tên dekabamona taxin echousa
tas symphônousas harmonias triodous;
prin men s' heptatonon psallon dia tessara pantes
Hellênes, spanian mousan aeiramenoi.
'The triple ways of music that are in concord' must be the three conjunct tetrachords that can be formed with ten notes (b c d e f g a b♭ c d). This is the scale of the Lesser Perfect System before the addition of the Proslambanomenos.
[12] Pherecrates cheirôn fr. 1 (quoted by Plut. de Mus. c. 30). It is needless to refer to the other traditions on the subject, such as we find in Nicomachus (Harm. p. 35) and Boethius.
[13] The term hyperypatê had all but disappeared from the text of Theon Smyrnaeus in the edition of Bullialdus (Paris, 1644), having been corrupted into hypatê or parypatê in every place except one (p. 141, 3). It has been restored from MSS. in the edition of Hiller (Teubner, Leipzig, 1878). The word occurs also in Aristides Quintilianus (p. 10 Meib.), where the plural hyperypatai is used for the notes below Hypatê, and in Boethius (Mus. i. 20).
It may be worth noticing also that Thrasyllus uses the words diezeugmenê and hyperbolaia in the sense of nêtê diezeugmenôn and nêtê hyperbolaiôn (Theon Smyrn. l. c.).
[14] The Introduction to Harmonics (eisagôgê harmonikê) which bears the name of Euclid in modern editions (beginning with J. Pena, Paris, 1557) cannot be his work. In some MSS. it is ascribed to Cleonides, in others to Pappus, who was probably of the fourth century A. D. The author is one of the harmonikoi or Aristoxeneans, who adopt the method of equal temperament. He may perhaps be assigned to a comparatively early period on the ground that he recognises only the thirteen keys ascribed to Aristoxenus—not the fifteen keys given by most later writers (Aristides Quint., p. 22 Meib.). For some curious evidence connecting it with the name of the otherwise unknown writer Cleonides, see K. von Jan, Die Harmonik des Aristoxenianers Kleonides (Landsberg, 1870). The Section of the Canon (kanonos katatomê) belongs to the mathematical or Pythagorean school, dividing the tetrachord into two major tones and a leimma which is somewhat less than a semitone. In point of form it is decidedly Euclidean: but we do not find it referred to by any writer before the third century A. D.—the earliest testimony being that of Porphyry (pp. 272-276 in Wallis' edition).
[15] Plato, Rep. p. 399: ouk ara, ên d' egô, polychordias ge oude panarmoniou hêmin deêsei en tais ôdais te kai melesin. Ou moi, ephê, phainetai. Trigônôn ara kai pêktidôn kai pantôn organôn hosa polychorda kai polyarmonia dêmiourgous ou threpsomen. Ou phainometha. Ti de? aulopoious ê aulêtas paradexei eis tên polin? ê ou touto polychordotaton, kai auta ta panarmonia aulou tynchanei onta mimêma? Dêla dê, ê d' hos. Lyra dê soi, ên d' egô, kai kithara leipetai, kai kata polin chrêsima; kai au kat' agrous tois nomeusi syrinx an tis eiê.
The aulos was not exactly a flute. It had a mouthpiece which gave it the character rather of the modern oboe or clarinet: see the Dictionary of Antiquities, s. v. tibia. The panarmonion is not otherwise known, and the passage in Plato does not enable us to decide whether it was a real instrument or only a scale or arrangement of notes.
[16] The passage quoted above from the Knights of Aristophanes (p. 7) is sufficient to show that a marked preference for the Dorian mode would be a matter for jest.
[17] Die Lehre von den Tonempfindungen, p. 367, ed. 1863.