DORIAN and PHRYGIAN Reconsidered from a non-harmonic point of view. by -:- A. J. HIPKINS, F.S.A. Printed by Novello & Co., Ltd . ^ for Private Circulation, ffeLondon, 1903. A'V^ ^ » V -v» t'« £ i « A.o Vrt V ■. ,Av -■ V'.- ; y;*V;V V ■ -^ • , Z 1 ‘ •J'C ' ■» A?; 3 ^ ■' *’:-*> ^ % 4 * .V- <> ■ >. ’* A- . i ■‘ V "^^ • • • , . *'A’ ■ ’ ' i - . ■ ■■ '^. . isJ *'■ '■' .•.'V'' V. 'A* -^^7..'* , .A S*^ ♦ ■' 1 » F‘-i ;«■■■. 'i-. » DORIAN and PHRYGIAN Reconsidered from a non-harmonic point of view. by -:- A. J. HIPKINS, F.S.A. /\>V/VA.>V>V/V>NyN/V/VyN/^/N/VA, Printed by Novello & Co.^ Ltd.^ for Private Circulation^ London, 1902. V ML 3 ^ 12 - Digitized by the Internet Archive in 2016 4; https://archive.org/details/dorianphrygianreOOhipk DORIAN AND PHRYGIAN Beconsidered from a Non-harmonic ])oint of view. The Greek word Harmonia is usually rendered by scale or mode. Either word may explain a succession of musical notes fitted and complete in itself within the consonance of an octave, although the order and measure of the intervals may be arbitrary. The foundation of a scale is instrumental, not vocal ; it comes from the stops on the fingerboard of a stringed instrument, or the lateral holes in a pipe. Vocal music in its origin must be referred back to speech, to accent and modulation of the voice, the development of sustained voice sounds, to synthesis rather than to analysis, with freedom in the dimensions of intervals. Scale is used pre- ferentially for a recognized succession of notes, but mode for their characteristic measurement. No natural order is to be predicated for either. The Dorian, or Hellenic, mode was historically a Lyre accordance, tetrachordal from the grasp of a previous finger- board, and usually septimal in harmonic character; the presumed fingerboard instrument, or Pandoura, having its congeners in the Egyptian Nefer and Babylonian Tanbour. If the old iEolian mode was the same as the old Hypo- Dorian, it was closely allied to the normal Dorian. The Phrygian, an Asiatic mode, was based upon the position of the lateral holes of the Aulos, as is well-known a pipe instrument blown with a reed ; and the stopping thereof, in its nature, Hexachordal rather than Tetrachordal. The Ethos, the aesthetic effect of the instrument, was in its character approximate to that of the Scottish Highland Bagpipe, a survival of an Eastern scale. The lower tetra- chord of the Makat double pipes (b.c. 1100) discovered by Mr. Flinders Petrie in the Fayoum, is, as I heard them played with an Arghoul reed, similar, although with some difference in the succession of the characteristic intervals. Dorian and Phrygian according to Aristotle were entirely different in character, and being so would be of separate 4 DOKIAN AND I'lIRYC^TAN. origin and incommensurable. Not as tlie mere shifting of a Diatonic Minor mode as is generally accepted, a modal system Dr. Monro attributes to Ptolemy. The Greek names of the Lyre octave followed those given to the strir^gs of the instrument, due to their relative position and proximity to the player. Our letter notation can express their order equally well ; but neither can inform us as to their measure or pitch. The Greek names of the Aulos notes, excepting the fundamental note and its octave, which were apparently in early times not used, bore the national modal names corres- ponding to their use as pitch prompters for the reciting notes required. Be it remembered, the Greek intervals, as in all non-harmonic Eastern scales, were steps varying in measure according to the system accepted; never the mental analysis of common chords as in the Harmonic intonation proper to our modern — particularly our vocal, music. Pythagorean ratios outside the Fourth, Fifth, and to some extent, the whole Tone, were practically non-existent, or were, at least, very much restricted in the Greek music of the Classical period. It can be shown they ultimately made their way hy the greater ease of tuning with Fourths and Fifths. In the study of Classical Greek music it is essential to put aside our cherished ideas of chords and tonality of scale ; of sharps, flats, and key relationships. Also the modern chromatic scale which had then no existence outside theory. To recognise the value of quarter and three-quarter tones ; their fitness for musical expression and pleasure to the ear. To appreciate septimal intervals (the ratios of f, f and also f), and to regard scales rather in descending than in ascending- order. To estimate tuning as done by ear mainly, and not by experimenting with arithmetical ratios, which would be difficult to render with anything near precision, since their appeal is more to the mind. Westphal went