The words Hypophrygion aulon have also been condemned by Westphal (Aristoxenus, p. 453). He points out the curious contradiction between pros tên tôn aulôn trypêsin blepontes and the complaint ti d' esti pros ho blepontes ... ouden eirêkasin. But if pros tên ... blepontes was a marginal gloss, as Westphal suggests, it was doubtless a gloss on aulon, and if so, aulon is presumably sound. Since the aulos was especially a Phrygian instrument, and regularly associated with the Phrygian mode (as we know from Aristotle, [ see p. 13]), nothing is more probable than that there was a variety of flute called Hypo-phrygian, because tuned so as to yield the Hypo-phrygian key, either by itself or as a modulation from the Phrygian.
In this scheme the important feature—that which marks it as an advance on the others referred to by Aristoxenus—is the conformity which it exhibits with the diatonic scale. The result of this conformity is that the keys stand in a certain relation to each other. Taking any two, we find that certain notes are common to them. So long as the intervals of pitch were quite arbitrary, or were practically irrational quantities, such as three-quarters of a tone, no such relation could exist. It now became possible to pass from one key to another, i. e. to employ modulation (metabolê) as a source of musical effect. This new system had evidently made some progress when Aristoxenus wrote, though it was not perfected, and had not passed into general use.
[4] An objection to this identification has been based on the words of Pollux, Onom. iv. 78 kai harmonia men aulêtikê Dôristi, Phrygisti, Lydios kai Iônikê, kai syntonos Lydisti ên Anthippos exeure. The source of this statement, or at least of the latter part of it, is evidently the same as that of the notice in Plutarch. The agreement with Plato's list makes it probable that this source was some comment on the passage in the Republic. If so, it can hardly be doubted that Pollux gives the original terms, the Platonic Lydisti and Syntonolydisti, and consequently that the later Lydian is not to be found in his Lydios (which is a 'relaxed' mode), but in his syntonos Lydisti. There is no difficulty in supposing that the mode was called syntonos merely in contrast to the other.
[5] It seems not impossible that this difficulty with regard to the 'slack Lydian' and Hypo-lydian may be connected with the contradiction in the statement of Aristoxenus about the schemes of keys in his time ([p. 18]). According to that account, if the text is sound, some musicians placed the Mixo-lydian a semitone below the Dorian—the Hypo-dorian being again a semitone lower. In this scheme, then, the Mixo-lydian held the place of the later Hypo-lydian. The conjecture may perhaps be hazarded, that this lower Mixo-lydian somehow represents Plato's 'slack Lydian,' and eventually passed into the Hypo-lydian.
[6] Aristides Quintilianus uses tropos as the regular word for 'key:' e.g. in p. 136 en tê tôn tropôn, hous kai tonous ekalesamen, ekthesei. So Alypius (p. 2 Meib.) dielein eis tous legomenous tropous te kai tonous, ontas pentekaideka ton arithmon. Also Bacchius in his catechism (p. 12 Meib.) hoi tous treis tropous adontes tinas adousi; Lydion, Phrygion, Dôrion; hoi de tous hepta tinas; Mixolydion, Lydion, Phrygion, Dôrion, Hypolydion, Hypophrygion, Hypodôrion, toutôn poios estin oxyteros? ho Mixolydios, k.t.l. And Gaudentius (p. 21, l. 2) kath' hekaston tropon hê tonon. Cp. Dionys. Hal. De Comp. Verb. c. 19.
[7] Anonymi scriptio de Musica (Berlin. 1841).
[8] This is especially evident in the case of the Lichanos; as was observed by Aristides Quintilianus, who says (p. 10 Meib.): hai kai tô genei lichanoi prosêgoreuthêsan, homônymôs tô plêttonti daktylô tên êchousan autas chordên onomastheisai. But Tritê also is doubtless originally the 'third string' rather than the 'third note.'
[9] The correspondence between ancient and modern musical notation was first determined in a satisfactory way by Bellermann (Die Tonleitern und Musiknoten der Griechen), and Fortlage (Das musicalische System der Griechen).
[10] This observation was made by ancient writers, e.g. by Adrastus (Peripatetic philosopher of the second cent. A.D.): epêuxêmenês de tês mousikês kai polychordôn kai polyphthongôn gegonotôn organôn tô proslêphthênai kai epi to bary kai epi to oxy tois pro[:y]parchousin oktô phthongois allous pleionas, homôs k.t.l. (Theon Smyrn. c. 6).
[11] The epigram is quoted in the pseudo-Euclidean Introductio, p. 19 (Meib.): ho de (sc. Iôn) en dekachordô lyra (i.e. in a poem on the subject of the ten-stringed lyre):—