[Footnote 1: _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 [Greek: 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.] [Footnote 2: If Hypo-phrygian is the same as the older Ionian (p. 11), the coincidence is complete for the time of Aristotle. Plato treats the claim of Ionian to rank among the Hellenic modes as somewhat doubtful (_Laches_, p. 188).] It may be urged that this hypothesis is inconsistent with our interpretation of the passage of the _Problems_ about the tonic character of the Mesê. If _a_ is key-note, it was argued, the mode is that of the _a_-species (Hypo-dorian, our Minor), or at most--by admitting the tetrachord Synêmmenôn--it includes the _e_-species (Dorian of Helmholtz). The answer may be that the statement of the _Problems_ is not of this absolute kind. It is not the statement of a technical writer, laying down definite rules, but is a general observation, or at best a canon of taste. We are not told how the predominance of the Mesê is shown in the form of the melody. Moreover this predominance is not said to be exercised in music generally, but in all _good_ music ([Greek: panta gar ta chrêsta melê pollakis tê mesê chrêtai]). This may mean either that tonality in Greek music was of an imperfect kind, a question of style and taste rather than of fixed rule, or that they occasionally employed modes of a less approved stamp, unrecognised in the earlier musical theory. § 36. _Conclusion._ The considerations set forth in the last chapter seem to show that if difference of mode or species cannot be entirely denied of the classical period of Greek music, it occupied a subordinate and almost unrecognised place.