Chapter IV: Part 4

[Footnote 1: So Bacch. p. 19 Meib. [Greek: theseis de tetrachordôn hois to melos horizetai eisin hepta? synaphê, diazeuxis, hypodiazeuxis, k.t.l.] (see the whole passage).]

Westphal also finds the nomenclature by position implied in the passage of the Aristotelian _Problems_ (xix. 20) which deals with the peculiar relation of the Mesê to the rest of the musical scale. The passage has already been quoted and discussed (_supra_, p. 43), and it has been pointed out that if the Mesê of the Perfect System ([Greek: mesê kata dynamin]) is the key-note, the scale must have been an octave of the _a_-species. If octaves of other species were used, as Westphal maintains, it becomes necessary to take the Mesê of this passage to be the [Greek: mesê kata thesin], or Mesê by position. That is, Westphal is obliged by his theory of the Modes to take the term Mesê in a sense of which there is no other trace before the time of Ptolemy. But--

(1) It is highly improbable that the names of the notes--Mesê, Hypatê, Nêtê and the rest--should have had two distinct meanings. Such an ambiguity would have been intolerable, and only to be compared with the similar ambiguity which Westphal's theory implies in the use of the terms Dorian, &c.

(2) If the different species of the octave were the practically important scales, as Westphal maintains, the position of the notes in these scales must have been correspondingly important. Hence the nomenclature by position must have been the more usual and familiar one. Yet, as we have shown, it is not found in Aristotle, Aristoxenus or Euclid--to say nothing of later writers.

(3) The nomenclature by position is an essential part of the scheme of Keys proposed by Ptolemy. It bears the same relation to Ptolemy's octaves as the nomenclature by 'value' bears to the old standard octave and the Perfect System. It was probably therefore devised about the time of Ptolemy, if not actually by him.

§ 31. _Scales of the Lyre and Cithara._

The earliest evidence in practical music of any octaves other than those of the standard System is to be found in the account given by Ptolemy of certain scales employed on the lyre and cithara. According to this account the scales of the lyre (the simpler and commoner instrument) were of two kinds. One was Diatonic, of the 'colour' or variety which Ptolemy recognises as the prevailing one, viz. the 'Middle Soft' or 'Tonic' ([Greek: diatonon toniaion])[1].

[Footnote 1: We may think of this as a scale in which the semitones are considerably smaller, _i.e._ in which _c_ and _f_ are nearly a quarter of a tone flat.]

The other was a 'mixture' of this Diatonic with the standard Chromatic ([Greek: chrôma suntonon]): that is to say, the octave consisted of a tetrachord of each genus. These octaves apparently might be of any _species_, according to the key chosen[1]. On the cithara,--which was a more elaborate form of lyre, confined in practice to professional musicians,--six different octave scales were employed, each of a particular species and key. They are enumerated and described by Ptolemy in two passages (_Harm._ i. 16 and ii. 16), which in some points serve to correct each other.[2]

[Footnote 1: Ptol. _Harm._ ii. 16 [Greek: periechetai de ta men en tê lyra kaloumena sterea tonou tinos hypo tôn tou toniaiou diatonou arithmôn tou autou tonou, ta de malaka hypo tôn en tô migmati tou malakou chrômatos apithmôn tou autou tonou]. Here [Greek: tonou tinos] evidently means 'of any given key,' and [Greek: tou autou tonou] 'of that key.' There is either no restriction, or none that Ptolemy thought worth mentioning, in the choice of the key and species.]

[Footnote 2: The two passages enumerate the scales in a slightly different manner. In i. 16 they are arranged in view of the genus or colour into--

Pure Middle Soft Diatonic, viz.--
[Greek: sterea], of the lyre.
[Greek: tritai] } of the cithara.
[Greek: hypertropa] }

Mixture of Chromatic, viz.--
[Greek: malaka], of the lyre.
[Greek: tropika], of the cithara.

Mixture of Soft Diatonic, viz.--
[Greek: parypatai], of the cithara.

Mixture of [Greek: diatonon syntonon], viz.--
[Greek: lydia] } of the cithara.
[Greek: iastia] }

It is added, however, that in their use of this last 'mixture' musicians are in the habit of tuning the cithara in the Pythagorean manner, with two Major tones and a [Greek: leimma] (called [Greek: diatonon ditoniaion]).

In the second passage (ii. 16) the scales of the lyre are given first, then those of the cithara with the key of each. The order is the same, except that [Greek: parypatai] comes before [Greek: tropika] (now called [Greek: tropoi]), and [Greek: lydia] is placed last. The words [Greek: ta de lydia hoi tou toniaiou diatonou] [sc. [Greek: arithmoi periechousi]] [Greek: tou dôriou] cannot be correct, not merely because they contradict the statement of the earlier passage that [Greek: lydia] denoted a mixture with [Greek: diatonon syntonon] (or in practice [Greek: diatonon ditoniaion]), but also because the scales that do not admit mixture are placed first in the list in both passages. Hence we should doubtless read [Greek: ta de lydia hoi <tou migmatos> tou <di>toniaiou diatonou tou Dôriou].]

Of the six scales two are of the Hypo-dorian or Common species (_a-a_). One of these, called [Greek: tritai], is purely Diatonic of the Middle Soft variety; the intervals expressed by fractions are as follows:

_a_ 9/8 _b_ 28/27 _c_ 8/7 _d_ 9/8 _e_ 28/27 _f_ 8/7 _g_ 9/8 _a_

The other, called [Greek: tropoi] or [Greek: tropika], is a mixture, Middle Soft Diatonic in the upper tetrachord, and Chromatic in the lower:

_a_ 9/8 _b_ 22/21 _c_ 12/11 _c_[Symbols: sharp] 7/6 _e_ 28/27 _f_ 8/7 _g_ 9/8 _a_

Two scales are of the Dorian or _e_-species, viz. [Greek: parypatai], a combination of Soft and Middle Soft Diatonic:

_e_ 21/20 _f_ 10/9 _g_ 8/7 _a_ 9/8 _b_ 28/27 _c_ 8/7 d 9/8 _e_

and [Greek: lydia], in which the upper tetrachord is of the strict or 'highly strung' Diatonic ([Greek: diatonon syntonon]--our 'natural' temperament):

