| 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 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—
| 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.
§ 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 [38]. 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 [39].
The music of the three hymns is noted in the Lydian key (answering to the modern scale with one ♭). 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 ♭). 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.