the third and fourth and seventh and eighth, and in a diatonic minor scale between the second and third and seventh and eighth, are termed Diatonic Semitones. But a semitone produced as in the chromatic scale by raising the pitch of a sound by a sharp (or its 66 TEXT BOOK OF MUSICAL ELEMENTS. equivalent) thus or lowering it by a flat t r22I#Z2I (or its equivalent) thus s 2 5*5 is called a Chromatic Semitone. 270. A diatonic interval increased or lessened by a chromatic semitone produces a Chromatic Interval, except in the increase of a perfect fourth and the decrease of a perfect fifth, as shown in § 274. 271. A major interval or a perfect fifth increased by a semi- tone is called an Augmented Interval. Such an interval may be produced by raising the pitch of the upper note or lowering the pitch of the lower note of the major or perfect interval. Thus — Kg. 112. Aug. 6ths. Aug. 5ths. iy-frH BBb fc tr -s>- "&=*- -- Or an augmented interval may be produced from a minor interval by raising the upper note and depressing the lower note each a semitone, or, by what is equivalent, raising the upper note a whole tone or depressing the lower a whole tone. Thus — Fig. 113. Aug. 2nd. Aug. 2nd. Aug. 6th. Aug. 6th. m ^ "tetfs 1 - sxzz: IXZ2I ~C2Z m 272. A minor interval or a perfect fourth decreased by a semi- tone is called a Diminished Interval. Such an interval may be produced by lowering the pitch of the upper note or raising the pitch of the lower note of the minor or perfect interval. Thus — Fig. 114. . Dim. 7th. Dim. 4th. I idSSi ic Or a diminished interval may be produced from a major interval by depressing the upper note and raising the lower note each a semitone, or, by what is equivalent, depressing the upper note a whole tone or raising the lower note a whole tone. Thus — Fig. 115. „ -Dim. 3rd. Dim. 7th. Dim. 3rd. Dim. 7th. i %\ Ota *&■ INTERVALS. 67 273. The intervals which may be augmented are the 2nd, 5th, and 6th, and those which may be diminished the inversions of these, viz., the 7th, 4th, and 3rd, thus — Kg. 116. Au gmented. Diminished. "2nd! "" oth. 6th. 7th. 4th. 3rd. «=z *= IfczzzJ^ibzzz 1 S3Z te -gg- 5 It will be seen that chromatic intervals, like the diatonic intervals, change their quality by inversion ; augmented become diminished, and vice versa. Some writers treat all intervals as alike subject to augmentation and diminution. But only the augmented and diminished intervals already named have any real existence in music. Others appear only in enharmonic transitions; thus an augmented 3rd ^. equivalent of a perfect 4th. Doubly is written as ffty tt i -j "n augmented and doubly diminished the enharmonic fF 3 ^— intervals> as .£__ may, too, appear on paper, but the doubly C xrjj&^ augmented 5th and doubly diminished 3rd *J are false representations of a major 6th and minor 2nd respectively. 274. In all chromatic intervals one of the sounds will need an accidental to express it. Not every interval, however, that has an accidental against one of the notes representing it is a chromatic are both diatonic intervals, being imperfect fifth andtritone interval. Thus the following SjElE: I fourth in the scales of A and B'2 respectively. 275. To ascertain the nearest key to which an interval belongs that has an accidental against one or both its notes, and so to deter- mine whether it is a diatonic or chromatic interval, it is only necessary to seek out or think of the first key signature which has such a sharp or flat in it, as the case may be. Thus in the following n the first signature with a DJf in it is that of interval JFt~u~~^ the key of E. The interval, must at least, 5 , » Tritone 4th », 6 > Imperfect 5th ,» 6 » Perfect 5th ,, 7 , Minor 6th ,» 8 > Major 6th t> 9 , Minor 7th »> 10 >> Major 7th », 11 Octave », 12 , Chromatic Intervals. Diminished 3rd, 2 semitones. Augmented 2nd, 3 „ Diminished 4th, 4 „ Augmented oth, 8 Diminished 7th, 9 Augmented 6th, 10 CHAPTER XVI. THE ELEMENTS OF HARMONY. 278. Intervals for harmony purposes are further divided into two classes — consonant and dissonant. The former class is also subdivided into perfect and imperfect consonances. The 4th, 5th, and 8ve are termed perfect consonances, and the 3rd and 6th are termed imperfect consonances. 279. The 2nd, 7th, imperfect 5th, pluperfect 4th, and all chromatic intervals are included among dissonances. 280. The primary element in harmony is a combination of consonant intervals. Such a combination is termed a Concord, in contradistinction to a combination of sounds that includes a dissonance, which is called a Discoejd. 281. The interval upon which modern harmony is founded is a third. When two thirds, one major and one minor, are placed one above another a perfect fifth is embraced, and the combination is termed a Chord. It is also called by some writers a common chord, and by others, from its including three sounds, a Triad. 282. A chord can be raised upon each note of the major scale but the seventh — Eig. 117. i 9 It will be seen that these are not all alike. Those on the first, fourth, and fifth of the scale have the first 3rd major, and these chords are called major chords. Those on the second, third, and sixth of the scale have the first 3rd minor, and these chords are called minor chords. 70 TEXT BOOK OF MUSICAL ELEMENTS. 283. Isolated chords may be named after the pitch note on which they are raised, as the chord of C, or the chord of Qt, &c. But in an orderly succession of chords they are considered in relation to the scale in which they stand, and are named from the degree of the scale upon which they are raised. Thus the chord raised on the first of the scale is called the chord of the Tonic, the chord on the fifth of the scale the chord of the Dominant, and so on. See § 19 for the names of the notes of the scale. 284. The notes of the minor scale upon which chords can be raised are seen in the following — Fig. 118. 