a Nêtê Hyperbolaiôn \ Tetrachord g Paranêtê Hyperbolaiôn } Hyperbolaiôn f Tritê Hyperbolaiôn / e Nêtê Diezeugmenôn d Paranêtê Diezeugmenôn \ Tetrachord c Tritê Diezeugmenôn } Diezeugmenôn b Paramesê / d Nêtê Synêmmenôn \ Tetrachord c Paranêtê Synêmmenôn } Synêmmenôn b flat Tritê Synêmmenôn/ a Mesê \ g Lichanos Mesôn } Tetrachord f Parhypatê Mesôn } Mesôn e Hypatê Mesôn / d Lichanos Hypatôn \ Tetrachord c Parhypatê Hypatôn } Hypatôn b Hypatê Hypatôn / a Proslambanomenos [Footnote 1: The correspondence between ancient and modern musical notation was first determined in a satisfactory way by Bellermann (_Die Tonleitern und Musiknoten der Griechen_), and Fortlage (_Das musicalische System der Griechen_).] No account of the Perfect System is given by Aristoxenus, and there is no trace in his writings of an extension of the standard scale beyond the limits of the original octave. In one place indeed (_Harm._ p. 8, 12 Meib.) Aristoxenus promises to treat of Systems, 'and among them of the perfect System' ([Greek: peri te tôn allôn kai tou teleiou]). But we cannot assume that the phrase here had the technical sense which it bore in later writers. More probably it meant simply the octave scale, in contrast to the tetrachord and pentachord--a sense in which it is used by Aristides Quintilianus, p. 11 Meib. [Greek: synêmmenôn de eklêthê to holon systêma hoti tô prokeimenô teleiô tô mechri mesês synêptai], 'the whole scale was called conjunct because it is conjoined to the complete scale that reaches up to Mesê' (_i.e._ the octave extending from Proslambanomenos to Mesê). So p. 16 [Greek: kai ha men autôn esti teleia, ha d' ou, atelê men tetrachordon, pentachordon, teleion de oktachordon.] This is a use of [Greek: teleios] which is likely enough to have come from Aristoxenus. The word was doubtless applied in each period to the most complete scale which musical theory had then recognised. Little is known of the steps by which this enlargement of the Greek scale was brought about. We shall not be wrong in conjecturing that it was connected with the advance made from time to time in the form and compass of musical instruments[1]. Along with the lyre, which kept its primitive simplicity as the instrument of education and everyday use, the Greeks had the cithara ([Greek: kithara]), an enlarged and improved lyre, which, to judge from the representations on ancient monuments, was generally seen in the hands of professional players ([Greek: kitharôdoi]). The development of the cithara showed itself in the increase, of which we have good evidence even before the time of Plato, in the number of the strings.