THE INTERPRETATION OF GREEK MUSIC

I. INTONATION IN GENERAL Inadequacy of our Theory. To whoever may desire to understand the music of ancient Greece, I would recommend that he put away from his mind that sense of superiority which our progress in counterpoint, harmony, form and orchestration has engendered, and devote his attention to the shortcomings of our music, for they relate to those very matters concerning which Greek music has the most to teach us. Our music has come down to us from remote ages through the Greek system. The first stage in its progress was marked by the collection of a multiplicity of Harmonies and modes, not unlike those upon which the classical music of India is based. Of the diatonic scales, some were soft, employing septimal or soft intervals, and others were hard, employing semi- tones, and major and minor tones, differing among themselves in the order in which these intervals were strung together. The Greeks may have added to this collection. Their chief contributions to musical progress, however, were instrumental heterophony and the science of intervals. They were driven to the use of the former by the tyranny of the ' metrici.' Thus the long and short of Greek poetry led indirectly to the harmonic system of music, which is one of the main achievements of European civilisation. The founda- tions of musical science were laid by Pythagoras. The results of his labours were soon apparent in the classification of the enormous number of scales in use, the adoption of a musical notation based upon an intricate system of correlated keys, and the art of modulation. In the break-up of Roman and Greek civilisation, the subtle distinctions between the various Harmonies were the first features of the music to go under. Curiously enough, the innovations introduced by the master minds of Greece survived in the art of modulation, and the contrapuntal tradition. A new series of keys was invented. This degenerated, under the growing influence of keyed instruments, and the craze for unlimited modulation, into the musical freak of equal temperament, in which a scale, grotesquely out of focus, is set up as a standard and basis of theory. Players on the pianoforte and organ perform tempered music in tempered tones to admiring audiences. Orchestras are given tempered music to play, and are expected to find out for themselves without the guidance of an adequate theory, how to bring it into focus. Naturally enough, the Pythagorean or ditonal scale, which employs major tones only, and is for that reason the nearest thing in the hard diatonic to equal temperament, has an immense vogue. It is perhaps the ugliest scale that was ever put J.H.S.—VOL. XLII. K 134 E. CLEMENTS together. The Indians and Greeks combined a ditonal , for the sake of the contrast, with some other form of diatonic. There is no evidence * that they ever sang or played, as we do, in the ditonal scale. I think that we too would tire of it if it were not wrapped up in various ways and disguised by much modulation. The theory, notation and terminology of temperament are unequal to the task of interpreting the Greek keys and describing the Greek Harmonies. I propose to name the intervals with which real music is concerned in the simplest terms possible, and to make slight alterations in the accidentals of the staff notation. The theory of real music, treated from the standpoint of the musician, is a new science. Intervals. Of the names of intervals in the following table, some are new, such as those which include the appellation ' soft,' and the terms used to differentiate the varieties of the . I have seen the terms false fifth and false fourth applied, quite unnecessarily, to the diminished fifth and augmented fourth. As I use them, they point out a vital distinction. The ' soft' intervals are derived from septimal harmony, that is, directly or indirectly, from the seventh partial tone. The others can all be got from different combinations of the first six partial tones and the intervals formed /3 4 9\ by them. Thus the fourth from the fifth gives the major tone ( » -r „ = «)•

The fourth less the is the semitone ( = -=- j= Y>). The major

1 xl. -X • XV -J T -X ft 16 135\ ™ tone less the semitone is the residual semitone ;-!-re= -r^). lhe major third less the major tone is the minor tone ( r -r ^ = -_- J; and the minor tone less the semitone is the small residual semitone ( — -r ir. = ST)- The rough , one of the most important intervals in music, contains a minor tone and a semitone ( ^ X ,-~ = o_). If the major tone be subtracted from 32 9 256\ os -r o = ) (Jit o

1 The use of the ditonal numbers for space prevents my doing more than pre- the notes of the Lydian key, by late and senting a bald outline of the views I hold ignorant authors (such as ' Anonymus '), is regarding the history of music, no evidence, in my opinion. Want of THE INTERPRETATION OF GREEK MUSIC 135

TABLE OF INTERVALS FROM THE FIFTH TO THE SEMITONE c i n i n ne a Interval. Ratio. Interval. Ratio. n e intege r inte g th e aten t o t o th e Conten t