1 IE -& -$&z T5T 2 6 285. There are fewer chords in all than in the major scale, but half the number are major chords and half minor chords as before. A chord raised on the seventh degree of either scale, or on the second degree of the minor scale, would give an imperfect 5th, and a triad raised on the third degree of the minor scale would give an augmented 5th. Such combinations have no place among concords. 286. The chords that are most used in each scale are those of the tonic, dominant, and subdominant, and they are called the principal or foundation chords of the scale, comprising as they do all its separate degrees ; see the following — Fig. 119. 1£^==2tt QAJi*& SS£& 1 i v iivv&irvviv i v i ivi&vrv v iv The Eoman figure I stands for Tonic, V for Dominant, and IV for Subdominant. 287. The lowest note of a chord is called its Boot, the next above, its Third ; and the next above that its Fifth. These are called the constituents of the chord. When an octave is added to TEE ELEMENTS OF HARMONY. 71 the root, as " m the combination is sometimes called a complete chord. 288. All the chords in the foregoing examples are said to be in their root position. The upper notes may be variously placed, and either constituent may be doubled, as — Fig. 120. $ but the position of the chord as a whole is not thereby affected. 289. The constituent which is most freely doubled is the root, and next to that the fifth. The third is less freely doubled than either of the other constituents. The fifth may be omitted, but not the third. The way in which a chord is made up, with doubled root, or with doubled fifth, &c, is called the Constitution of a chord. 290. The order in which the upper notes of a chord are placed, as in the previous example, affects what is termed the Distribution of a chord. That distribution is the best which gives the largest interval at the bottom and the upper intervals at more or less equal distances, thus — Fig. 121. Good. Bad or Indifferent. I -T2- ZZ2Z ZZ2Z ~g?~ W=W- rzz: -rrr -7ZT IZ2I 221 ~g?~ -g7~ ~CT~ ESE re: ZZ2Z ;z2i 291. The chords can be so arranged as that either of the constituents shall stand lowest. When any other constituent than the root is placed lowest the chord is said to be inverted. If the third is placed lowest thus Z2I 3S the chord is said to be in its first inversion ; if the fifth is placed lowest thus 3E_ 3 the chord is said to be in its second inversion. 72 TEXT BOOK OF MUSICAL ELEMENTS. 292. Chords are expressed by figures placed over or under the bass notes. A bass which shews the chords that are to accompany it is called a Figured Bass. 293. In the root position of a complete chord when the con- stituents stand in the normal order shewn in the examples of § 287, the intervals counting from the lowest are a 3rd, 5th, and 8th. The figures | {named from the top downwards) are therefore used to express the root position of a ohord. The figures, are, however, but seldom used for the root position, it being understood that a bass note unfigured is to bear a chord in its root position. "When it is necessary to figure a root position, as when there are two chords on one bass note, Sj or s is generally sufficient. 294. In the first inversion of a chord when the constituents stand in their normal order, as shewn in the example in § 290, the intervals are a 3rd and 6th. The figures § are, therefore, used to express the first inversion of a chord. This figuring is generally abbreviated to 6, and a first inversion of a chord is known as a chord of the sixth. 295. In a second inversion of a chord, when the constituents stand in their normal order, as shewn in the example in § 290. the intervals are a 4th and 6th. The figures | are therefore used to express the second inversion of a chord, which is known as the six four position. 296. When any constituent is affected by an accidental the figure that represents the altered note is preceded by the cor- responding accidental, thus — Fig. 122. i ^ $5 mi TZ2Z. m *> 221 *= m ±t IZ2C -frg- t« 56 Q3 ® 297. An altered third to the bass as in the last two cases of the previous example, is generally expressed by the accidental alone. Thus, under the Gr a t| would be sufficient, and under the D| would express the figuring. See further in § 314. TEE ELEMENTS OF HASMONT. 73 298. When the interval is raised a semitone, whether by a Jf or fa it is sometimes expressed by a short oblique line drawn through the figure. 299. All the chords already named (§ 282 and § 284) are available in their first inversions. The first inversion of the imperfect chords standing on the seventh degree of both scales, and on the second degree of the minor scale, are also available as concords. Tig. 123. „ Major. _, --. ^>'^ ~ „ Minor. , yEg^BE f- = 1 yEg=gEg|g zS - The minor scale, even in first inversions, has still one chord' less. The first inversion of a triad on the third degree of the scale would still include a dissonance, i.e., a diminished 4th. 300. The chords that can be used in their second inversions are those of the tonic, dominant, and subdominant only. Pig. 124. Major. Minor. illj=igy=FF^l m E^ mi ~p~ 301. The first inversions are used with almost the same freedom as the root positions, but the second inversions are under many restrictions. 302. The rules that govern the use of the second inversions and that regulate the succession of chords and the progression of the several constituents in joining chord to chord form the chief points for attention in the study of harmony. It is beyond the scope of this work to do more than briefly refer to the most important of these points.* 303. The chords in Fig. 119 though they have the scale running through them, are all more or less isolated from each other ; they succeed in anything but a pleasant manner. Some of the successions have no element of union between them. Others have, such as * A oomplete study of the subject may be made from the author's " Text Book of Harmony." 