Note 46 — § 35. Evidence for Scales of different species.

Harmonik und Melopöie, p. 356 (ed. 1863): 'Die älteste griechische Tonart ist demnach eine Molltonart.... Aus Kleinasien wurden zunächst zwei Durtonarten nach Griechenland eingeführt, die lydische und phrygische.' In the 1886 edition of the same book (p. 189) Westphal discovers a similar classification of modes implied in the words of Plato, Rep. p. 400 a tri' atta estin eidê ex hôn hai baseis plekontai, hôsper en tois phthongois tettara hothen hai pasai harmoniai. But Plato is evidently referring to some matter of common knowledge. The three forms or elements of which all rhythms are made up are of course the ratios 1: 1, 2: 1 and 3: 2, which yield the three kinds of rhythm, dactylic, iambic and cretic (answering to common, triple, and quintuple time). Surely the four elements of all musical scales of which Plato speaks are not four kinds of scale (Harmonien-Klassen), but the four ratios which give the primary musical intervals—viz. the ratios 2: 1, 3: 2, 4: 3 and 9: 8, which give the Octave, Fifth, Fourth and Tone.