[Footnote 1: The fullest account of this curious fragment of notation is that given by Bellermann in his admirable book, _Die Tonleitern und Musiknoten der Griechen_, pp. 61-65. His conjectures as to its origin do not claim a high degree of probability. See the remarks on pp. 97-99.] [Footnote 2: Cp. Plato, _Rep._ p. 531: [Greek: kai smikrotaton einai touto diastêma, hô metrêteon.] It may even be that this sense of [Greek: harmonia] was connected with the use for the Enharmonic genus. It is at least worth notice that the phrase [Greek: ha ekaloun harmonias] in this passage answers to the adjective [Greek: enarmoniôn] in the passage first quoted (compare the words [Greek: peri autôn monon tôn hepta oktachordôn ha ekaloun harmonias] with [Greek: peri systêmatôn oktachordôn enarmoniôn monon]).] The use of [Greek: harmonia] as an equivalent for 'System' or 'division of the scale' appears in an important passage in Plato's _Philebus_ (p. 17): [Greek: all', ô phile, epeidan labês ta diastêmata hoposa esti ton arithmon tês phônês oxytêtos te peri kai barytêtos, kai hopoia, kai tous horous tôn diastêmatôn, kai ta ek toutôn hosa systêmata gegonen, ha katidontes hoi prosthen paredosan hêmin tois hepomenois ekeinois kalein auta harmonias, k.t.l.] In this passage,--which has an air of technical accuracy not usual in Plato's references to music (though perhaps characteristic of the _Philebus_),--there is a close agreement with the technical writers, especially Aristoxenus. The main thought is the application of limit or measure to matter which is given as unlimited or indefinite--the distinction drawn out by Aristoxenus in a passage quoted below (p. 81). The treatment of the term 'System' is notably Aristoxenean (cp. _Harm._ p. 36 [Greek: ta systêmata theôrêsai posa te esti kai poia atta, kai pôs ek te tôn diastêmatôn kai phthongôn synestêkota]). Further, the use of [Greek: harmonia] for [Greek: systêma], or rather of the plural [Greek: harmoniai] for the [Greek: systêmata] observed by the older musical theorists, is exactly what is noticed by Aristoxenus as if it were more or less antiquated. Even in the time of Plato it appears as a word of traditional character ([Greek: hoi prosthen paredosan]), his own word being [Greek: systêma]. It need not be said that there is no such hesitation, either in Plato or in Aristotle, about the use of [Greek: harmoniai] for the modes. The same use of [Greek: harmonia] is found in the Aristotelian _Problems_ (xix. 26), where the question is asked, [Greek: dia ti mesê kaleitai en tais harmoniais, tôn de oktô ouk esti meson], _i.e._ how can we speak of the Mesê or 'middle note' of a scale of eight notes?