3 702 8 1. Fifth 2 13. Soft tone . 7 231 40 680 9 2. False fifth 27 14. Major tone 8 204 64 10 3. Diminished fifth 610 45 15. Minor tone y 182 45 16 4. Augmented fourth 590 32 f 16. Semitone . 15 112 27 135 5. False fourth 520 17. Residual semitone 20 128 92 4 6. Fourth 498 18. Diminished semitone . 256 3 243 90 9 7. Soft 435 19. Soft semitone . 21 7 85 81 20 8. Ditone 408 20. Small residual semitone 25 64 70 5 24 9. Major third 386 V 21. Small soft semitone . 4 28 63 6 10. Minor third 316 27 5 32 11. Rough minor third 294 27 12. Soft minor third . 7 267 6

To these may be added the simple quarter-tone or comma^.; cents 22 j. This interval results when the minor tone is subtracted from the major tone, or the rough minor third from the minor third, or the diminished semitone from the semitone. There are other varieties of ' quarter-tone,' but their importance is not such as to demand a special terminology. The quarter- tone in general may be defined as the remainder when one variety of semitone is subtracted from another. I propose also to use the term enharmonic in a special sense. If two notes differ in pitch by a simple quarter-tone I shall call the lower note the ' enharmonic' of the higher note. Thus, if the upper note in the interval of the fifth be replaced by its enharmonic, the false fifth will result. Accidentals: Hard. I take c t] as the enharmonic of c tj, and c tj as the enharmonic of c C|. I distinguish the sharps in the same manner, using the signs $, JJ, Jf, and for the flats I take 4-, -k an(l ^- In *^e matter of tuning, pitch C will be c" tj. The table which follows shows how the notes are con- nected by strings of just fifths; separate signs for the different octaves are omitted, being unnecessary.

2 Intervals 7 to 9 are all varieties of the major third. 136 E. CLEMENTS

ENHARMONIC PROGRESSION

1st string. 2nd stringstring.. 3rd strinstring 4th string, aft a» aft dtt g« °tt f ft f J+ ffc 1 B 1 tt b* H etj e^ alj q dh a gtdh] gfi

b=k b^. bb e 4 e -k e b a=k a -k ab d-k db g-k gb c -k cb f 4 fb

The ditonal scale, being built up from fifths only, will take its notes from one and the same string. Hence notes of the same string will give the following intervals,;—the fifth, fourth, ditone, rough minor third, major tone, diminished semitone. If the semitone or minor third above a given note be required, it will be found in the next higher string; the major third will be found in the next lower string. The note which is a minor tone above a given note also belongs to the next lower string. It may be observed that the low sharps, (ft) belong to the first string, the low naturals (tj) to the second, and the low flats (-k) to the third; the ordinary sharps (#) belong to the second, the ordinary naturals (I}) to the third, and the ordinary flats (b) to the fourth. We can manage to dispense with high flats, but will on some rare occasions require three extra low flats (kt). I think the following progression by semi- tones is worth the space it occupies, as it is easily memorised, and when grasped makes the whole system clear. The skhismatic progression is indispensable. The skhisma is the difference (approximately 2 cents) between the major thirds and the nearest approach to that interval to be got from a string of fifths.

386 - (5 X 1200 — 8 X 702) = 386 - 384 = 2. THE INTERPRETATION OF GREEK MUSIC 137

PROGRESSION BY THE JUST SEMITONE ,-5 )3 \15/ Strings 1. 2. • 3. 4. f # gB att b h c (SJ gtt a^ bb c J( d t| e b f« gQ ab aft btj c t; d b g£ atj b-K ct? H J h L f b

C t] d -k f b g-fet

PROGRESSION BY THE SKHISMA String. i- • a8 dtt 2. aft dftgJt cj{ fft bt) etja 3. ftt bH eH at} d^ g^ c^ ft] b^ e^ a^ d^ g^. c-fc. f^ 4. gbcbfb last table teaches us that, for all practical purposes, a high sharp is equivalent to an ordinary flat, an ordinary sharp to a low flat, and a low sharp to an extra low flat.