_e_ 28/27 _f_ 8/7 _g_ 9/8 _a_ 9/8 _b_ 16/15 _c_ 9/8 _d_ 10/9 _e_

Westphal (_Harmonik und Melopöie_, 1863, p. 255) supposes a
much deeper corruption. He would restore [Greek: ta de lydia
[kai iastia hoi tou migmatos tou syntonou diatonou tou ... ta
de ...] hoi tou toniaiou diatonou tou Dôriou]. This introduces
a serious discrepancy between the two passages, as the number
of scales in the second list is raised to eight (Westphal
making [Greek: iastia] and [Greek: iastiaioliaia] distinct
scales, and furthermore inserting a new scale, of unknown
name). Moreover the (unknown) scale of unmixed [Greek:
diatonon toniaion] is out of its place at the end of the list.
Westphal's objection to [Greek: lydia] as the name of a scale
of the _Dorian_ species of course only holds good on his
theory of the Modes.

The only other differences between the two passages are:

(1) In the scales of the lyre called [Greek: malaka] the
admixture, according to i. 16, is one of [Greek: chrômatikon
syntonon], according to ii. 16 of [Greek: chr. malakon]. But,
as Westphal shows, Soft Chromatic is not admitted by Ptolemy
as in practical use. It would seem that in the second passage
the copyist was led astray by the word [Greek: malaka] just
before.

(2) The [Greek: iastia] of i. 16 is called [Greek:
iastiaioliaia] in ii. 16. We need not suppose the text to be
faulty, since the two forms may have been both in use.

Another point overlooked in Westphal's treatment is that
[Greek: diatonon syntonon] and [Greek: d. ditoniaion] are not
really distinguished by Ptolemy. In one passage (i. 16) he
gives his [Greek: lydia] and [Greek: iastia] as a mixture with
[Greek: d. syntonon], adding that in practice it was [Greek:
d. ditoniaion]. In the other (ii. 16) he speaks at once of
[Greek: d. ditoniaion]. This consideration brings the two
places into such close agreement that any hypothesis involving
discrepancy is most improbable.

In practice it appears that musicians tuned the tetrachord _b-e_ of this scale with the Pythagorean two Major tones and [Greek: leimma].

Of the remaining scales one, called [Greek: hypertropa], is Phrygian in species (_d-d_), and of the standard genus:

_d_ 9/8 _e_ 28/27 _f_ 8/7 _g_ 9/8 _a_ 9/8 _b_ 28/27 _c_ 8/7 _d_

One, called [Greek: iastia], or [Greek: iastiaioliaia], is of the Hypo-phrygian or _g_-species, the tetrachord _b-e_ being 'highly strung' Diatonic or (in practice) Pythagorean, viz.:

_g_ 9/8 _a_ 9/8 _b_ 256/243 _c_ 9/8 _d_ 9/8 _e_ 28/27 _f_ 8/7 _g_

Regarding the tonality of these scales there is not very much to be said. In the case of the Hypo-dorian and Dorian octaves it will be generally thought probable that the key-note is _a_ (the [Greek: mesê kata dynamin]). If so, the difference between the two species is not one of 'mode,'--in the modern sense,--but consists in the fact that in the Hypo-dorian the compass of the melody is from the key-note upwards, while in the Dorian it extends a Fourth below the key-note. It is possible, however, that the lowest note (_e_) of the Dorian octave was sometimes the key-note: in which case the _mode_ was properly Dorian. In the Phrygian octave of Ptolemy's description the key-note cannot be the Fourth or Mesê [Greek: kata thesin] (_g_), since the interval _g-c_ is not consonant (9/8 × 9/8 × 28/27 being less than 4/3). Possibly the lowest note (_d_) is the key-note; if so the scale is of the Phrygian mode (in the modern sense). In the Hypo-phrygian octave there is a similar objection to regarding the Mesê [Greek: kata thesin] (_c_) as the key-note, and some probability in favour of the lowest note (_g_). If the Pythagorean division of the tetrachord _g-c_ were replaced by the natural temperament, which the language used by Ptolemy[1] leads us to regard as the true division, the scale would exhibit the intervals--

_g_ 5/4 _b_ 6/5 _d_ 7/6 _f_ 8/7 _g_

which give the natural chord of the Seventh. This however is no more than a hypothesis.

It evidently follows from all this that Ptolemy's octaves do not constitute a system of _modes_. They are merely the groups of notes, of the compass of an octave, which are most likely to be used in the several keys, and which Ptolemy or some earlier theorist chose to call by the names of those keys.

[Footnote 1: _Harm._ i. 16 [Greek: plên kathoson adousi men akolouthôs tô dedeigmenô syntonô diatonikô, kathaper exestai skopein apo tês tôn oikeiôn autou logôn parabolês, harmozontai de heteron ti genos] (sc. the Pythagorean), [Greek: xynengizon men ekeinô, k.t.l.]]

§ 32. _Remains of Greek Music._

The extant specimens of Greek music are mostly of the second century A.D., and therefore nearly contemporary with Ptolemy. The most considerable are the melodies of three lyrical pieces or hymns, viz. (1) a hymn to Calliope, (2) a hymn to Apollo (or Helios),--both ascribed to a certain Dionysius,--and (3) a hymn to Nemesis, ascribed to Mesomedes[2]. Besides these there are (4) some short instrumental passages or exercises given by Bellermann's _Anonymus_ (pp. 94-96). And quite recently the list has been increased by (5) an inscription discovered by Mr. W. M. Ramsay, which gives a musical setting of four short gnomic sentences, and (6) a papyrus fragment (now in the collection of the Arch-duke Rainer) of the music of a chorus in the _Orestes_ of Euripides. These two last additions to our scanty stock of Greek music are set out and discussed by Dr. Wessely of Vienna and M. Ruelle in the _Revue des Études Grecques_ (V. 1892, pp. 265-280), also by Dr. Otto Crusius in the _Philologus_, Vol. LII, pp. 160-200[1].

