. It may be that the diagrams to which Aristoxenus refers made use of these duplicates: that is to say, they may have made use of all four positions of a character (such as
) whether the interval to be filled was a tone or a semitone. If so, the seven intervals would give twenty-eight characters (besides the upper octave-note), and apparently therefore twenty-eight dieses. Some traces of this use of characters in four positions have been noticed by Bellermann (Tonleitern, p. 65).]
[22] 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.]
[23] Cp. Plato, Rep. p. 531: kai smikrotaton einai touto diastêma, hô metrêteon. It may even be that this sense of harmonia was connected with the use for the Enharmonic genus. It is at least worth notice that the phrase ha ekaloun harmonias in this passage answers to the adjective enarmoniôn in the passage first quoted (compare the words peri autôn monon tôn hepta oktachordôn ha ekaloun harmonias with peri systêmatôn oktachordôn enarmoniôn monon).
[24] So in Plato, Leg. p. 665 a: tê dê tês kinêseôs taxei rhythmos onoma eiê, tê d' au tês phônês, tou te oxeos hama kai bareos synkerannymenôn, harmonia onoma prosagoreuoito.
[25] Ptol. Harm. ii. 6. After drawing a distinction between difference of key as affecting the whole of a melody or piece of music and as a means of change in the course of it—the distinction, in short, between transposition and modulation proper—he says of the latter: hautê de hôsper ekpiptein autên (sc. tên aisthêsin) poiei tou synêthous kai prosdokômenou melous, hotan epi pleon men syneirêtai to akolouthon, metabainê de pê pros heteron eidos, êtoi kata to genos ê kata tên tasin. That is to say, the sense of change is produced by a change of genus or of pitch. A change of species is not suggested. So Dionys. Hal. De Comp. Verb. c. 19 hoi de ge dithyrambopoioi kai tous tropous (keys) meteballon, Dôrikous te kai Phrygious kai Lydious en tô autô asmati poiountes; kai tas melôdias exêllatton, tote men enarmonious poiountes, k.t.l.
[26] Since this was written I have learned from Mr. H. S. Jones that the form
for beta occurs on an inscription dated about 500 B.C., viz. Count Tyszkiewicz's bronze plate, published simultaneously by Robert in the Monumenti Antichi pubblicati per cura della reale Accademia dei Lincei, i. pp. 593 (with plate), and Fröhner in the Revue Archéologique, 1891 July-August, pp. 51 ff. Pl. xix. Mr. Jones points out that this