Accidentals : Soft. The hard minor seventh, a discordant interval, such 2 9 16 as c t] to b -£», or g ty to f tj, is the octave less the major tone (rvj = ^; cents 996). When this interval is flattened to a certain point, it is resolved into a 7 rich soft semi-consonance, without beats, the soft minor seventh, j, cents 969. In the notation, we shall mark the relationship between these intervals by a similarity of sign, and draw attention to the septimal origin of the soft minor seventh by using the figure 7. The soft counterpart of b -^ will be b -^. 7,

3 A low sharp is here followed by a low note takes the lower variety of accidental, natural, a low natural by a low flat, and so The varieties of hard diatonic are therefore on. If both are naturals or flats, the lower easily described. 138 E. CLEMENTS of b b, b b7, of d 13, d t)7, of f % f {{7. In the chord of the seventh g t] b t) d t; f 6, the root, fifth and seventh belong to the same string. It is therefore a matter of extreme simplicity to discover a note which is a soft tone below, or a soft minor third above a given note. For example, a -^.7 is a soft minor third above f fyan d d b 7 a soft minor third above b b. Suggestions for a Keyboard. The niceties of intonation with which we have to deal need not arouse any misgiving. One need not have a phenome- nally good ear to learn to detect major tones, minor tones and soft intervals. I have known an uneducated Indian girl pick up in a very short time the soft intervals of some of the rarer Indian ragas, and sing them with accuracy and without the slightest hesitation. When a European audience rewards a singer or soloist on the violin or 'cello with rapturous applause because of the exquisite feeling he has shown, the secret of his success is to be discovered in the felicity with which he has (perhaps unconsciously) managed his quarter- tones and other intonational nuances.4 Gifted musicians constantly employ these shades of meaning. My own limited experience further leads me to the opinion that the more highly educated and trained the performer the less sense of harmony does he exhibit. The best way to train the ear to detect real intervals is to have an American organ constructed with seventeen notes to the octave, to arrange suitable music for it, and to familiarise one's self with different scales. I suggest the following keyboards and tuning, the one on the left for European music, and the one on the right to render the extant specimens of Greek music accurately intoned.

I. II.

EUROPEAN KEYBOARD GREEK KEYBOARD 1 : aw i i s ck,|«U, b

The extra keys may be coloured red; they should be raised above the black keys and should be placed sufficiently far back to allow of easy access to the black keys. It is possible to place seventeen vibrators with their action side by side without widening the octave unduly. These keyboards will present no great difficulty to the player.

4 I have often heard really musical soloists jodeling for two voices, I have heard it in indulge in septimal harmony. In Swiss the lower part. THE INTERPRETATION OF GREEK MUSIC 139

TUNING METHOD (WITHOUT BEATS) I. II. Fifths from c I5 (1) up g ^-d ^—a b^ (1) up g d.-d b-a tj (2) down f Q-b J^-e -k.. (2) down f H-b -K-e Major thirds from cb, (1) up e u- (1) up e Ij. (2) down a b. (2) down ab. Fifths from a b (1) up e b-b b-f tt. (1) up e b-b b. (2) down d Nb- (2) down d b-g \). Fifths from e t) (1) up b up b tj-f ft-c \ (2) down a The owner should learn to tune the instrument himself. Vibrators will not keep in tune for long ; and in real music everything depends upon accuracy.

II. GREEK INTONATION Preliminary. No one can tackle the Greek notation with any chance of success unless he makes a preparatory study of the structure of scales. Pythagoras was the father of this branch of science. Other philosophers could devise no better method than to lump together all the scales they knew and guess what equal division of the octave might produce all the notes required. This method was followed in ancient India. The number guessed was 22. The octave was conceived of as consisting of 22 srutis, of which 4 went to the major tone, 3 to the minor tone and 2 to the just semitone. I mention this fact as I find the sruti figures convenient for the brief description of true diatonic scales. In Greece, musical philosophers thought the tetrachord the most useful instrument for the classification of scales.5 They divided their into three genera, the enharmonic, chromatic and diatonic. Aristoxenos was a prolific writer who has been extensively quoted by later authors. He scorned the application of numbers to music.6 He preferred his own slipshod method of guesswork. Like the rest of the Greeks he thought in terms of the E mode. In order that what he says on the subject of the three genera may be better understood, I give the typical tetrachords in staff notation—•