[Footnote 2: It seems needless to set out these melodies here. The first satisfactory edition of them is that of Bellermann, _Die Hymnen des Dionysius und Mesomedes_ (Berlin, 1840). They are given by Westphal in his _Musik des griechischen Alterthumes_ (1883), and by Gevaert, _Musique de l'Antiquité_, vol. i. pp. 445 ff.; also in Mr. W. Chappell's _History of Music_ (London, 1874), where the melodies of the first and third hymns will be found harmonised by the late Sir George Macfarren.

The melody published by Kircher (_Musurgia_, i. p. 541) as a fragment of the first Pythian ode of Pindar has no attestation, and is generally regarded as a forgery.]

The music of the three hymns is noted in the Lydian key (answering to the modern scale with one [symbol: flat]). The melody of the second hymn is of the compass of an octave, the notes being those of the Perfect System from Parhypatê Hypatôn to Tritê Diezeugmenôn (_f - f_ with one [symbol: flat]). The first employs the same octave with a lower note added, viz. Hypatê Hypatôn (_e_): the third adds the next higher note, Paranêtê Diezeugmenôn (_g_). Thus the Lydian key may be said, in the case of the second hymn, and less exactly in the case of the two others, to give the Lydian or _c_-species of the octave in the most convenient part of the scale; just as on Ptolemy's system of Modes we should expect it to do.

This octave, however, represents merely the _compass_ (_ambitus_ or _tessitura_) of the melody: it has nothing to do with its _tonality_. In the first two hymns, as Bellermann pointed out, the key-note is the Hypatê Mesôn; and the mode--in the modern sense of that word--is that of the octave _e - e_ (the Dorian mode of Helmholtz's theory). In the third hymn the key-note appears to be the Lichanos Mesôn, so that the mode is that of _g-g_, viz. the Hypo-phrygian.

[Footnote 1: Of the discovery made at Delphi, after most of this book was in type, I hope to say something in the _Appendix_.]

Of the instrumental passages given by the _Anonymus_ three are clearly in the Hypo-dorian or common mode, the Mesê (_a_) being the key-note. (See Gevaert, i. p. 141.) A fourth (§ 104) also ends on the Mesê, but the key-note appears to be the Parhypatê Mesôn (_f_). Accordingly Westphal and Gevaert assign it to the Hypo-lydian species (_f - f_). In Westphal's view the circumstance of the end of the melody falling, not on the key-note, but on the Third or Mediant of the octave, was characteristic of the Modes distinguished by the prefix _syntono-_, and accordingly the passage in question is pronounced by him to be Syntono-lydian. All those passages, however, are mere fragments of two or three bars each, and are quoted as examples of certain peculiarities of rhythm. They can hardly be made to lend much support to any theory of the Modes.

The music of Mr. Ramsay's inscription labours under the same defect of excessive shortness. If, however, we regard the four brief sentences as set to a continuous melody, we obtain a passage consisting of thirty-six notes in all, with a compass of less than an octave, and ending on the lowest note of that compass. Unlike the other extant specimens of Greek music it is written in the Ionian key--a curious fact which has not been noticed by Dr. Wessely.

INSCRIPTION WITH MUSICAL NOTES.

[Music:

[Greek: hos-on zês phai-nou.
mê-den hol-ôs sy ly-pou.
pros o-li-gon es-ti to zên.
to te-los ho chro-nos a-pai-tei.]

]

The notes which enter into this melody form the scale _f[Symbols: sharp]-g-a-b-c[Symbols: sharp]-d-e[-f[Symbols: sharp]]_, which is an octave of the Dorian species (_e - e_ on the white notes). Hence if _f_[Symbols: sharp], on which the melody ends, is the key-note, the _mode_ is the Dorian. On the other hand the predominant notes are those of the triad _a-c[Symbols: sharp]-e_, which point to the key of _a_ major, with the difference that the Seventh is flat (_g_ instead of _g_[Symbols: sharp]). On this view the music would be in the Hypo-phrygian mode.

However this may be, the most singular feature of this fragment remains to be mentioned, viz. the agreement between the musical notes and the _accentuation_ of the words. We know from the grammarians that an acute accent signified that the vowel was sounded with a rise in the pitch of the voice, and that a circumflex denoted a rise followed on the same syllable by a lower note--every such rise and fall being quite independent both of syllabic quantity and of stress or _ictus_. Thus in ordinary speech the accents formed a species of melody,--[Greek: logôdes ti melos], as it is called by Aristoxenus[1]. When words were _sung_ this 'spoken melody' was no longer heard, being superseded by the melody proper. Dionysius of Halicarnassus is at pains to explain (_De Comp. Verb._, c. 11), that the melody to which words are set does not usually follow or resemble the quasi-melody of the accents, _e.g._ in the following words of a chorus in the _Orestes_ of Euripides (ll. 140-142):--

[Greek: siga siga leukon ichnos arbylês
tithete, mê ktypeite;
apoprobat' ekeis' apopro moi koitas,]

[Footnote 1: _Harm._ p. 18 Meib. [Greek: legetai gar dê kai logôdes ti melos, to synkeimenon ek tôn prosôdiôn, to en tois onomasi; physikon gar to epiteinein kai anienai en tô dialegesthai].]

he notices that the melody differs in several points from the spoken accents: (1) the three first words are all on the same note, in spite of the accents; (2) the last syllable of [Greek: arbylês] is as high as the second, though that is the only accented syllable: (3) the first syllable of [Greek: tithete] is lower than the two others, instead of being higher: (4) the circumflex of [Greek: ktypeite] is lost ([Greek: êphanistai]), because the word is all on the same pitch; (5) the fourth syllable of [Greek: apoprobate] is higher in pitch, instead of the third. In Mr. Ramsay's inscription, however, the music follows the accents as closely as possible. Every acute accent coincides with a rise of pitch, except in [Greek: hoson], which begins the melody, and in [Greek: esti], for which we should perhaps read the orthotone [Greek: esti]. Of the four instances of the circumflex accent three exhibit the two notes and the falling pitch which we expect. The interval is either a major or a minor Third. In the other case ([Greek: zês) the next note is a Third lower: but it does not seem to belong to the circumflexed syllable. All this cannot be accidental. It leads us to the conclusion that the musical notes represent a kind of recitative, or imitation of spoken words, rather than a melody in the proper sense of the term.

