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 tetrachord, 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 semitone. 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 major third 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 minor third, 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 r a c n n e g i i ne t Ratio. n Interval. Interval. t e Ratio. e intege inte th ten th a o o t Conten 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 ditone 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.