I §, 1 a b ^ p ENHARMONIC CHROMATIC DIATONIC

5 A scale might take tetrachord X fol- xx, yy, xy, yx. lowed by tetrachord Y. Thus two tetra- 6 Dr. Maeran's Harmonics of Aristoxenos, chords might explain four scales, namely, Oxford, 1902, p. 189. 140 E. CLEMENTS The two intervals between the hypate and the lichanos were termed the pyknon; the hypate was the barypyknos, the parhypate the mesopyknos, and the lichanos the oxypyknos. The hypate and were 86yyot eo-T&rre? or invariable tones and the parhypate and lichanos Kivovjxevoi, that is of course having regard to the construction of tetrachords. Aristoxenos gives one species of enharmonic, three chromatic, namely syntono-, hemiolio-, and malako-chromatic, and two diatonic, the soft, malako-diatonic, and the hard, syntono-diatonic. He tells us that the enharmonic pyknon contains two enharmonic dieses. He estimates elsewhere that the enharmonic diesis amounts to one fourth of the difference between the fifth and fourth.7 The enharmonic pyknon gives a lichanos a half tone above the hypate. He describes no other enharmonic tetrachord. He lays down that the lowest chromatic lichanos is one-sixth of a tone higher than the enharmonic. He also informs us that the tendency in his time was to degrade the enharmonic into a variety of the chromatic by widening the pyknon (Harmonic, i. 25). (Harmonic, i. 14) describes a number of tetrachords by relative string lengths. The enharmonic he gives may be represented thus g tj, a -^.7, a [>, c p. In such a scale, melody would naturally fall into some such figure as g fy a b, ctj, a-p. 7, gt}, the intervals being semitone (y~), major third [-rj, soft ditone 9\ /27\ " =•) small soft semitone L . I have not space to discuss the rest of Ptolemy's scales. The inference to be drawn is that the enharmonic pyknon consisted of two intervals, semitone, quarter-tone,8 in that order, amounting together to a just semitone; the chromatic contained two , and the diatonic a semitone followed by a tone. The Diatonic falls into two broad classes, the soft, which employs septimal harmony, and the hard. The latter includes the ditonal and the True Diatonic. The True Diatonic is made up of three major tones, two minor tones and two just semitones. There are five varieties in common use in our own music. They were also contained in the Greek system of keys, as I shall show. Other forms of true diatonic scale are possible. As we think mostly in terms of the major scale, I give the five scales in that form. In order that the scales may be the better compared on the first of the two organs above described, I give two examples of each. The position of the false fourth or fifth, which is an important factor in the harmony, is shown by brackets, and the sruti figures are given below each scale.

' This is the major tone. The diesis of s According to the classification herein Aristoxenos was a conception of no practical followed. ' Quarter-tone ' is here used in its value. general sense. THE INTERPRETATION OF GREEK MUSIC 141

TRUE DIATONIC SCALES

COMMON CHORDS

I. Ionian Scale. (2 Major, 1 Minor.)

4 3 2 4 4 3 2 4 3 2 4 4 3

II. Just Major Scale. (3 Major, 2 Minor.)

4324342 4324342

III. Aeolian Scale. (2 Major, 3 Minor.)

3424342 3424342

IV. Dorian Scale. (I Major, 2 Minor.)

3 4 2 3 4 4 2 3 4 2 3 4 4 2

V. Scale of Raga Kanada (Indian). (1 Major, 1 Minor.)

4 4 2 3 4 3 2 4 4 2 3 4 3 2

In our music, diatonic passages of any length rarely remain faithful to one form of scale. Enharmonic changes are the rule rather than the exception. An example of Scale I is the opening theme of Tschaikowsky's Seasons—Jtily; of Scale II, the first theme of Beethoven's Pastoral Symphony; of Scale III, the main theme of the Andante from the fifth Symphony. Our Minor (descending melodic form) is generally in Scale III. IV and V are found in passing modula- tions, more especially the former. The fifth Symphony of Beethoven—-first phrase in octaves—seems to me, as played, very like No. V, A mode. I conclude this subsection with a note on the subject of modes. The C mode may be taken in Scales I, II, or III. IV is used when a passing modulation is made into the supertonic minor. I and IV suit the D mode, both fourth and fifth coming out true, but I is preferable as IV gives what is very little else than a variety of the minor mode. The oriental D mode is almost always in Scale I. 142 E. CLEMENTS The E mode may be taken in II, III, or IV ; its ethos varies from sweetness to strength in that order. The same remark applies to the A mode which may be taken in Scales II, III, IV, or V. Scale V gives an extremely rugged and manly scale, very popular in India. The G mode is best in Scale I, and the F mode in Scale II. The B mode is merely a variety of the E mode, and need not be discussed separately. In harmonising the modes, if he wishes to preserve their purity, the student must avoid spurious concords. No common chord which contains either a false fifth, or a ditone, or a rough minor third, is permissible. The ditone may be replaced chromatically by the minor third, the rough minor third may be replaced chromatically by the major third, or, in suitable positions, the third of the chord may be omitted. The ditone, or rough minor third, or the corresponding sixths, may occur between passing notes.