74 TEXT BOOK OF MUSICAL ELEMENTS. the succession of the chord of the tonic by the chord of the dom- inant, and vice versa, in the first two successions, where each chord has a note that is common to the other. The same is the case in the succession of the chord of the tonic by the chord of the sub- dominant (and vice versa). Those chords succeed each other best which have a note in common between them. 304. But the chords in Fig. 119 disagreeably succeed because as representing three different melodies or parts the upper and lower parts proceed all through in fifths. If an upper octave of the root were added to the chords, making four parts, the succession would scarcely be improved, the upper part would then move all through in octaves with the- lowest part or bass, and the third part would move as before in fifths with the lowest part. 805. Consecutive fifths and consecutive octaves are prohibited between any two parts. 306. These intervals may, however, occur in two successive chords, so long as they are not between the same parts. Thus in the following case — Fig. 125. £ the octave in the first chord is between the bass and the tenor parts, and in the second chord it is between the bass and soprano parts. The fifth in the first chord is between the tenor and contralto parts, and in the second chord it is between the bass and tenor parts. In each case the chord is complete, the " note in common " is retained in one part, and the other constituents of the first chord move to the nearest note of the second chord. This makes the smoothest connection of chord to chord which it is possible to have. 307. If a bar is put between the chords of the previous example so as to bring the last chord on an accent the form of a Perfect Cadence or clos^e will be illustrated. This cadence is used for the final ending of a composition. 308. The leading note in the perfect close invariably rises to the tonic, as it generally does elsewhere. THE ELEMENTS OF HABM0N1. 76 309. Other cadences of a less conclusive kind for the closes of intermediate movements are the Dominant Cadence, or half close (a), formed by reversing the tonic cadence, and the Plagal Cadence (i), in which the tonic chord is preceded by the sub- dominant chord instead of the dominant. Fig. 126. (a) $ -4- -7TJ- T i 7='" @E£ p There are many other cadences, but the three named are the principal. 310. In the perfect cadence the fourth of the scale is often introduced in the dominant chord as a dissonant 7th to the root, converting the combination into what is termed the discord of the Dominant Seventh. This discord, from its containing both the fourth and the seventh of the scale better defines the key (§ 261) than the dominant concord. The discord also gives a note in common to the subdominant chord that often precedes the cadence chords. Fig. 127. ~l- i ^ -T3- ^m The Dominant Seventh is therefore more often used in a perfect close than the plain concord, and in modern music this discord is as freely used as a concord in other places than the close. 311. The description of this discord and the mention of the chief rules that apply to its use must conclude this outline of the subject of harmony and the text of this work. 76 TEXT BOOK OF MUSICAL ELEMENTS. 312. The discord of the Dominant Seventh comprises four constituents — root, third, fifth, and seventh— rising in the order of thirds from the lowest root thus I - • m • a s *-* r j i* i* • r- W-— ® - P— 1 f r W W •j — tH — *~~ J 1 p =1=2= y^— r =e=fc ^g^ l^^ ^a^ £=f 9 65. Describe a compound measure. 66. What kind of note is used for the undivided pulse of a compound measure? 82 TEXT BOOK OF MUSICAL ELEMENTS. 67. Write the following with a dotted minim instead of a dotted crotchet for the pulse, and say what is the measure of each example — i ^=^ ^ $ r- * i * l\> V U =tz=t -j — F-' ^ -I h i - :*=* a=i 3fc^: 68. Write the following with a dotted crotchet instead of a dotted minim for the pulse, say what is the measure, and mark thus a each note that has a secondary accent — i 4 UU4 SE :S=afc J rJ #■ ^ I 3=1= i ?z:- S St *3t 5 69. Describe the method of beating duple time, triple time, and quadruple time. CHAPTER VI. 70. Explain what is a time signature. 71. What does the upper figure of a time signature represent ? What the lower figure. 72. Give the time signatures of the examples in Exercises 63 and 64. QUESTIONS AND EXERCISES. 83 73. State what kind of measure the following signatures represent duple, triple, or quadruple — and write two measures of each, i | I S } 74 State by what figure the upper numeral of every signature of com- pound time can be divided. 75. Give the time signatures of the examples in Exercises 67 and 68. 76. State what kind of measure the following signatures represent, and write two measures of each — | A 1 2 jj | l g 2 77. What kind of measure is expressed by this sign for a signature— C\ 78. What other signature is used instead of | ? and what is the time called when this signature is used ? 79. For what other time than duple time is this sign (jj occasionally used for a signature ? CHAPTER VII. 80. Name the pitch sounds between which the semitones occur. 81. Give the pitch note from which the order of tones and semitones coincides with that of a major scale, and state what the scale founded on this note is called. 82. How are other semitones produced than those found in the scale just named ? 83. How can a sound be raised a semitone ? Give the sign used for the purpose, and state its name. 84. How can a sound be lowered a semitone ? Give the sign used for the purpose, and state its name. 85. To form a scale of G what pitch note is altered, and how ? 86. What parts of the scales of C and G correspond ? 87. Taking the upper tetrachord of one scale as the foundation or lower tetrachord of another, what is the note of the original scale that needs altering for the new scale ? ■ 88. Write on the bass staff the scales of D, A, and E, in ascending order, with the sharps that are necessary placed against the respective notes. 89. State which scales are founded upon raised pitch names. 90. State which scale has only B unaltered in pitch, and which scale has a sharp against every note of it. 91. State how a key signature is formed. 92. Write on the bass staff the signatures of all the scales having sharps. 