wrong by his insistence upon modes derived from the Major Common Chord of which the Greeks knew nothing. We must be careful, as I have said, to avoid the false lures held out by modern scales and systems. The greatest care can hardly prevent the enquirer from tripping, so fascinating are apparently obvious comparisons. My own DOlUAN AND PHRYGIAN. O study of this perplexing subject is due to the imperfect presentment of the Greek modes, in a Lecture “on the Musical Scales of Various Nations ” by the late Dr. A. J. Ellis, read before the Society of Arts, London, 1885 (published in the Journal of the Society, No. 1688, Yol. XXXIII, with a subsequent Appendix), in which I had some share, and we were both content to follow the too easy tabulation of Helmholtz. As concerns myself, my position is that of a simple enquirer accredited with some knowledge of music and of musical instruments, and as having been associated with Ellis in the examination and comparison of several Eastern non-harmonic scales in which we were assisted by skilled native performers, With Plato Greek musical history, apart from tradition, may he said to begin. The modes quoted in the dialogue between Socrates and Glaucon are six in number, and their names are national or tribal ; Dorian, Ionian, Phrygian and Lydian. There is no tetrachordal, hexa- or heptachordal definition. Two are described by Glaucon as high and plaintive ; the mixed and the tense Lydian (tense obviously referring to the Lyre), he adds “and such like.” These Socrates excludes from the use of the guardians of youth. Two are soft and convivial, the Ionian and the Lydian which are called slack (again referring to the Lyre). The Dorian and Phrygian remain as answering to the requirements of Socrates for sober enjoyment, courage and temperance. In the Laches, Phrygian is excluded as not being Hellenic, the Dorian alone answering that requirement. There Plato rejects Ionian, Phrygian, and Lydian. It is clear the accepted order of the Greek modes, analogous to the Church Modes ; defined by the note from which each starts, of which there are seven, changing the intervals as they occur in the octave, as may be done on the white keys of a piano, will not explain Plato’s characterisation. In this order the Dorian octave is at the top ; the Phrygian a tone lower, the Lydian another tone lower ; the Mixo-lydian a semitone lower than the Lydian ; the intervals supposed to be of Pythagorean dimensions, 2*04, equal semitones and Leimmas or remainders, E. S. 0‘90. Westphal, possessed, as I have said, by the Major Common Chord, discovers a Byntono-lydian derived from the major I) DORIAN AND PHRYGIAN. Third of this chord, a wliole tone helow the Mixo-lydian, and, by analogy, the Mixo-lydian is, according to him, referable to another major Third derived from the Ionian or Hypo- phrygian ! No one should read Plato’s description with attention and accept such topsy-turvydom ! Monro’s identification of these modes with the so-called Transposition Keys, a solution I had arrived at myself before I had his authority to support me, is reasonable and, I believe, in the main correct, but until Proslamhanomenos was added, we can hardly talk about keys. The Tonal system was incomplete. For convenience of grouping, key signatures of fiats have been chosen to define the order of the Greek scales and their pitch, starting with the Lydian as D minor in the descending form. This answers very well for a chain of Fourths up to E flat minor, which serves for the Mixo- lydian, only the pitch is too high, being in the f — f ' octave, for average male voices which we may take as now to have been baryton. If we accept an f — f • octave we shall find the Dorian Mese, at the French Diapason normal, a minor Third too high. At that pitch d — d' is nearer the mark. The difference from the usual letter notation, e — eh is, of course, a whole tone. By the transposition from tenor to baryton the Dorian Mese is equal to our note g, the fourth space of the bass clef. I now prefer to regard Plato’s Harmoniai as named from melodic systems comprising simple reciting notes ruling the nome, melody-type or chant, while inflections and cadences appropriate to the verse from a sense of beauty clustered round and adorned it ; the nomes could not have been unlike the Indian Kagas, and we may suppose a similar origin and use for them. From the nomes by a process of evolution and definition came the modes, still with much freedom, until the mechanical rigidity of instrumental construction, of wind instruments stopped with finger holes, and stringed instru- ments with fingerboards, forced musical practice into well- defined scales. As intervals in Non-harmonic scales — and in ancient times there were no other — were steps, not mental references to the analysis of common chords, there was a liberty of choice comparing with that observable in some Eastern scales of the present day. I must insist upon the DORIAN AND PHRYGIAN. 