The Introduction of Alypius. The Introduction of Alypius is the only comprehensive guide to the Greek notation extant. It is a fragment of uncer- tain date. It purports to exhibit the whole range of keys, that is to say fifteen, in the diatonic and chromatic genera, and six and part of three others in the enharmonic. In the first key, the Lydian, in the chromatic genus, four of the notes which mark the distinction between that genus and the diatonic are crossed out. The first thing to notice is that the enharmonic, whenever exhibited, is identical with the chromatic. The second is that all the keys in all the genera follow the terminology of the E mode. It is the pyknon from the hypate to the lichanos in the E mode tetrachord which is changed to mark the genus. Nevertheless, the parhypate suffers no change in passing from one genus to another. Alypius has therefore not only confounded the chromatic with the enharmonic,9 but has likewise, in his enharmonic keys, confounded the parhypate with the lichanos. Bellermann worked out the order of tones and half tones in the diatonic keys. The question which is still unanswered is—what was the order of major and minor tones? The amazing opinion of Bellermann and Westphal that the Greeks were well acquainted with equal temperament is based upon no evidence beyond a stupid passage from that unscientific writer, Aristoxenos.10 As regards pitch, Bellermann makes the Lydian key start from D. I prefer C, as it simplifies the notation, and gives a much more comfortable compass to the extant compositions. The keys are in what was known as the Greater Complete System. The section called the synemmenon, which I have enclosed in brackets, served as a modulatory bridge between each key and the next. The Hypolydian key and all the keys between the Lydian and Hyperdorian are of the same pattern. The paranete synemmenon and trite diezeugmenon in these keys are distinguished by different signs, although, at first sight, they seem to stand for the same note. Herein lies the clue to the Harmony. No other scale will fit into the scheme except Scale IV. When that scale is applied to the keys named, the whole notation of the diatonic stands revealed.

9 See the remarks of Aristoxenos above 10^Macran, p. 207. quoted. THE INTERPRETATION OP GREEK MUSIC 143

THE DIATONIC KEYS Lydian—Scale IV—

vv 1 7 i R 4> c P M i o ru z E u-e-x M''II }rLFCn< VNZ flyher/yclicut — *Sca(& IV—

/v CUT< VNZ /• /n iv

ohk rVfia i —

39 7m TOM CPMI e He t-l/F U.OT Con <

7FHtTnM AHT l rtLDn <>N

M'A'H'T' i •Scale, IV — I tin

J)orScin. _ IV—

tTn OKH HAH TB*± fl EuJH/\ia K A > n< > N / \ -/ 7>y $khismatte Transhosition. .

»H- fi

J/yperabr/an —

V/ltTHOKH ZA* r B O'K'H' C\A N / Scale.M^ «/'

UMHHVTXTCOKnOK H 5Rh3HmCKA OKA > 144 A-eoliC\ AMKA Jfyperaeo/ian. - PCa/eM'

^* ^ m XTCOK I 2 A U-e-0' 0'K'l'Z'A' K'AVC'V

d. u. In-tmy i-vx. to I —

CMf= <|) C 0 T C O K I Z A FCK TCKA

CLU.LCJ;CV\A into pcate TT —

^

WH71XK0Z I Z K / Z A U-e-O'

Jfype-7-lon.lurL — • >J cate- in ^ p cede

lXCOl I Z EU-e-A u-6-o'^'i'Z'