If any considerable specimen of the music of Euripides had survived, it might have solved many of the problems with which we have been dealing. The fragment before us extends over about six lines in dochmiac metre (_Orestes_ 338-343), with the vocal notation: but no single line is entire. The key is the Lydian. The genus is either Enharmonic or Chromatic. Assuming that it is Enharmonic--the alternative adopted by Dr. Wessely--the characters which are still legible may be represented in modern notation as follows:

[Music: [_Euripides_, _Orestes 338-344_.

[Greek: (katolo)phy-ro-mai; ma-te-ros (haima sas ho d' ana)bak-cheu-ei;
ho me-gas (olbos ou monimo)s en bro-tois;
a-na (de laiphos hôs ti)s a-ka-tou tho-as ti-na(xas daimôn)
kat-e-kly-sen (deinôn ponon) hôs pon-tou labrois k.t.l.

]

It should be observed that in the fragment the line [Greek: katolophyromai katolophyromai] comes before 338 ([Greek: materos k.t.l.]), not after it, as in our texts[1].

[Footnote 1: I need not repeat what is said by Dr. Wessely and M. Ruelle in defence of the genuineness of our fragment. They justly point to the remarkable coincidence that the music of this very play is quoted by Dionysius of Halicarnassus (_l. c._). It would almost seem as if it was the only well-known specimen of music of the classical period of tragedy.

The transcription of Dr. Crusius, with his conjectural restorations, will be found in the _Appendix_. I have only introduced one of his corrections here, viz. the note on the second syllable of [Greek: kateklysen].]

The notes employed, according to the interpretation given above, give the scale _g-a-a*-a#-d-e-e*_. If the genus is Chromatic, as M. Ruelle is disposed to think, they are _g-a-a#-b-d-e-f_. When these scales are compared with the Perfect System we find that they do not entirely agree with it. Whether the genus is Enharmonic or Chromatic the notes from _a_ to _e*_ (or _f_) answer to those of the Perfect System (of the same genus) from Hypatê Mesôn to Tritê Diezeugmenôn. But in either case the lowest note (_g_) finds no place in the System, since it can only be the Diatonic Lichanos Hypatôn. It is possible, however, that the scale belongs to the period when the original octave had been extended by the addition of a tone below the Hypatê--the note, in fact, which we have already met with under the name of Hyper-hypatê (p. 39). Thus the complete scale may have consisted of the disjunct tetrachords _a-d_ and _e-a_, with the tone _g-a_. It may be observed here that although the scale in question does not fit into the Perfect System, it conforms to the general rules laid down by Aristoxenus for the melodious succession of intervals. It is unnecessary therefore to suppose (as Dr. Wessely and M. Ruelle do) that the scale exhibits a _mixture_ of different genera.

It must be vain to attempt to discover the tonality of a short fragment which has neither beginning nor end. The only group of notes which has the character of a cadence is that on the word [Greek:(olo)phypomai], and again on the words [Greek: en brotois], viz. the notes _a# a* a_ (if the genus is the Enharmonic). The same notes occur in reversed order on [Greek: akatou] and [Greek: (kat)eklusen]. This seems to bear out the common view of the Enharmonic as produced by the introduction of an 'accidental' or passing note. It will be seen, in fact, that the Enharmonic notes (_a*_ and _e*_) only occur before or after the 'standing' notes (_a_ and _e_).

Relying on the fact that the lowest note is _g_, Dr. Wessely and M. Ruelle pronounce the mode to be the Phrygian (_g-g_ in the key with one [Symbols: flat], or _d-d_ in the natural key). I have already put forward a different explanation of this _g_, and will only add here that it occurs twice in the fragment, both times on a short syllable[1]. The important notes, so far as the evidence goes, are _a_, which twice comes at the end of a verse (with a pause in the sense), and _e_, which once has that position. If _a_ is the key-note, the mode--in the modern sense--is Dorian (the _e_-species). If _e_ is the key-note, it is Mixo-lydian (the _b_-species).

[Footnote 1: Dr. Crusius, however, detects a [Symbols: phi]; (the sign for _g_) over the first syllable of [Greek: kateklusen] and the second syllable of [Greek: pontou]. There is little trace of them in his facsimile.]

§ 33. _Modes of Aristides Quintilianus._

The most direct testimony in support of the view that the ancient Modes were differentiated by the succession of their intervals has still to be considered. It is the account given by Aristides Quintilianus (p. 21 Meib.) of the six Modes ([Greek: harmoniai]) of Plato's _Republic_. After describing the genera and their varieties the 'colours,' he goes on to say that there were other divisions of the tetrachord ([Greek: tetrachordikai diaireseis]) which the most ancient musicians used for the [Greek: harmoniai], and that these were sometimes greater in compass than the octave, sometimes less. He then gives the intervals of the scale for each of the six Modes mentioned by Plato, and adds the scales in the ancient notation. They are of the Enharmonic genus, and may be represented by modern notes as follows:--

Mixo-lydian _b-b*-c-d-e-e*-f-b_
Syntono-lydian _e-e*-f-a-c_
Phrygian _d-e-e*-f-a-b-b*-c-d_
Dorian _d-e-e*-f-a-b-b*-c-e_
Lydian _e*-f-a-b-b*-c-e-e*_
Ionian _e-e*-f-a-c-d_

Comparing these scales with the Species of the Octave, we find a certain amount of correspondence. As has been already noticed (p. 22), the names Syntono-lydian and Lydian answer to the ordinary Lydian and Hypo-lydian respectively. Accordingly the Lydian of Aristides agrees with the Hypo-lydian species as given in the pseudo-Euclidean _Introductio_. The Dorian of Aristides is the Dorian species of the _Introductio_, but with an additional note, a tone below the Hypatê.