7 instrumental origin of all scales; vocal music was at first musical speech — vitalised as poetry, and culminating in the Lyric which is pure emotion but too indefinite for system. Of what I venture to put forward I dare not assume proof ; I offer my suggestions for what they are worth. If they are set aside I shall be content to have tried to solve a problem as many have done before me without success, hut with the hope that I may have held out a clue to a more fortunate enquirer. Let us therefore assume the Dorian and Phrygian modes allowed by Socrates to be practically the notation or order of simple melody types with reciting notes, let us say G, for the Dorian answering to Mese, and A, for the Phrygian note at about French pitch. The G, would be appropriate to a baryton and give the impression of manly character. The Phrygian A, from the higher pitch, would be more exciting, yet without passion, or this note would not be used nowadays for the monotone of our Cathedral Services. Assuming the relative order indicated later by Aristoxenus we shall find the pitch-note of the Tense or Syntono-lydian about b, and the Mixo-lydian c', above which note ordinary male voices could not bear a continuous strain. These would be among the tighter strung notes of the Lyre; the highest note, NHe; in this scheme of pitch answering to d*, was rejected for vocal purposes, although used in the Krousis or instrumental accompaniment. The slack lower notes were of easier vocal production for reciting ; according to Socrates their effect was soft and convivial and therefore not acceptable to the guardians. The slack Lydian following my scheme of pitch would have for a reciting note, the f sharp, or a note between f sharp and f natural of the upper region of the bass clef : the Ionian, e. These would be for the symposium, not the theatre or public assembly. Such notes were more suited for the aged who had to resign the tones and accents of vigorous manhood. It will be seen that Glaucon contrasts the slack with the tense Lydian ; the one is too low, the other too high, as is also the mixed Lydian ; I cannot say what characterised the Lydian modes, no hint is given by our authorities except that the Lydian was allied to the Phry- gian, although differing from it as is shown by the three-part 8 DORIAN AND PHRYGIAN. nome of Sacadas of Argos, rather than the Dorian ; the Mixo-lydian may have had certain characteristics from both, later defined in form by Lamprocles the Athenian, though not in pitch. It is possible the high d', the note above the Mixo- lydian pitch note may have been alluded to Glaucon when he added ‘‘ and such like,” referring to another too high mode. But this note as a pitch note would be extreme, not to be maintained by an average voice for any length of time, even with the help of cadences. It would offend the temperate Greek, opposed in his iesthetic nature to mani- festations of excess. The modern Opera reflects this voice distribution in Plato : drinking songs are given to the bass voice (Der Freischiitz, Hamlet), those of manly and noble character to the baryton, while the high tenors are the exponents of love and grief (La Favorita, Trovatore, Tristan). With Aristotle we find a difference of character distinctly asserted between the Dorian and Phrygian, the other scales, he says, being mere varieties of these two. The Dorian and Phrygian together were the mean between tense and slack, but it is clear from Aristotle that they differed in form, that is to say, in the measurement of the intervals, as might be between a tetrachordal Dorian species carried on to the Lyre from a fretted fingerboard instrument, and a Phrygian Aulos, a wind instrument with lateral holes, the intervals of which would be mainly determined by their spacing for the convenience of the fingers. On the one hand we have the evolution of a septimal scale, the soft or malakon Diatonon, on the other a bagpipe scale with three quarter tones, a tradition of which is preserved in the Homatoji'’ of Ptolemy. It is possible the divergence between Dorian and Phrygian had been lessened in Plato’s time by the occasional employ- ment of Lyre and Aulos together ; modifications in tuning the one and by using the lip power which the player could call upon with the other, would end in a kind of temperament which the ear would accept as tolerable, but hardly the Pythagorean tuning with which the Malakon and Homaton accordances had no direct relation; nor had the Enharmonic. The Pythagorean was a theoretical, not empiric, non- harmonic system. But it must be remembered as early as DORIAN AND PHRYGIAN. 