Jf-ypolydiccn. — Scale 1V~ iad aW

H5 146 E. CLEMENTS The notation ignores the skhisma. No question of temperament is involved, as the Greeks never constructed an instrument to take the whole system of keys. Indeed, some of the keys were never used. I have made the necessary transposition at the most convenient point. Let us now turn to the so-called chromatic and enharmonic keys. Of these, the Hyperlydian, Hypophrygian, Phrygian, Hyperphrygian and Hypo- dorian, all of which are in Scale IV, make use of signs which we have already identified. These keys, whether designated chromatic or enharmonic, prove to be built up of tetrachords of the type c t|, d -^., d [,, ft). They are arranged in the order c t], d t>, d -^., ft}, the parhypate and lichanos having changed places. These are enharmonic and not chromatic tetrachords. The Hyperaeolian and Hypoionian enharmonic and chromatic, which likewise use signs already ascertained, give a chromatic scale, which may be represented thus :— btj, ctj, eft e t], i% gtj, gJJ, H The rest of the keys contain four new signs :— *f and its octave >.,and and its octave A. Alypius gives the instru- mental sign of the third of these as b. Aristides Quintilianus (Meibom. p. 21) uses .1, which appears, from the instrumental scheme below, to be cor- rect. An examination of the remaining chromatic keys on the lines already indicated easily establishes Y and N to be a !ft (skhismatic b 1&) aQd V and A to be d ^ (skhismatic e =feu). In the Lydian and Hypolydian enharmonic keys, Alypius takes e =fet and b =fe= as enharmonics of e \> and b |j respectively. He is followed in this by Aristides Quintilianus. The three manuscript hymns, in most recensions, use e -k. as enharmonic to e [>. Some recensions of the hymns to and , however, give A, which may be meant for A (e^)- In tne instrumental notes to the song from Orestes, ~\ (corresponding to the vocal V or e^) again appears. From the context, it is evidently a wrong note, being intended for e -^ (f). I think there is good reason to hold that the frame of the instrumental scheme (which see below) led the ignorant to suppose wrongly that e ^ and b =^ were the correct enharmonics of e t> and b t>. The truth of my interpretation is established not only by the versions it presents of the old Greek compositions but by the extraordinarily ingenious alphabetical arrangements here set forth :— THE VOCAVOCAL SCHEMSCHEME

CM25-BO ABTA EZH0I K

F7H

THE INSTRUMENTAINSTRUMENTAL SCHEMSCHEME (Sharp(Sharpss skhismaticallskhismatically changechanged intinto flats.)flats.)

\ 1 Z/-\ N / \ [u] i

CuD TL1

hxriHyfl 147 148 E. CLEMENTS It is evident from the instrumental scheme that the fully developed kithara was tuned to the ditonal scale. This was undoubtedly one of the many innovations brought in by the Pythagoreans. To them also must be awarded the credit for inventing the notation, and not to Aristoxenos. The bar of the kithara enabled the player to tighten the strings by any interval up to a full semitone. In India, the bina, which is the principal instrument, is tuned to a collection of notes based not upon any favourite scale, but upon con- siderations of convenience. The nuances, which transform the fret notes into the required scale, are obtained by" pressing hard upon the wire or drawing it to one side. The Pythagorean method was similar; the bar gave any note required. The adoption of the relative string lengths of the ditonal scale for the intervals of the Lydian key by late and ignorant authors, such as Anonymus u and Aristides Quintilianus, is therefore no longer a mystery, and the assertion that Greek music was founded upon the ditonal scale stands refuted. Other Notational Signs. The Epitaph of Seikelos, an inscription discovered by Sir W. M. Ramsay at Tralles, and the "papyrus fragment containing a chorus from Orestes (lines 338 to 343) bear rhythmic signs. The length of the notes is shown by marks placed above them, — for a note of two time-units and _i for one of three. A note upon which the beat comes bears a dot. In the chorus, a distinction is drawn between beats, one kind being denoted by a dot above the note, and the other by a dot at one side. I assume that the former method marks the main stress, and the latter a subsidiary stress. The epitaph makes use of the following additional signs (1) ^ as in I K, and (2) x as in CXI- These are dealt with in Anonymus de Musica. Bellermann takes X to mean staccato, X to mean quasi-staccato, and ^ to mean legato. ^ is there applied to different notes, while the other two signs are also applied to repetitions of the same note. From this, and judging by the peculiarities of oriental music in general, I think it is more likely that ^ stood for portando or the glide, X for the ' leap,' that is for the absence of glide, and X for staccato. The staccato sign was sometimes written thus, X.