The Phrygian of Aristides is not the Enharmonic Phrygian species; but it is derived from the diatonic Phrygian octave _d-e-f-g-a-b-c-d_ by inserting the enharmonic notes _e*_ and _b*_, and omitting the diatonic _g_. By a similar process the Mixo-lydian of Aristides may be derived from the diatonic octave _b-b_, except that _a_ as well as _g_ is omitted, and on the other hand _d_ is retained. If the scale of the Syntono-lydian is completed by the lower _c_ (as analogy would require), it will answer similarly to the Lydian species (_c-c_).

§ 34. _Credibility of Aristides Quintilianus._

But what weight can be given to Aristides as an authority on the music of the time of Plato? The answer to this question depends upon several considerations.

1. The date of Aristides is unknown. He is certainly later than Cicero, since he quotes the _De Republica_ (p. 70 Meib.). From the circumstance that he makes no reference to the musical innovations of Ptolemy it has been supposed that he was earlier than that writer. But, as Aristides usually confines himself to the theory of Aristoxenus and his school, the argument from silence is not of much value. On the other hand he gives a scheme of notation containing two characters, [Symbol: [] and [Symbol: *], which extend the scale two successive semi-tones beyond the lowest point of the notation given by Alypius[1]. For this reason it is probable that Aristides is one of the latest of the writers on ancient music.

[Footnote 1: This argument is used, along with some others not so cogent, in Mr. W. Chappell's _History of Music_ (p. 130).]

2. The manner in which Aristides introduces his information about the Platonic Modes is highly suspicious. He has been describing the various divisions of the tetrachord according to the theory of Aristoxenus, and adds that there were anciently other divisions in use. So far Aristides is doubtless right, since Aristoxenus himself says that the divisions of the tetrachord are theoretically infinite in number (p. 26 Meib.),--that it is possible, for example, to combine the Parhypatê of the Soft Chromatic with the Lichanos of the Diatonic (p. 52 Meib.). But all this concerns the genus of the scale, and has nothing to do with the species of the Octave, with which Aristides proceeds to connect it. It follows either that there is some confusion in the text, or that Aristides was compiling from sources which he did not understand.

3. The Platonic Modes were a subject of interest to the early musical writers, and were discussed by Aristoxenus himself (Plut. _de Mus._ c. 17). If Aristoxenus had had access to such an account as we have in Aristides, we must have found some trace of it, either in the extant _Harmonics_ or in the quotations of Plutarch and other compilers.

4. Of the four scales which extend to the compass of an octave, only one, viz. the Dorian, conforms to the rules which are said by Aristoxenus to have prevailed in early Greek music. The Phrygian divides the Fourth _a-d_ into four intervals instead of three, by the sequence _a b b* c d_. As has been observed, it is neither the Enharmonic Phrygian species (_c e e* f a b b* c_), nor the Diatonic _d-d_, but a mixture of the two. Similarly the Mixo-lydian divides the Fourth _b_-_e_ into four intervals (_b b* c d e_), by introducing the purely Diatonic note _d_. The Lydian is certainly the Lydian Enharmonic species of the pseudo-Euclid; but we can hardly suppose that it existed in practical music. Aristoxenus lays it down emphatically that a quarter-tone is always followed by another: and we cannot imagine a scale in which the highest and lowest notes are in no harmonic relation to the rest.

5. Two of the scales are incomplete, viz. the Ionian, which has six notes and the compass of a Seventh, and the Syntono-lydian, which consists of five notes, with the compass of a Minor Sixth. We naturally look for parallels among the defective scales noticed in the _Problems_ and in Plutarch's dialogues. But we find little that even illustrates the modes of Aristides. The scales noticed in the _Problems_ (xix. 7, 32, 47) are hepta-chord, and generally of the compass of an octave. In one passage of Plutarch (_De Mus._ c. 11) there is a description--quoted from Aristoxenus--of an older kind of Enharmonic, in which the semitones had not yet been divided into quarter-tones. In another chapter (c. 19) he speaks of the omission of the Tritê and also of the Nêtê as characteristic of a form of music called the [Greek: spondeiakos tropos]. It may be said that in the Ionian and Syntono-lydian of Aristides the Enharmonic Tritê (_b*_) and the Nêtê (_e_) are wanting. But the Paramesê (_b_) is also wanting in both these modes. And the Ionian is open to the observation already made with regard to the Phrygian, viz. that the two highest notes (_c d_) involve a mixture of Diatonic with Enharmonic scale. We may add that Plutarch (who evidently wrote with Aristoxenus before him) gives no hint that the omission of these notes was characteristic of any particular modes.

6. It is impossible to decide the question of the modes of Aristides without some reference to another statement of the same author. In the chapter which treats of Intervals (pp. 13-15 Meib.) he gives the ancient division of two octaves, the first into dieses or quarter-tones, the second into semitones. The former of these ([Greek: hê para tois archaiois kata dieseis harmonia]) is as follows:

[1] 2 3 4 5 6 7 8 9 10 11 12

[Symbols: -o < 6 1-1 9 L J A V E 3]
[Symbols: o- > 9 n 6 J r- v 0 3 E]

13 14 15 16 17 18 19 20 21 22 23 24

[Symbols: 3.. N 1-1 3 E , '- cc > < Y Y]
[Symbols: r a..1-1 E 3 A ,'- 33 < Y]

After every allowance has been made for the probability that these signs or some of them have reached us in a corrupt form, it is impossible to reduce them to the ordinary notation, as Meibomius sought to do. The scholar who first published them as they stand in the MSS. (F. L. Perne, see Bellermann, _Tonleitern_, p. 62) regarded them as a relic of a much older system of notation. This is in accordance with the language of Aristides, and indeed is the only view consistent with a belief in their genuineness. They are too like the ordinary notation to be quite independent, and cannot have been put forward as an improvement upon it. Are they, then, earlier? Bellermann has called our attention to a peculiarity which seems fatal to any such claim. They consist, like the ordinary signs, of two sets, one written above the other, and in every instance one of the pair is simply a reversed or inverted form of the other. With the ordinary signs this is not generally the case, since the two sets, the vocal and instrumental notes, are originally independent. But it is the case with the three lowest notes, viz. those which were added to the series at a later time. When these additional signs were invented the vocal and instrumental notes had come to be employed together. The inventor therefore devised a pair of signs in each case, and not unnaturally made them correspond in form. In the scale given by Aristides this correspondence runs through the whole series, which must therefore be of later date. But if this is so, the characters can hardly represent a genuine system of notation. In other words, Aristides must have been imposed upon by a species of forgery.