9 Plato, Dorian auloi are mentioned as well as Phrygian and Lydian, and an Aulos, the invention attributed to Pronomus of Thebes, on which all three modes could be set. This is, however, a tradition mentioned by Pausanius. The Aulos had, in Plato's time, the greater number of notes. Aristotle thinks Socrates should not have left the Phrygian with tlie Dorian because, being the same as the Aulos, it was necessarily orgiastic and emotional. The Dorian appears first in the archaic sacrificial Spondeiasmus based upon the soft malakon septimal Diatonic scale. By the rejection of the characteristic septimal interval came the old Enharmonic, without the quarter Tones. Somewhere between we may place the coloured chromatic varieties. Let us try to elucidate this development by presupposing a Pandoura, a fingerboard instrument with or without frets, with which the grasp of the hand could conveniently stop the interval of a Fourth ; we will presently consider the smaller intervals. The Lyre would gain pre-eminence over this early Pandoura by its greater power, as in Hellas music was an open-air art. With the Lyre the reciting note, eventually called Mese, as the middle note of a mode or scale, was taken as the measure of a Fourth ; it was twanged by the thumb of the right hand ; the next lower note, Lichanos, was twanged by the index, the fore-finger, which determined the Diatonic, Chromatic, or Enharmonic species. This was the true Hellenic. The Aulos, of nearly equal authority, was derived from Asia Minor. The note of the pipe itself does not appear in early days to have been used ; it may have been false in relation to the finger-hole series, but the six holes had national, modal names attributed to them which gave in succession notes in something like bagpipe order ; the characteristic interval being a Third, which is neuter, neither major nor minor. ^ I do not assert that Egyptian or Babylonian peculiarities of scale were directly transferred to Greece, but the hole-boring of pipes is likely to produce results everywhere the same or nearly resembling. The 1 “ Keclierches sur VHistoire d(' la gamme Arabe," J. P. N. Land, Leyden, 1884, p. 50. “ Les flutes cVal Farabi '^ — the “ wosta ” of Zalzal. 10 DOmAN AND DHKA'GIAN. difference between Lyre and Aulos may help us to compre- hend the distinction drawn by Aristotle between Dorian and Phrygian. With Aristoxenus we are near the end of the great classic period ; the scale-building principle theoretically, if not practically, advanced. His knowledge was in advance of his time, and his prophetic gaze, in the twelve-note scale of equal intervals illuminated the bed-rock upon which J. S. Bach built. But the exact measures of the concurrent musical systems were not then accurately defined. He says, “ Musicians arrange their keys very much as the different cities regulate the days of their month,” that is to say differently, and he gives two scales, one of which appears to be a Lyre scale with an Aulos note added ; the other is certainly an Aulos scale having no relation to any Lyre scale whatever. The first is Diatonic with tones and semitones which appear to be Pythagorean. Following the text as given by Monro, the Hypo-dorian is a tone below the Dorian and the Phrygian a tone above it. The Lydian is again a tone above the Phrygian. The Mixo-lydian is unexpectedly inserted between the Hypo-dorian and the Dorian. Finally an Aulos note, of later introduction, the Hypo-phrygian is placed lowest. If it were not for the Mixo-lydian this system would be a simple one of five notes ascending, Parhypate, Lichanos, Mese, Paramese and Trite. But even Monro has not succeeded in explaining the intrusion of the Mixo-lydian note. The later Hypo-dorian had not as yet appeared with either Aulos or Lyre. About the second system there can be no doubt, the national names of the reciting notes follow the holes of the Aulos, then six in number for the six available fingers ; thus, and in ascending order, Hypo-phrygian, a f-tone interval, Hypo- dorian, another |-tone, Dorian, a whole tone, Phrygian, another f-tone, Lydian, again a f-tone Mixo-lydian; equivalent in their order, but not in measure to Parhypate, Lichanos, Mese, Paramese, Trite and ParanHL NHe, as already said, was not recognised as a vocal note. Accommodating this Aulos system to Ptolemy’s Homaton, and adopting A = 482 as an easier number for simple calculation than A *435, we may adopt this vibration number for the reciting note of the Phrygian scale. DORIAN AND rilRYOIAN. 