III. SCALES, HARMONIES AND MODES The Greeks employed three different methods of representing scales. In discussing the structure of scales, as we have seen, they made use of the tetra- chord. In exhibiting the modes of a Harmony, they adopted the full octave (Ptolemy, Harmonic i. 16, ii. 14). It was also customary to show the tessitura of a composition by stringing together the actual notes contained. This method was probably the most ancient, as the further back one goes in the history bf music, the more importance seems to be attached to matters of compass. The Dorian, for example, was in early times only allowed to descend a tone below the hypate. I think it very likely that this circumstance led the Church to suppose that the Dorian was a D mode. To illustrate my meaning, I give a few compass scales. 11 Anonymus de Musica, edited by Bellermann (Berlin, 1841). THE INTERPRETATION OF GREEK MUSIC 149

ARISTIDES QUINTILIANUS Lydian * Dorian i C PTIl IE A 8- Cu FCuO

Ionian * Phrygian kI 1 R V C M / c P n \ z E A v r L i c n < F Cu < C u Z

Mixolydian Syntonolydian

a ©-^ p: 7Rv4>cpnz IR v CM ZL1CCV0C TL 1 CH

OTHER SCALES God Save the King (in A°) The Epitaph The Chorus

* The Lydian and Ionian appear to be misnamed. There are also mistakes in the notation. J.H.S.—VOL. XLII. L 150 E. CLEMENTS As regards the genera, we may acquire some further knowledge from the Greek compositions. The enharmonic or chromatic sometimes formed the sole basis of a composition. The enharmonic genus was much favoured in the strict classical school represented by the of . The enharmonics were frequently omitted, leaving a pentatonic scale as in the opening of the long hymn to . The enharmonic genus was often mixed with the diatonic as in other passages in the same hymn, and in the chorus from Orestes. A sparing use of the genus was also made in compositions in diatonic scales. This will be observed in each of the three manuscript hymns. The enharmonic seems to have been employed, like the chromatic chord of modern times to add piquancy to the music. The manner of its employment is well-deserving- of study. The phrase e \>, d % e ^., b -k, a \>, g tj, b -^ in the hymn to provides a beautiful climax to the melody. We have many such instances in our own music, but no one except the naturally gifted musician pays any attention to them. The following excerpt from the ' haunting' melody in the Unfinished Symphony is given in two renderings, A and B :—

B

In the passage marked a b, g ft a t) is followed first by e tj, which, being a just fourth below a tj, leaves no doubt as to the intonation, and then by the enharmonically raised pair g JJ, a t}. Similarly, in the hymn to Calliope, e |» is separated by one note d tj from its enharmonic e -^., and the changed intonation is emphasised by a leap to b ^. Schubert, needless to say, was neither a victim of the temperament habit, nor of the ditonal habit. A is therefore what he intended, and it is in the best- Greek manner. I heard a small and well-trained French orchestra play the symphony. The 'cellos, who were led on that occasion by a celebrated soloist, played as in A. The violins replied with B. The next day in answer to my questions, the conductor said he had noticed the difference. The rendering of the 'cellos made certain notes flat. The rendering of the violins was plus juste, by which he meant, as he admitted, more in tune with the piano ! Rendering B, to my mind, degrades the music into a kind of musical pun. And that is the rendering which is generally given. The surviving examples of Greek music throw very little light upon THE INTERPRETATION OF GREEK MUSIC 151 the treatment of chromatic scales. There are interesting passages in the first of the mural hymns in which the chromatic, diatonic and enharmonic are all used together. The hymn to Calliope also employs a chromatic note. The orthodox Greek chromatic genus is still to be found in India in the Karnatic raga Kanakangi amongst others. It is not, however, an interesting scale. Most of the Greek chromatic scales must have been compounded of mixed chromatic and diatonic tetrachords. Finally, to revert to the enharmonic genus, melodies in purely enharmonic scales would be much appreciated by the musical experts of India or Persia, at the present day. The best Indian singers make a lavish use of enharmonic changes. To the European, the singer appears to attack Ms notes in a slovenly way, beginning a little sharp or flat and sliding on to the correct pitch. That style of singing is strongly suggested by the chorus from Orestes. The Harmonies and Modes. The modal scale, as used by Ptolemy, and by European musicians, takes no count of the compass of a composition. In the Greek system it stretched downwards for the space of an octave, either from the diezeugmenon, or from the mese ; we take bur scales from tonic to tonic. Aristotle compares the mese to the conjunction in speech, because it frequently recurs, and links the other notes together.12 The mese, in that view, was the predominant note of the melody, or more briefly, the pre- dominant.13 The hypate was the final, upon which the voice came to rest naturally, and without effort.14 These remarks will be found to apply most aptly to all the compositions except the last two manuscript hymns. Those hymns, to Helios and Nemesis, make the hypate 15 the predominant, and the mese the final. This brings us to the important distinction embodied later on in the terms authentic and plagal. In the Byzantine period they were known as eZSo? dreXe