93. In a signature of sharps how is the key note most readily recognised ? 94. To form a scale of F what pitch note is altered, and how ? 95. What parts of the scales of C and F correspond? 96. Taking the lower tetrachord of one scale for the upper tetrachord of another, what is the note of the original scale that needs altering for the new scale ? 84 TEXT BOOK OF MUSICAL ELEMENTS. 97. Write in ascending order on the treble staff the scales of ~E\> and A|j, and in descending order on the bass staff the scales of B? and !)[>, with the flats that are necessary placed against the respective notes. 98. State which scale has a flat against every note of it, and which scale has only one note without a flat. 99. Write on the bass staff the signatures of all the scales having flats. 100. In a signature with flats how is the key note most readily recognised P CHAPTER VIII. 101. Give the pitch note from which the order of tones and semitones coincides with that of the only other kind of diatonic scale than the major scale that is in use, and state what such a scale is called. 102. State between what sounds of a minor scale the semitones naturally occur. 103. State the difference between the first tetrachord of the minor scale and that of the major scale. 104. What alteration is needed to make the upper tetrachord of the minor scale satisfactory ? 105. Write the form of the harmonic minor scale of A. 106. State what other sound of a minor scale than the seventh is occasionally altered. 107. Describe the form of the altered diatonic minor scale. 108. State in what circumstances the minor scale is found in its original form. 109. How is a minor scale most readily distinguished from the major? 110. State what is understood by the term relative minor, and upon which note of a major scale does the relative minor begin ? 111. State what other relation a minor scale has to a major, and give the term used to express the relation. 112. Which of the two major scales that are related to a minor scale does the signature of a minor scale agree with ? 113. Write on the bass staff the signatures of the minor scales of B, D, C, CJ,andBt,. 114. Write on the treble staff the signatures of the minor scales of Eb, E, G, G», F, and FJ. 115. Name in order the sharps found in the signature of AS minor, and the flats in the signature of A\> minor. CHAPTER IX. 116. Give the sign used tor raising a semitone a note that is already sharp in the signature, and state its name QUESTIONS AND EXERCISES. 85 117. State the minor scales with sharps that require a double sharp for the leading note. 118. Give the sign used for raising by a semitone a note that is flat in the signature, and state its name. 119. State the minor scales with flats that require a natural for the leading note. 120. State by what means a note is lowered a whole tone from its normal pitch. 121. In what circumstances has a 9 the effect of a b. 122. Write all the signs used for accidentals, and state which of them are used only as such. 123. What is a eautionary accidental ? 124. State how a note that has been raised by a double sharp is reduced by a semitone, and how a note that has been lowered by a double flat is increased by a semitone. 125. In what other circumstances than as accidentals are naturals used ? 126. What is a chromatic scale ? 127. Write the modern or harmonic form of the chromatic scale ascending from G. 128. Write the chromatic scale in D, ascending and descending, according to the arbitrary form. CHAPTER X. 129. What is meant by an enharmonic change ? 130. Shew by examples in what two other ways each of these notes can be represented at the same pitch — ^m §s= I 131. State which of the scales with flats have enharmonic counterparts to scales with sharps, naming those that correspond. 132. State in what circumstances the notation of one scale is written for the enharmonic equivalent of another. CHAPTER XI. 133. For what universal purpose is a semibreve rest used ? 134. Show two methods of representing a silence of five measures and a silence of eight measures. 135. Describe a syncopation. 86 TEXT BOOK OF MUSICAL ELEMENTS. 186. Write the following in i time, and state which of the notes are P ri= 3t a >l* ?m* :f=2^i S=^ ^ =t=t 187. Write the following in f time, and point out the syncopations — m ■#— r# r 1ft* r ^S 53 B *=*= ^ 138. Substitute the signs for silence for the notes marked thus * — -*-$- I P=t Si jF7 =st =P=P -CJ-^ fc=t 139. What is a triplet ? Give an example in I and one in 1 time. 140. What is the effect when several successive triplets are used in a simple measure ? , 141. How is a pulse in compound measure sometimes divided. 142. By what means are crotchets or minims grouped for a triplet ? 143. What is the general use of a slur ? ' 144. Describe what is meant by staccato, and give the various signs used for the purpose. 145. What is the meaning of sostenuto, and by what signs is it some- times expressed ? 146. Explain this sign n\ and say how it is sometimes qualified. 147. How is the rate of movement usually indicated ? 148. Explain the meaning of J = 80 and ' . = 60 ; state what kind of measures are referred to and what instrument. 149. Name two or three words by which the general pace of a move- ment may be conveyed, and state what else is indicated by them than the 150. Explain these signs : : D.C., D.S., £. 151. What does Fine mean, and in what other way is the same thing 1? 152. How is the repetition of a short passage expressed ? QUESTIONS AND EXEROLUSS. 87 153. Show the abbreviation for the repetition of this figure in all the pulses of the measure — -H-* and for the repetition of this in the next measure m ,fff 154. Show how the following passage may be abbreviated — 155. Explain the use of the word tremolo. CHAPTER XII. 156. Explain the use of the signs 8va, con 8va, 8va bassa, and loco. 157. Explain how a combination of sounds are performed in arpeggio, and give the sign used for the purpose. 158. What are grace notes ? 159. Give the specific names for the small notes in the following examples — &%fjji i J« B and briefly describe the way in which they are performed. 