11 to S t- rt o 00 173 • _b> 00 10 CD § 9 ^ rH t- 1 -^ 'Cfi 10 (n 00 o3 , — . rP <© c3 pH •+= X rrt G ^ 6 ^ P.a 0 ‘rP :2 0 H ^ 0 rO «D P 05 S CO P 2 -f cS C« p S « 00 K eS • H ‘£1 00 § GO P 5 Q CO O Cti ^ (X» >p CO 10 ^ CO 10 CO &D _u >7. ^ 01 A 6 ffi TlH O 00 Ti 00 S 2.^ !►« t; K*~> H w H O rt^ GO CO bD .2 OQ O & cc d o3 <0^ o bD c3 pH t>^ > o3 ^<0 d CO o d c5 ^ X X P G Ttl o ® CO S <32 O ^ ^ -s .S 2 b- cp d 02 p ce ^ G H ■£ CJD ^ ^ P G o G ^ > 02 G 2 CO ^ ^ P ^ 2 ^ ^ rp c3 O 02 G^ ^ d p CO p- G i g i -2 bD G O - n3 p a .P G ^ "x cS X o ’2 o -t-3 c5 • ^ Q sP O X CO O CO X G ^ o P X G fH ^ -2 P3 o O g. ^ i-P ■ 02 ^ G PG p o S ^ Ph &) i "o c3 5 o .2 Ph I ^ G ^ ^ 2 rH G P rP G p Ph O 2 4:5 ^ 2 ^ o >. 4:1 2 ^ P3 ^ ^ bD ‘x .2 pm -(J o ce pG Ph 2 .2 G P ■^ _| le >.^ 2 M .. '-P cG o 3 TG G p 02 t> P X ;h ® P G X M np P c3 G P '-C ^ 2 P PG G 2 r 2 ^ p -G cr* G W .2 5 p T ^ X p G ^ II X G •2 ^ o "p ^ o ^ rw G r-H -M P 2 o :2 4= -+4 c3 c3 G Ph G G > >. r-H G -— ! G 0 01 00 GO • d C/2 |l § W CS rp ncS P c3 o Ph G vP ZD ^ G P ^ O ^ 'a I G P X G g g 2: -^^ "g 2 ^ Jh G Ph <32 - S .a w 12 DOllIAN AND PHRYGIAN. The Diatonic Scale had in the oldest tradition the first place, and in the so-called Instrumental Notation the unmodified letters are those from which, by change of position, the Enharmonic and Chromatic notes are defined. I do not limit the Diatonic genus to whole Tones and Leimmas — such a definition is inadequate to represent an order of notes that being neither Chromatic, nor Enharmonic, if not preceding the one and the other as we have reason to believe it did, was at least of equal antiquity. We have no distinguishing name for an order governed by the whole or the I septirnal Tone, but Diatonic. Let us first consider the S 2 ) 0 )uleias)m)s, the Libation nome, which from its sacred character was long preserved unaltered. We must go back to the fingerboard of the Pandoura to explain it ; the Lyre cannot. Marking a fret at f the length of the string and pressing upon it while twanging the longer section, produces the interval of a Eourth E.S. 4*98. Then halving the distance between this fret and the nut or capotasto, the new fret will give the septirnal whole tone ^ = E.S. 2*31. Halving this again we should find the Diatonic Semitone = E.S. 1*12. But an early scheme seems to have been adopted resembling that of the Tanbour of Bagdad ^ by which the string was divided into 40 equal parts, 10 of which were within the interval of the Fourth and convenient grasp of the hand. We have now the following available intervals, |g, the Fourth J = E. S. 4*98. From the nut E. S. *90, the Pythagorean Leiwma, or remainder when the Ditone has been found; |g = E. S. 1*82, the minor whole Tone, and = I E. S. 2*31, the septirnal whole Tone. The Greeks went no further than this halving and quartering expedient, their soft Diatonic or Malakon. In this way WestphaTs Diatonon Malakon or Spondeiasmos is easy to explain. Eclysis Ekbole E F (G) A Dieses 2 Or on the fingerboard : to E.S. 0 0*90 2-31 4-98 1 Land, Kecherches sur I histoire de la Gamme Arabe, p. 73. 2 Die Music des griechischen Alterthumes. Leipzig 1883, p. 32. ® F * represents F raised a | Tone. DORIAN AND I'lIRYOIAN. Extending this to a live-note scale we might compare it with a rationalised Javanese “ Salendro.”^ E.S. 0 2*31 4-98 7*02 9*69 12*00 Eatios i i i Y i Ptolemy’s Diatonon Malakon is this septimal Scale reversed, the e to being the ratio f = E. S. 2*67 in order to include the Minor whole Tone or E. S. 1*82. The septimal Ethon or character is unaltered. As late as Ptolemy the Diatonon Malakon was the prevailing scale with the Lyre and larger Cithara, or it was mixed with the Tense Chromatic, Chroma simtonoiif in the upper tetrachord. Monro, p. 85, gives these scales with some differences for which Ptolemy is responsible, but there can be no doubt about the general principle. The Chromatic Scale was also evolved from this fretted scheme, transferred, like the Diatonic, to the L}Te. Our authorities are late, but have the weight of tradition in their favour. Archytas, the teacher of Plato, according to Ptolemy, divides for his chromatic Pifknon the Pythagorean whole Tone E.S. 2*04, but Eratosthenes, circa 240 b.c., is more accurate in dividing the minor whole Tone E.S. 1*82, the Jg. Ptolemy himself, in the second century a.d., divides E.S. 1*82 for his Chroma Malakon ; Ptolemy’s Chroma simtonon dividing the septimal whole Tone E.S. 2*31 I should call a Diatonic scale. The Chromatic appears to have been restricted in use compared with the Enharmonic ; the Chroma Hemiolion and Chroma Malakon, as usually