12 Prob. xix. 20. See also Prob. 36. 15 Or the nete. 13 This term is preferred to 'dominant,' 16 Bryennios (circ. 1400 A.D.) JohnWallis, being free from ambiguity. Opera Math. iii. 259. Oxon. 1699. 11 Prob. xix. 334. 17 Meibom. p. 37; Macran, 128. 193. 152 E. CLEMENTS Hypophrygian, Hypodorian, and Dorian by an interval of three-fourths of a tone. . . .' There is no reason therefore to connect the Aeolian with the Hypodorian of later times.18 We can identify the harmony with certainty from another source. The ' Introduction' formerly attributed to Euclid (Meibom. 20. 1) contains this passage, descriptive of the keys: ' Two Lydian keys, a higher, and a lower also called Aeolian; two Phrygian, one low also called Ionian, and one high; one Dorian; two Hypolydian, a higher, and a lower, also called Hypoaeolian; two Hypophrygian, of which the lower is also called Hypoionian.' This description accurately corresponds to the keys of Alypius, if we omit the Hypodorian and the high keys (Hyperlydian, etc.), three of which are merely low keys transposed an octave higher. The modes which formed the nucleus of the keys are at once apparent if we take octave scales upwards from either R (e \>) or n (e -feu) in the ' higher ' keys, and r(dtj) in the ' lower ' keys.19 The instrumental notes involved in this collec- tion of scales include eight of the groups of three, beginning respectively with the letters rKFCKn

THE HIGHER MODES 1. Hypolydian. 2. Lydian. 3. Hypophrygian.

3442 342 3423442 4423423

4. Phrygian. 5. Dorian.

4234423 2344234

THE LOWER MODES 1. Hypoaeolian. 2. Aeolian. 3. Hypoionian.

3 4 4 2 3 4 2 3 4 2 4 3 4 2 3 4 2 4 3 2 4 4. Ionian.

3 2 4 1 3 2 4 18 Heraclides was a pupil of Plato. are, in that sense, functional names. Each 19 As the notes are named by Alypius mode, however, had its own mese, the mese the mese is always the base of a Dorian of position. This is clear from Ptolemy's tetrachord. The names have regard to scales, and from other indications. the theoretical structure of the keys. They THE INTERPRETATION OF GREEK MUSIC 153 The first batch are in one Harmony, Scale IV. That can be. no other than, the national scale far excellence, the Dorian. If the lower keys of Alypius be examined it will be found that they form a kind of patchwork cementing the whole structure. Two of them, the Aeolian and Ionian, are in distinctive Harmonies to which the others are merely introductory. Their titles are sufficient to proclaim that they are the two other famous Harmonies, which, with the Dorian, represented the three tribes of Hellenes. The Dorian was therefore an E mode, the Aeolian a C mode, and the Ionian a D mode. The symmetry of these scales is apparent when one describes them in sruti figures with the point of conjunction emphasised.

234 — 4 — 234; 342 — 4 — 342; 324 — 4 — 324. Let me add that our Harmonies are the major and minor (descending melodic form). The former is supposed to be the just major (Scale II.), and the latter is the Aeolian, A mode. It is quite a mistake to think of the minor as the A mode of the major. This is only so, speaking generally, in equal temperament or the ditonal. As Mr. J. Curtis points out,20 the Pythagoreans persuaded the theatre to accept the whole range of Dorian modes. In this way the -rp6-no