160. Give the names of these signs, <-< and \, and explain their use. 161. Show by examples how accidentals affect a turn. 162. Give the names for these signs, tr. w and y, and show by example their effect. 88 TEXT BOOK OF MUSICAL ELEMENTS. CHAPTER XIII. 168. Give the meanings of the following words and state which affect intensity, movement, or style — Pianissimo, Moderate, Morendo, Tempo, Crescendo, Stringeado, Con moto, Marcato, Animato. 164. Explain the following signs, f, ~^^s-, mp, a rf, _-^^, and dim. CHAPTER XIV. 165. • Explain what is meant by Solo, Duet, Trio, Quartet. 166. Explain the use of Sou, Totti, Cantobis, and Decani. 167. Name the chief divisions of voices in choral music, and give the ordinary compass of each. 168. What is understood by mixed voices ? by equal voices $ 169. What is a score? 170. Name and briefly describe the different varieties of scores. 171. By what means are staves grouped for a score f 172. Write the example in § 159 in ordinary vocal score and condense the parts again in two staves for an harmonium or organ score to be written under the vocal score. 173. Condense the following into short score — 3me 5^ £ -+-*- as L*W^*A. QUESTIONS AND EXERCISES. 89 1E32£* IE -»»' tf I s i a h ^ k K - 5SI^ ^= *&**J2 $ *=» r *r f ^m^gn - 174. Explain what is meant by transposition. 175. Transpose the example of Fig. 62 a tone higher. 176. Transpose the bass part of Ex. 173 a major 3rd lower. 177. Transpose the example of Kg. 80 into the tenor staff. 178. Transpose the contralto part of the example in Ex. 173 to the alto staff. 179. Transpose the treble part of the example in Fig. 66 a tone lower. 180. Transpose the bass part of the same example a tone lower on the tenor staff. CHAPTER XV. 181. Define an interval, 182. What does the term degree describe ? 188. What other term than degree describes a tone or semitone ? 184. How are intervals named ? 185. Specify the different intervals found within a scale ? 186. What is the change called which some intervals undergo when they are found below the first of the scale instead of above it ? 187. State which intervals are termed major and minor. 188. How are the intervals of the 4th and 5th qualified ? 189. What is a tritone ? 190. Name the following intervals — !N _Ci_fi-L zcsr rgig ^-j: 90 TEXT BOOK OF MUSICAL ELEMENTS. 191. Add notes (within the scale) above the following — 3rd 7th 4th 3rd 2nd 5th 4th 3rd 7th 4th i rzz: «--> -T2 - and notes below the following — J> < =» a ^ rs r z z 2Z ~g?~ -i^r- «-■ 5th 2nd 7th 3rd 3rd 7th 4th 6th 5th 6th to make the intervals named, and specify the quality of each interval aa perfect, imperfect, pluperfect, major or minor. 192. What is the inversion of an interval ? 193. State the rule by which it may be ascertained what an interval becomes when inverted. 194. State the changes of quality that are produced by the inversion of the different intervals. 195. State the difference between a simple and a compound interval. 196. How may the designation of a compound interval be ascertained from its simple form ? 197. Define the terms Diatonic Interval and Chromatic Interval. 198. Explain a chromatic semitone. 199. Define an augmented interval and a diminished interval. 200. State which intervals may be augmented and which may be diminished. ■ 201. Name the following intervals — 1 ! Ez r-*fr^r^s=iS=sF TTJ—tf ?. iT 3 flraO S"^-*^ 202. Convert each of the following into chromatic intervals and specify each in its converted form — 1 w ■>&- ~s>~ ■^bo a ty ■^- _ ='" 203. Name all the following intervals — ill ■■ g c? &= > ^J^T^^^J^^M ? g> f&- QUESTIONS AND EXERCISES. 91 204. Add notes above the following to make the intervals named — Ma 3rd Imp. 5th Aug. 6th Dim. 7th Flup. 4th Min. 3rd Dim. 4th 1 &—!" b^ -^ to j | a — ^-^ E 3 CHAPTER XVI. 205. State which ai'e the consonances, perfect and imperfect. 206. State all the intervals included among dissonances. 207. What ia a concord ? What a discord f 208. What is the interval upon which modern harmony is founded ? 209. Define a chord. 210. State upon which notes of the major scale chords can be formed, which are major and which minor. 211. Write on the bass staff all the chords just mentioned and name them according to the degree of the scale. 212. State how many chords are found in the minor scale, major and minor, naming them according to the degrees upon which they are raised. 213. State which of the chords in the minor are found in the relative major, and give their names in each scale. 214. State which major chord of the minor scale needs an accidental to express it, and which note of the chord requires the accidental. 215. State the objection to a triad on the leading note, and what other note of the minor scale would furnish a similar triad. 216. Place such signatures for a treble staff before the following chords as will make each of them respectively first a tonic, then a dominant, and then a subdominant chord of a major scale— 217. Place treble or bass clefs before the following combinations to make them minor chords. Then name them both in their relation to a major scale and to its relative minor — 218. Name the constituents of a chord, and say what is understood by a complete chord. 219. Explain the terms constitution and distribution as applied to chords. 92 TEXT BOOK OF MUSICAL ELEMENTS. 220. Write complete chords in the root position in various distributions on C within the treble staff, and on F and G spread over the bass and treble staves. 221. Explain what is meant by the inversion of a chord ; state which constituent stands lowest in the first inversion and which in the second inversion. 222. Write in short score first inversions of chords in various good distributions, using the following bass notes, which are not in any case to be doubled in the constitution of the chord. State under each inversion the pitch name of the root. m EgE =?