7. Does the fragment of the _Orestes_ tell for or against the Modes described by Aristides?

The scale which is formed by the notes of the fragment agrees, so far as it extends, with two of the scales now in question, viz. the Phrygian and the Dorian. Taking the view of its tonality expressed in the last chapter (p. 93), we should describe it as the Dorian scale of Aristides with the two highest notes omitted. The omission, in so short a fragment, is of little weight; and the agreement in the use of an additional lower note (Hyper-hypatê) is certainly worth notice. On the other hand, the Dorian is precisely the mode, of those given in the list of Aristides, which least needs defence, as it is the most faithful copy of the Perfect System. Hence the fact that it is verified by an actual piece of music does not go far in support of the other scales in the same list.

If our suspicions are well-founded, it is evident that they seriously affect the genuineness of all the antiquarian learning which Aristides sets before his readers, and in particular of his account of the Platonic modes. I venture to think that they go far to deprive that account of the value which it has been supposed to have for the history of the earliest Greek music.

For the later period, however, to which Aristides himself belongs, these apocryphal scales are a document of some importance. The fact that they do not agree entirely with the species of the Octave as given by the pseudo-Euclid leads us to think that they may be influenced by scales used in actual music. This applies especially to the Phrygian, which (as has been shown) is really diatonic. The Ionian, again, is perhaps merely an imperfect form of the same scale, viz. the octave _d-d_ with lower _d_ omitted. And the Syntono-lydian may be the Lydian diatonic octave _c-c_ with a similar omission of the lower _c_. § 35. _Evidence for Scales of different species._

The object of the foregoing discussion has been to show, in the first place, that there was no such distinction in ancient Greek music as that which scholars have drawn between Modes ([Greek: harmoniai]) and Keys ([Greek: tonoi] or [Greek: tropoi]): and, in the second place, that the musical scales denoted by these terms were primarily distinguished by difference of _pitch_,--that in fact they were so many keys of the standard scale known in its final form as the Perfect System. The evidence now brought forward in support of these two propositions is surely as complete as that which has been allowed to determine any question of ancient learning.

It does not, however, follow that the Greeks knew of no musical forms analogous to our Major and Minor modes, or to the mediaeval Tones. On the contrary, the course of the discussion has led us to recognise distinctions of this kind in more than one instance. The doctrine against which the argument has been mainly directed is not that ancient scales were of more than one species or 'mode' (as it is now called), but that difference of species was the basis of the ancient Greek Modes. This will become clear if we bring together all the indications which we have observed of scales differing from each other in species, that is, in the _order_ of the intervals in the octave. In doing so it will be especially important to be guided by the principle which we laid down at the outset, of arranging our materials according to chronology, and judging of each piece of evidence strictly with reference to the period to which it belongs. It is only thus that we can hope to gain a conception of Greek music as the living and changing thing that we know it must have been.

1. The principal scale of Greek music is undoubtedly of the Hypo-dorian or common species. This is sufficiently proved by the facts (1) that two octaves of this species (_a-a_) constitute the scale known as the Greater Perfect System, and (2) that the central _a_ of this system, called the Mesê, is said to have been the key-note, or at least to have had the kind of importance in the scale which we connect with the key-note (Arist. _Probl._ xix. 20). This mode, it is obvious, is based on the scale which is the descending scale of the modern Minor mode. It may therefore be identified with the Minor, except that it does not admit the leading note.

It should be observed that this mode is to be recognised not merely in the Perfect System but equally in the primitive octave, of the form _e - e_, out of which the Perfect System grew. The important point is the tonic character of the Mesê (_a_), and this, as it happens, rests upon the testimony of an author who knows the primitive octave only. The fact that that octave is of the so-called Dorian species does not alter the _mode_ (as we are now using that term), but only the compass of the notes employed.

The Hypo-dorian octave is seen in two of the scales of the cithara given by Ptolemy (p. 85), viz. those called [Greek: tritai] and [Greek: tropoi], and the Dorian octave (_e - e_) in two scales, [Greek: parupatai] and [Greek: ludia]. It is very possible (as was observed in commenting on them) that the two latter scales were in the key of _a_, and therefore Hypo-dorian in respect of mode. The Hypo-dorian mode is also exemplified by three at least of the instrumental passages given by the _Anonymus_ (_supra_, p. 89).

2. The earliest trace of a difference of species appears to be found in the passage on the subject of the Mixo-lydian mode quoted above (p. 24) from Plutarch's _Dialogue on Music_. In that mode, according to Plutarch, it was discovered by a certain Lamprocles of Athens that the Disjunctive Tone was the highest interval, that is to say, that the octave in reality consisted of two conjunct tetrachords and a tone:

[Music: Mesê Disj. Tone]

As the note which is the meeting-point of the two tetrachords is doubtless the key-note, we shall not be wrong in making it the Mesê, and thus finding the octave in question in the Perfect System and in the oldest part of it, viz. the tetrachords Mesôn and Synêmmenôn, with the Nêtê Diezeugmenôn. How then did this octave come to be recognised by Lamprocles as distinctively Mixo-lydian? We cannot tell with certainty, because we do not know what the Mixo-lydian scale was before his treatment of it. Probably, however, the answer is to be sought in the relation in respect of pitch between the Dorian and Mixo-lydian keys. These, as we have seen (p. 23), were the keys chiefly employed in tragedy, and the Mixo-lydian was a Fourth higher than the other. Now when a scale consisting of white notes is transposed to a key a Fourth higher, it becomes a scale with one [Symbol: Flat]. In ancient language, the tetrachord Synêmmenôn (_a-b[Symbol: Flat]-c-d_) takes the place of the tetrachord Diezeugmenôn. In some such way as this the octave of this form may have come to be associated in a special way with the use of the Mixo-lydian key.

