§ 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' (diatonon toniaion) [34]. The other was a 'mixture' of this Diatonic with the standard Chromatic (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 [35]. 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 [36]. Of the six scales two are of the Hypo-dorian or Common species (a-a). One of these, called tritai, is purely Diatonic of the Middle Soft variety; the intervals expressed by fractions are as follows:

a9/8 b28/27 c8/7 d9/8 e28/27 f8/7 g9/8 a

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

a9/8 b22/21 c12/11 c♯7/6 e28/27 f8/7 g9/8 a

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

e21/20 f10/9 g8/7 a9/8 b28/27 c8/7 d9/8 e

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

e28/27 f8/7 g9/8 a9/8 b16/15 c9/8 d10/9 e

Westphal (Harmonik und Melopöie, 1863, p. 255) supposes a much deeper corruption. He would restore 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 iastia and iastiaioliaia distinct scales, and furthermore inserting a new scale, of unknown name). Moreover the (unknown) scale of unmixed diatonon toniaion is out of its place at the end of the list. Westphal's objection to 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 malaka the admixture, according to i. 16, is one of chrômatikon syntonon, according to ii. 16 of 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 malaka just before.

(2) The iastia of i. 16 is called astiaioliaia 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 diatonon syntonon and d. ditoniaion are not really distinguished by Ptolemy. In one passage (i. 16) he gives his lydia and iastia as a mixture with d. syntonon, adding that in practice it was d. ditoniaion. In the other (ii. 16) he speaks at once of 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 leimma.

Of the remaining scales one, called hypertropa, is Phrygian in species (d-d), and of the standard genus:

d9/8 e28/27 f8/7 g9/8 a9/8 b28/27 c8/7 d

One, called iastia, or iastiaioliaia, is of the Hypo-phrygian or g-species, the tetrachord b-e being 'highly strung' Diatonic or (in practice) Pythagorean, viz.:

g9/8 a9/8 b256/243 c9/8 d9/8 e28/27 f8/7 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 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 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 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 [37] leads us to regard as the true division, the scale would exhibit the intervals—

g5/4 b6/5 d7/6 f8/7 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.