= T ^ 223. Write in short score second inversions of chords, using the following bass notes, and state the pitch names of the roots. W 224. What is a figured bass ? Give the full figuring of a chord in its root position, in its first inversion, and its second inversion. 225. Figure in the ordinary way the bass of the following example — ! 1 £^2ZJ_ jz 3 A =8= 1=2Z V **- A± m i ffi-fr-8- ?=c W^ % rb—rd- i d d £ak ■3=tL f=f=T £S -TTJ- r> r> ?=- ^^ I I I m A A J- A QUESTIONS AND EXEBOISES. 93 i2— Kt— sir 2=t se ^^^ ZZ2- P =i= S J AJlA s 22- 226. State what is the effect of an accidental without a figure placed under a bass note. 227. Give the figuringa of the chords with accidentals in the examples of Figs. 118, 123, and 124. 228. Figure in the ordinary way the bass of the following — it -I- i± 5JE -I- 1= S ^= 7) Tz~- ■P"' 1 z&z ZC2Z *=L I J s 221 ^2= I^Z 221 ^ £ 22 22Z ^S= ^ J I 1 S=£= -C2_ g — &^- _J. ££2= ^fffr- :g=g= p 229. State what the following is an example of (W g — and how often such a combination can occur in a minor scale and in a major. 230. State which chords of a scale are used in their second inversions. 231. Write chords in short score according to the following figured "22~ 321 r> \> &— fri t« 2 Js" J bS 8a S bS 94 TEXT BOOK OF MUSICAL ELEMENTS. 232. Write chords in short score according to the following figured m $& r*> -£?- 3fe tea -ear bs 4 6 | 86 | b 6 | 233. State the several keys in which each of the chords of the six-four position in Ex. 231 could be used. 234. State the keys in which the chords of the six-four in Ex. 232 could be used. 235. Are first inversions or second inversions used with equal freedom to root positions ? 236. State what is the element of union between two chords that favours a good succession. 237. Name chords that have an element of union between them. 238. State what intervals may not succeed each other in any two parts. 239. State what succession of chords form a perfect cadence. 240. Write .perfect cadences in the keys of D, G, F, B|j. 241. What is a half- close ? Give examples in the keys of A and E. 242; What is a plagal cadence ? 243. Describe the discord of the Dominant Seventh, naming its con- stituents. Write examples of the discord in keys G, F, and A. 244. Name all the dissonances found in the complete form of the discord 245. Resolve these dissonances — fe=faifci! s= = t! 22 - 246. Convert the following combinations into discords of the Dominant Seventh by adding the accidentals necessary, and resolve the discords, first in the major and then in the minor. State the key in each case and figure the discords in the ordinary way. i rg=: m 22Z I h=gz zzzz i 221 m ls= m\ I }— - a: 247. State how many inversions there are of the Dominant Seventh. 248. Give the full figurings of the Discord in all its positions. QUESTIONS AND EXEBOISES. 95 249. Write in short score discords of the Dominant Seventh according to the following figured basses, and resolve each discord in the major. ^== P == W^*= B 4 i 5 3 2 250. Write in short score according to the following figured basses, and resolve each discord in the minor. -^fS= ===== ~ - 8 *J it 251. Write as in previous exercise, according to the following basses, and resolve each discord in the major of the keys indicated by the acciden- tals found in the bass or against the figures. State the key in each case. Bb z^2=z £fc<=2: M=\e== 6 f4 r4 5 *2 <>3 252. Write as in previous exercise, resolve each discord in major, and state keys. e== n= &m= E* 55 IS 3 253. Write as in previous exercise, and resolve each discord in the minor of the keys indicated by the accidentals. State the key in each case. m^= e== m Z2Z a hi n 2 3 254. Write as in previous exercise, resolve each discord in minor, and state keys. ^m §^i ^m i i § 97' INDEX. *»• The numbers refer to the Sections. Accent ... {64 Chords of the Major scale ... .. 528* , primary ... ... ... ... 76 of the Minor scale .. 284 , secondary 76, 78, 86 Chorus , .. 225 Acciaccutura ... 209 , Semi .. 225 Accidentals ... 148 Chromatic Intervals ... .. 269 , Effects of 160-152 , Table of .. 277 , Cautionary ... 153 Scale .. 161 Accolade ... 237 Semitone .. 270 Alia breve time ... 97 C in alt .. 48 capellatime ... 97 Clef .. 24 Alphabetical order of flats in scales... 122 , Alto .. 41 order of sharps in scales ... 115 , Bass .. 26 Pitch Names 28,104 , Tenor .. 40 Alterations of notes, Artificial 106, 112 , Treble .. 26 Altered diatonic Minor scale ... ... 129 Common Time .. 76 Alto clef ... 41 Signature .. 96 staff ... 41 Compass of voices .. 229 Appoggiatura ... 208 Compound appoggiatura .. 21] , Compound ... 211 Duple measure .. 8b Arbitrary Chromatic Scale ... ... 164 Intervals .. 265 Arpeggio ... 206 Measure .. 82 Augmented Intervals 271, 273 ■ Time ., 81 Auxiliary note ... 212 Quadruple Time .. 85 — TripleTime .. 84 Bar 68,71 Concord .. 280 Bass ... 227 Conductor .. 88 Clef ... 26 Con espressione .. 223 Figured 292-298 Consecutive fifths 3< 5,306 Staff ... 26 octaves 3 5,306 Beating Time ... 89 Consonances, Imperfect .. 278 Beats ... 70 .Perfect .. 278 Beat, The ... 210 Consonant Intervals .. 278 Bind ... 58 Contralto .. 227 Bis 196 Crotchet 51,52 Brace ..'. 237 Breve ... 53 Da Capo .. 194 rest 173, 174 Dal Segno .. 194 Dash .. 186 Cadence, Dominant ... 309 Decani .. 226 Perfect ... 307 Degree .. .. 254 Plagal ... 309 Degrees of Intensity .. 220 Cantoris ... 226 of Movement .. 221 Cautionary accidentals ... 153 Demisemiquaver 51,52 CClef 39,40 Description of notes .. 52 Change, Enharmonic 165-171 Diapason Normal .. 49 Change of quality ... 25S , 264, 273 Diatonic Intervals .. 268 Characteristic of Minor scale... ... 127 .Table of .. 277 Choral Music ... 224 Scale ] 6,124 Chord ... 281 Diminished Intervals 2' 2, 273 Constituents ... 287 Direct ... ' .. 250 , Constitution of ... 289 Discord .. 280 , Complete ... 287 Dissonances .. 279 , Distribution of ... 290 Dissonant Intervals .. 279 , First inversion of 291, 801 Dominant .. 19 of the Sixth ... 294 Cadence .. 309 , Second inversion of 291, 800, 301 Seventh 3 10-318 98 INDEX. Dot , Double ... Dots over notes ... Dotted note Rests Double Bar Flat Sharp Duet Duple Time Duration Eighth Note Emphasis ... Enharmonic change Equal Voices Expression — — Marks Fifth , Imperfect Fifths, Consecutive Figured Bass Fine Flat. - 1 Double ... 