The Modes of Ancient Greek Music Part 8

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

Westphal also finds the nomenclature by position implied in the pa.s.sage of the Aristotelian _Problems_ (xix. 20) which deals with the peculiar relation of the Mese to the rest of the musical scale. The pa.s.sage has already been quoted and discussed (_supra_, p. 43), and it has been pointed out that if the Mese of the Perfect System ([Greek: mese 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 Mese of this pa.s.sage to be the [Greek: mese kata thesin], or Mese by position. That is, Westphal is obliged by his theory of the Modes to take the term Mese 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--Mese, Hypate, Nete 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: chroma 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 pa.s.sages (_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 te lyra kaloumena sterea tonou tinos hypo ton tou toniaiou diatonou arithmon tou autou tonou, ta de malaka hypo ton en to migmati tou malakou chromatos apithmon 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 pa.s.sages 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 pa.s.sage (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 doriou] cannot be correct, not merely because they contradict the statement of the earlier pa.s.sage 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 pa.s.sages. Hence we should doubtless read [Greek: ta de lydia hoi tou toniaiou diatonou tou Doriou].]

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 Melopoie_, 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 Doriou]. This introduces a serious discrepancy between the two pa.s.sages, 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 pa.s.sages are:

(1) In the scales of the lyre called [Greek: malaka] the admixture, according to i. 16, is one of [Greek: chromatikon 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 pa.s.sage 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 pa.s.sage (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: mese 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 compa.s.s 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 Mese [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 Mese [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--