given, seem to be geometrical variants approaching the Enharmonic ; I cannot offer an explanation for them, but I have shown them with the Enharmonic and Diatonon Malakon on four pianos tuned under my direction in a Lecture given by Mr. C. F. Abdy Williams at the Eoyal Academy of Music, on the 27th of February, 1895. The impression upon the audience was certainly favourable, especially when the scales were heard in descending order. The basis of the tuning was Equal Temperament which Aristoxenus might have approved of; the width of the intervals being determined by Fourths and Fifths and with Tuning Forks four vibrations a second apart, ^ A. J. Ellis on the Musical Scales, etc., Journal of the Society of Arts, 27th March, 1885, p. 510. 14 DORIAN AND PHRYGIAN. of which i have complete sets. Thus that which Westphal (p. 82) deemed not possible was easily made understand- able. Adopting E.S. 1*82 = fg as the width of the Chromatic pyknon, we may follow our fingerboard in further dividing at f§, thus finding Parhypate at E.S. 0*90, leaving out the Diatonic Lichanos E.S. 2' 31 altogether. The Enharmonic Scale was, according to tradition, first discovered by this omission of the Diatonic Lichanos, but the transference of Lichanos to the semitone E.S. 0*90, and by a further bisection, Parhypate on the fg fret, came early into general and much admired use. The Enharmonic pyknon of Eratosthenes was E.S. 0*44 and 0*46. An alternative bi- section of the E.S. 1*12 Semitone which was the empiric finger stopping without frets, would give for quarter tones E.S. 0*55 and 0-57. Both the Instrumental and Vocal Notations were contrived to represent the three genera, the Diatonic, Chromatic, and Enharmonic. They could not be sung or shown on any instrument and must be accepted as a rational endeavour to provide for all transpositions, the notations being elastic in their application. For instance no difference is shown between Lichanos malakon and Lichanos suntonon of the Diatonic genus, or between the characteristic notes of the Lyre and Aulos. The so-called Instrumental is noted in an ascending order ; the so-called Vocal, a descending one. It seems more likely both these Notations were originally of vocal intention, to prompt the note suited to the words. Neither can have been older than the classic period because of the inclusion of ProsJamhajiomenos and the clear exhibition of the greater Perfect System, which points to a late inven- tion. That archaic characters were used proves nothing. It is most likely the krousis was an extempore accompaniment with improvised interludes. To note it down implies a progress in instrumental performance by which it obtained certain rights in relation to the vocal. The Enneachord or nine-stringed Lyre is indicated by the Vocal lettering, but unless there were means of stopping the Lyre to shorten the strings, it far exceeds the capacity of the instrument to render it without setting the tuning for the genus or mode required. DORIAN AND PHRYGIAN. 15 An all-important question is that of the tuning. Only the Pythagorean system could be tuned throughout by Fourths and Fifths, and this facility in practice must have led to its final general adoption ; but not until the old Greek love of quarter and three-quarter tones had died out. These irregular intervals could only be tuned from fretted fingerboard instru- ments, or a monochord, an inconvenient aid to stringed instruments, which besides could never have stayed long in tune. Habit and a fine sense of hearing would provide, in practice, a tuning that would satisfy the player, the poet and the audience, but the accuracy of the intervals of the movable notes would not be more sure than what we get from Asiatic musicians nowadays. And the Aulos, which was probably defined by Ptolemy’s Homaton would rarely be blown true. How nearly string and wind become reconciled by the Greeks we have no means of knowing ! They are very near in our modern performances, but the wind band of a Wagner Opera, especially the large instruments, will show the difficulty of a problem in which heat plays a prominent part. The Aulos would be rarely in tune with the Lyre unless it were by accident, and neither would coincide faultlessly with the ratios of the Arithmeticians. The recognition of the whole Tone E.S. 2*04 between the Fourth and Fifth became important for the systematisation of Greek music. As the Disjunctive Tone, employed to recast the Mixo-lydian Mode or to introduce Hyper-hypaton or Proslamhanomenos, it brought about Octave scales and with them a conception of keys and tonality essential for a complete musical system. A. J. HIPKINS. Kensington, 25th October f 1902.