156 ... 57 186, 187 ... 56 ... 62 ... 73 U7 141 ... 224 ... 71 ... 71 ... 7 ... 61 ... 64 165-171 ... 230 ... 219 ... 220 ... 287 260, 261 805,306 292-298 ... 194 , 109 147 Flats in Scales, Alphabetical order of 122 Formation of Scales ... 105-111, 117-119 Foundation Chords of the Scale ... 286 Fourth 256 , Pluperfect 260, 261 Full 226 Score 232 GClef Grace notes Grand Staff Great Octave Stave irouped Notes Half Note Harmonic Chromatic Scale Minor Scale Harmonium, Score for... Harmony Imperfect Consonances. . . Fifths Intervals Intensity , Degrees of Interval, Denned Intervals , Augmented , Chromatic , Compound , Consonant , Diatonic , Diminished , Dissonant , Imperfect -, Major , Minor , Perfect , Simple , Table of ... 29 ... 207 ... 44 ... 47 ... 44 ... 183 ... 51 ... 163 ... 128 ... 286 ... 11 ... 278 260, 261 260, 261 ... 6 ... 220 ... 258 252-278 271,273 ... 278 ... 268 272, 273 279 260, 261 ... 258 ... 258 ... 259 ... 265 ... 277 Inversion ;262 of an Interval 263 Inverted Mordent 218 Turn 213 Key-board, Pianoforte 103 Key Signature 113 Signatures, Table of ... 114,121 Keys with Flats, Signatures of ... 121 with Sharps, Signatures of ...114 19 308 185 22 ...31,32,102 205 174 189 190 Legato Leger lines Lines and spaces of staff Loco Long LungaPausa Malzel's Metronome ... Major Intervals Keys , Relative Scale , Chords of the ... Measure, Compound ... , Unit of ... 17 ... 133 ... 17 67, , Simple Mediant ... ... Melody Metronome Middle C TVfiTiiTn ... ... ... ... Minor Intervals ... ... ... of the same Tonic Relative Scale , Altered Diatonic , Characteristic of , Chords of the , Harmonic , Modern , Original , Signatures of, with Flats , Signatures of, with Sharps Mixed Voices Mordent , Inverted Movement, Degreesof , Terms affecting rate of Movements, Designation of ... , Repetition of Musical sound terms Music, Choral ... 95 69,70 ... 79 ... 19 ... 11 ,.. 190 .. 34 61,52 .. 258 ... 135 ... 133 .. 126 ... 129 .. 127 .. 284 .. 128 .. 127 .. 130 .. 139 .. 139 .. 230 .. 217 .. 218 .. 221 .. 222 .. 191 .. 192 4 224 Natural , effects of ... Note, Auxiliary ... , Dotted in common Notes 143 144, 145, 146 212 56 ... 303, 806 50 , Artificial alterations of ... 106, 112 -, Description of 52 -, Grace 207 -, Grouped 65, 183 -, Tied 175, 178 INDEX. Normal diapason pitch Octave , Great , Once-marked ... , Small , Twice-marked ... Octaves, Consecutive ... Organ, Score for Original minor scale ... Ottavabassa Ottetto Pace Partitur (a score) Pause Perfect cadence Consonances -Intervals Pianoforte key-board ... Score Pitch Names, Alphabetical . , Standard of Plagal Cadence Pluperfect Fourth Points of -writing Primary accent Progression of leading note . Pulses • Quadruple Quality, Change of Quarter note Quartet Quaver Quintet Relative Major Minor Repetition signs Rjst, Breve , Whole-measure Rests , Dotted Rhythm ... ... >■■ Root Position Scale ... 149 ... 49 ... 202 ... 47 ... 47 ... 47 ... 47 805,306 ... 2S6 ... 130 ... 204 191, 221 ... 231 189,194 ... 307 ... 278 ... 259 ...103 ... 235 ...5, 47 28,104 ... 49 ... 309 260, 261 237-249 ... 76 76 258, 264, 273 51 224 51, 52 ... 133 ... 133 192-201 178, 174 172, 173 69, 177 ... 62 ...3,66 13 , Arbitrary Chromatic 164 , Chromatic 161 , Complete 14 , Diatonic 16, 124 series, Formation of 110,111,117, 118 , Foundation chords of 286 , Harmonic Chromatic 163 , Original Minor.. , Major , , Minor , , Standard Scales, Formation of ... with Flats with Sharps Score for Harmonium.. for Organ.. 130 17 126 105 105-111, 117-119 ... 118, 119 Ill 231 236 236 Score, Full J232 , Pianoforte 235 , Short 284 , Vocal 233 Secondary Accent 76,78,86 Second Inversions 300,301 ... 255 ... 48 61,52 ... 225 61,52 .. 186 15, 255 ... 270 ... 224 Sestet 224 Seventh, Dominant 310-313 Shake or Trill 216 Sharp 108 .Double 141 Sharps in Scales, Alphabetical orderof 115 Signatures, Common Time 96 Signatures of Keys 114, 121 of keys with Flats 121 of keys with Sharps 114 of Minor scales with Flats ... 139 ■ of Minor scales with Sharps... 139 Second Soprano staff Semibreve Semi-chorus Semiquaver Semi-staccato Semitone -, Chromatic , Table of Time ... .. 99 of Time ... 99 Signs, Repetition . 192-201 Simile ... 198 Simple Intervals ... 265 Measures ... 79 Time ... 79 Six-four position ... 295 Sixteenth note ... 61 Sixth, Chord of the ... 294 Slur ... 184 , Use of ... 185 Small Octave ... 47 Soli ... 225 Soprano ... 227 Staff ... 42 Sostenuto ... 188 Sound ... 2 Spaces :. 20,21 Staccato ... 186 Staff, Alto ... 41 , Grand ... 44 , Lines and spaces of .. 31,32 , Tenor ... 40 Standard C ... 48 of Pitch ... 49 Scale ... 105 Stave ... 21 , Great ... 44 Step ... 254 Style, Terms indicating Sub-dominant ... 223 ... 19 Sub-mediant ... 19 Sub-semitone ... 19 Sub-tonic ... 19 Super dominant ... 19 Supertonic ... 19 Syncopation ... 176 Table of key-signatures 114, 121 Tenor C ... 48 100 INDEX. Tenor Clef Staff Voice Terms affecting rate of movement indicating style Tetrachords Third Thirty-second note Tie Tied Notes Time — : , Beating ... , Common... , Compound , Duple ... , Quadruple , Simple ... Signatures Signatures, Table of , Triple Tone Tonic , Minor of tie same Transposition TrebleC Clef . (40 40 227 ... 18, 110 ... 266, 287 51 68 ... 176, 178 8, 70 89 76 81 71 76 79 91-98, 100, 101 ... 99 ... 75 15,255 ... 19 ... las ... 261 ... 48 Treble Staff {26 Voice 227 Tremolo 201 Triad 281 Trill 216 Trio 224 Triple Measure ... 75 Triplet 179 Tritone 260 Tune .. 9, 10, 12, 63, 65 Turn 212, 214 , Inverted ... 213 Tutti 225 Unit of Measure... 96 Vibration 2, 4, 5, 6, 7 Vocal Score 233 Voices, Compass of 229 , Equal 230 , Mixed ... 