However this may be, the change from the tetrachord Diezeugmenôn to the tetrachord Synêmmenôn, or the reverse, is a change of mode in the modern sense, for it is what the ancients classified as a change of System ([Greek: metabolê kata systêma])[1]. Nor is it hard to determine the two 'modes' concerned, if we may trust to the authority of the Aristotelian _Problems_ (_l. c._) and regard the Mesê as always the key-note. For if _a_ is kept as the key-note, the octave _a-a_ with one [Symbol: b] is the so-called Dorian (_e - e_ on the white notes). In this way we arrive at the somewhat confusing result that the ancient Dorian species (_e - e_ but with _a_ as key-note) yields the Hypo-dorian or modern Minor mode: while the Dorian mode of modern scientific theory[2] has its ancient prototype in the Mixo-lydian species, viz. the octave first brought to light by Lamprocles. The difficulty of course arises from the species of the Octave being classified according to their compass, without reference to the tonic character of the Mesê.

The Dorian mode is amply represented in the extant remains of Greek music. It is the mode of the two compositions of Dionysius, the Hymn to Calliope and the Hymn to Apollo (p. 88), perhaps also of Mr. Ramsay's musical inscription (p. 90). It would have been satisfactory if we could have found it in the much more important fragment of the _Orestes_. Such indications as that fragment presents seem to me to point to the Dorian mode (Mixo-lydian of Lamprocles).

3. The scales of the cithara furnish one example of the Phrygian species (_d-d_), and one of the Hypo-phrygian (_g-g_): but we have no means of determining which note of the scale is to be treated as the key-note.

[Footnote 1: Ps. Eucl. _Introd._ p. 20 Meib. [Greek: kata systêma de hotan ek synaphês eis diazeuxin ê anapalin metabolê ginêtai]. Anonym.

§ 65 [Greek: systêmatikai de] (sc. [Greek: metabolai]) [Greek: hopotan ek diazeuxeôs eis synaphên ê empalin metelthê to melos].]

[Footnote 2: As represented primarily by the analysis of Helmholtz, _Die Tonempfindungen_, p. 467, ed. 1863.]

In the Hymn to Nemesis, however, in spite of the incomplete form in which it has reached us, there is a sufficiently clear example of the Hypo-phrygian mode. It has been suggested as possible that the melody of Mr. Ramsay's inscription is also Hypo-phrygian, and if so the evidence for the mode would be carried back to the first century.

The Hypo-phrygian is the nearest approach made by any specimen of Greek music to the modern Major mode,--the Lydian or _c_-species not being found even among the scales of the cithara as given by Ptolemy. It is therefore of peculiar interest for musical history, and we look with eagerness for any indication which would allow us to connect it with the classical period of Greek art. One or two sayings of Aristotle have been thought to bear upon this issue.

The most interesting is a passage in the _Politics_ (iv. 3, cp. p. 13), where Aristotle is speaking of the multiplicity of forms of government, and showing how a great number of varieties may nevertheless be brought under a few classes or types. He illustrates the point from the musical Modes, observing that all constitutions may be regarded as either oligarchical (government by a minority) or democratical (government by the majority), just as in the opinion of some musicians ([Greek: hôs phasi tines]) all modes are essentially either Dorian or Phrygian. What, then, is the basis of this grouping of certain modes together as Dorian, while the rest are Phrygian in character? According to Westphal it is a form of the opposition between the true Hellenic music, represented by Dorian, and the foreign music, the Phrygian and Lydian, with their varieties. Moreover, it is in his view virtually the same distinction as that which obtains in modern music between the Minor and the Major scales[1]. This account of the matter, however, is not supported by the context of the passage. Aristotle draws out the comparison between forms of government and musical modes in such a way as to make it plain that in the case of the modes the distinction was one of pitch ([Greek: tas suntonôteras ... tas d' aneimenas kai malakas]). The Dorian was the best, because the highest, of the lower keys,--the others being Hypo-dorian (in the earlier sense, immediately below Dorian), and Hypo-phrygian--while Phrygian was the first of the higher series which took in Lydian and Mixo-lydian. The division would be aided, or may even have been suggested, by the circumstance that it nearly coincided with the favourite contrast of Hellenic and 'barbarous' modes[2]. There is another passage, however, which can hardly be reconciled with a classification according to pitch alone. In the chapters dealing with the ethical character of music Aristotle dwells (as will be remembered) upon the exciting and orgiastic character of the Phrygian mode, and notices its especial fitness for the dithyramb. This fitness or affinity, he says, was so marked that a poet who tried to compose a dithyramb in another mode found himself passing unawares into the Phrygian (_Pol._ viii. 7). It is natural to understand this of the use of certain sequences of intervals, or of cadences, such as are characteristic of a 'mode' in the modern sense of the word, rather than of a change of key. If this is so we may venture the further hypothesis that the Phrygian music, in some at least of its forms, was distinguished not only by pitch, but also by the more or less conscious use of scales which differed in type from the scale of the Greek standard system.

[Footnote 1: _Harmonik und Melopöie_, p. 356 (ed. 1863): 'Die älteste griechische Tonart ist demnach eine Molltonart.... Aus Kleinasien wurden zunächst zwei Durtonarten nach Griechenland eingeführt, die lydische und phrygische.' In the 1886 edition of the same book (p. 189) Westphal discovers a similar classification of modes implied in the words of Plato, _Rep._ p. 400 a [Greek: tri' atta estin eidê ex hôn hai baseis plekontai, hôsper en tois phthongois tettara hothen hai pasai harmoniai]. But Plato is evidently referring to some matter of common knowledge. The three forms or elements of which all rhythms are made up are of course the ratios 1: 1, 2: 1 and 3: 2, which yield the three kinds of rhythm, dactylic, iambic and cretic (answering to common, triple, and quintuple time). Surely the four elements of all musical scales of which Plato speaks are not four kinds of scale (_Harmonien-Klassen_), but the four ratios which give the primary musical intervals--viz. the ratios 2: 1, 3: 2, 4: 3 and 9: 8, which give the Octave, Fifth, Fourth and Tone.]

[Footnote 2: If Hypo-phrygian is the same as the older Ionian (p. 11), the coincidence is complete for the time of Aristotle. Plato treats the claim of Ionian to rank among the Hellenic modes as somewhat doubtful (_Laches_, p. 188).]

It may be urged that this hypothesis is inconsistent with our interpretation of the passage of the _Problems_ about the tonic character of the Mesê. If _a_ is key-note, it was argued, the mode is that of the _a_-species (Hypo-dorian, our Minor), or at most--by admitting the tetrachord Synêmmenôn--it includes the _e_-species (Dorian of Helmholtz). The answer may be that the statement of the _Problems_ is not of this absolute kind. It is not the statement of a technical writer, laying down definite rules, but is a general observation, or at best a canon of taste. We are not told how the predominance of the Mesê is shown in the form of the melody. Moreover this predominance is not said to be exercised in music generally, but in all _good_ music ([Greek: panta gar ta chrêsta melê pollakis tê mesê chrêtai]). This may mean either that tonality in Greek music was of an imperfect kind, a question of style and taste rather than of fixed rule, or that they occasionally employed modes of a less approved stamp, unrecognised in the earlier musical theory. § 36. _Conclusion._

The considerations set forth in the last chapter seem to show that if difference of mode or species cannot be entirely denied of the classical period of Greek music, it occupied a subordinate and almost unrecognised place.

The main elements of the art were, (1) difference of _genus_,--the sub-divisions of the tetrachord which Aristoxenus and Ptolemy alike recognise, though with important discrepancies in detail; (2) difference of pitch or _key_; and (3) _rhythm_. Passing over the last, as not belonging to the subject of _Harmonics_, we may now say that genus and key are the only grounds of distinction which are evidently of practical importance. No others were associated with the early history of the art, with particular composers or periods, with particular instruments, or with the ethos of music. This, however, is only true in the fullest sense of Greek music before the time of Ptolemy. The main object of Ptolemy's reform of the keys was to provide a new set of scales, each characterised by a particular succession of intervals, while the pitch was left to take care of itself. And it is clear, especially from the specimens which Ptolemy gives of the scales in use in his time, that he was only endeavouring to systematise what already existed, and bring theory into harmony with the developments of practice. We must suppose, therefore, that the musical feeling which sought variety in differences of key came to have less influence on the practical art, and that musicians began to discover, or to appreciate more than they had done, the use of different 'modes' or forms of the octave scale. Along with this change we have to note the comparative disuse of the Enharmonic and Chromatic divisions of the tetrachord. The Enharmonic, according to Ptolemy, had ceased to be employed. Of the three varieties of Chromatic given by Aristoxenus only one remains on Ptolemy's list, and that the one which in the scheme of Aristoxenus involved no interval less than a semitone. And although Ptolemy distinguished at least three varieties of Diatonic, it is worth notice that only one of these was admitted in the tuning of the lyre,--the others being confined to the more elaborate cithara. In Ptolemy's time, therefore, music was rapidly approaching the stage in which all its forms are based upon a single scale--the natural diatonic scale of modern Europe.

In the light of these facts it must occur to us that Westphal's theory of seven modes or species of the Octave is really open to an _a priori_ objection as decisive in its nature as any of the testimony which has been brought against it. Is it possible, we may ask, that a system of modes analogous to the ecclesiastical Tones can have subsisted along with a system of scales such as the genera and 'colours' of early Greek music? The reply may be that Ptolemy himself combines the two systems. He supposes five divisions of the tetrachord, and seven modes based upon so many species of the Octave--in all thirty-five different scales (or seventy, if we bring in the distinction of octaves [Greek: apo nêtês] and [Greek: apo mesês]). But when we come to the scales actually used on the chief Greek instrument, the cithara, the number falls at once to six. Evidently the others, or most of them, only existed on paper, as the mathematical results of certain assumptions which Ptolemy had made. And if this can be said of Ptolemy's theory, what would be the value of a similar scheme combining the modes with the Enharmonic and the different varieties of the Chromatic genus? The truth is, surely, that such a scheme tries to unite elements which belong to different times, which in fact are the fundamental ideas of different stages of art.

The most striking characteristic of Greek music, especially in its earlier periods, is the multiplicity and delicacy of the intervals into which the scale was divided. A sort of frame-work was formed by the division of the octave into tetrachords, completed by the so-called disjunctive tone; and so far all Greek music was alike. But within the tetrachord the reign of diversity was unchecked. Not only were there recognised divisions containing intervals of a fourth, a third, and even three-eighths of a tone, but we gather from several things said by Aristoxenus that the number of possible divisions was regarded as theoretically unlimited. Thus he tells us that there was a constant tendency to flatten the 'moveable' notes of the Chromatic genus, and thus diminish the small intervals, for the sake of 'sweetness' or in order to obtain a plaintive tone[1];--that the Lichanos of a tetrachord may in theory be any note between the Enharmonic Lichanos (_f_ in the scale _e-e*-f-a_) and the Diatonic (_g_ in the scale _e-f-g-a_)[2];--and that the magnitude of the smaller intervals and division of the tetrachord generally belongs to the indefinite or indeterminate element in music[3]. Moreover, in spite of the disuse of several of the older scales, much of this holds good for the time of Ptolemy. The modern diatonic scale is fully recognised by him, but only as one of several different divisions. And the division which he treats as the ordinary or standard form of the octave is not the modern diatonic scale, but one of the so-called 'soft' or flattened varieties. It is clear that in the best periods of Greek music these refinements of melody, which modern musicians find scarcely conceivable, were far from being accidental or subordinate features. Rather, they were as much bound up with the fundamental nature of that music as complex harmony is with the music of modern Europe.

[Footnote 1: Aristox. _Harm._ p. 23 Meib. [Greek: hoi men gar tê nun katechousê melopoiia ounêtheis monon ontes eiktôs tên ditonon lichanon] (_f_ in the scale _e-a_) [Greek: exorizousi; suntonôterais gar chrôntai schedon hoi pleistoi tôn nun. toutou d' aition to boulesthai glukainein aei. sêmeion de hoti toutou stochazontai, malista men gar kai pleiston chronon en tô chrômati diatribousin. hotan d' aphikôntai pote eis tên harmonian engus tou chromatos prosagousi, sunepismômenou tou êthous.]]