230 "Whole measure rest 172, 173 Whole Note 51 Writing, Points of 237-249 BTf THE SAME AUTHOR. TEXT BOOK OF HARMONY. SIXTH EDITION. The Saturday Review, in a notice of this work, a column in length, says: — " The object of this Text-book is to explain the facts of harmony in a simple manner, arranging them with a view to educational purposes, te supply trustworthy information amply illustrated by examples supple- mented by a course of exercises, and by these means gradually to lead the student up to the higher branches of the science. This end we consider the author has achieved with marked success ; for he places the different progressive steps in logical order, and, by carefully following the rules which he has laid down, the student will not fail to have attained a considerable acquaintance with his subject before he has gone very far into the study." " Mr. Oakey's new ' Text Book of Harmony ' is able to compete on its merits with any of the ordinary and well-known manuals on the subject. . . . The various divisions and sub-divisions of the subject are treated, speaking generally, in the ordinary way, but with unusual exactness and fulness of explanation. It is a book from which any private student of average intelligence may learn the subject and master it. . . . Mr. Oakey, by means of his original illustrations, and passages selected from different composers, has done much to show both the applications of theory to ordinary practical work, and the uses which the great musicians have made of them." — School Guardian. " Gives a wonderfully full and complete exposition of the laws of har- mony, arranged on a new and, as we think, admirable plan. The examples, which are exceedingly numerous, are given in both notations. The capital exercises are well arranged in order of difficulty, and afford ample practice." — Schoolmaster. ■' Among its good points are the stress laid upon melodic elegance even n early exercises, and the chapters on two and three part writing, and on the discords of the 9th, 11th, and 1 3th."— Music Trades Review. " There is much in it both valuable and interesting. Mr. Oakey's ex- perience as a teacher has been of great service to him. His Text Book, if not the best of books, is a very good one." — Academy. " In the present work every combination of sounds ordinarily used is exhaustively treated, and thus we have a vast amount of dogmatic teaching As a book of reference this Text Book of Harmony is extremely valuable, it being well and clearly written, and containing certain special features which must commend it to all thoughtful students." — The Orchestra and Musical Review. PRICE THREE SHILLINGS. J. CURWEN & SOJSS. 8, WARWICK LANE. LONDON. E.O BY THE SAMS AUTHOM. TEXT BOOK OP 60DNTERP0INT. SIXTH EDITION, ENLARGED. Containing over One Hundred Examples. Intended for the use of. Candidates for Musical Examinations, and for other Students. Contains clear and succinct rules amply illustrated by consistent examples. FROM THE PEEFACE. The success of the work as issued in its original form has far exceeded the most sanguine expectations ever entertained by the Author when it was first published. The concise form of the informa- tion which has proved so acceptable in the past editions is retained, as far as possible, in this. It will be found, however, that the rules are mostly amplified, and that in several cases they are supplemented by paragraphs in smaller type, that contain explanations of the general or special application of the rules. Besides the enlargement of the text, the number of examples is considerably increased for more ample illustration of all the various species in two, three, and four parts, and of combined counterpoints. There are also now included specimens, for which there was formerly no room, of counterpoints in triple and in compound times, and of five, six, seven, and eight-part counterpoint. " Mr. Oakey is the author of one of the best practical treatises on Counterpoint ever written ; the great merit of the book is that it is a small book containing the fundamental principles of :\a art, and not overloaded with an immense number of rules." — •* Orchestra and Musical Review. Price TWO SHILLINGS, Cloth. *.* All the musical examples are in both notations. J. CUUWEN & SONS. 8 & 9 WARWICK LANE. E.C. BY THE SAME AUTHOR. FIGURED BASS. From the Preface. The design of this short treatise on Figured Bass is not only to explain the main features of the system, but to show its application in all the various combinations and devices found in modern harmony. While this is the main subject, this work will also serve as an epitome of harmony, and its examples will furnish supplementary illustrations to the existing works that deal exclusively with this subject. From the "Musical Standard." Mr. Oakey's Text Books on Harmony and Counterpoint have long been accepted as models of their order ; and this latest work from his pen is a welcome addition to the limited number of really good books for students. Mr. Oakey treats his subject with the student's needs ever before him, and this little book, though small in compass, deals with a difficult subject in a broad and comprehensive fashion. A readable and workable book on figured Bass was much needed, and this work supplies that need fully and well. It is just what a text book on a by no means easy theme should be, clear, lucid, and simple, and yet so complete as to altogether cover the ground. From the "Music Trades Review." Not only are the rules of figuring clearly given, but many interesting remarks are made respecting the complexities of figuring modern harmony. This treatise gives multum in parvo. From the Nonconformist Musical Journal. The subject is treated in a simple and plain manner, which students will fully appreciate. Price, limp cloth, One Shilling. * # * All the musical examples are given in both notations. J. CTJKWEN & SONS, 8 & 9 WAEWICK LANE, E.G. THE MUSICAL HERALD: A Journal for the Professor, Amateur and Student of Music, With which is incorporated the " Tonio Sol-pa Reporter." Published on the 1st of each month, price '2d. Annual Subscription, post free, Ss. The "Musical Herald" is one of the cheapest of the musical papers. 1 t circulates over the whole of the United Kingdom, in Canada, the United States, Australia, India, South Africa, New Zealand and many other parts of the world. 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