The term 'Perfect System' (systÊma teleion) is applied by the technical writers to a scale which is evidently formed by successive additions to the heptachord and octachord scales explained in the preceding chapter. It may be described as a combination of two scales, called the Greater and Lesser Perfect System.

The Greater Perfect System (systÊma teleion meizon) consists of two octaves formed from the primitive octachord System by adding a tetrachord at each end of the scale. The new notes are named like those of the adjoining tetrachord of the original octave, but with the name of the tetrachord added by way of distinction. Thus below the original HypatÊ we have a new tetrachord HypatÔn (tetrachordon hypatÔn), the notes of which are accordingly called HypatÊ HypatÔn, ParhypatÊ HypatÔn, and Lichanos HypatÔn: and similarly above NÊtÊ we have a tetrachord HyperbolaiÔn. Finally the octave downwards from MesÊ is completed by the addition of a note appropriately called Proslambanomenos.

The Lesser Perfect System (systÊma teleion elasson) is apparently based upon the ancient heptachord which consisted of two 'conjunct' tetrachords meeting in the MesÊ. This scale was extended downwards in the same way as the Greater System, and thus became a scale of three tetrachords and a tone.

These two Systems together constitute the Perfect and 'unmodulating' System (systÊma teleion ametabolon), which may be represented in modern notation [9] as follows:

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' (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. 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 kai ha men autÔn esti teleia, ha d' ou, atelÊ men tetrachordon, pentachordon, teleion de oktachordon. This is a use of 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 [10]. Along with the lyre, which kept its primitive simplicity as the instrument of education and everyday use, the Greeks had the cithara (kithara), an enlarged and improved lyre, which, to judge from the representations on ancient monuments, was generally seen in the hands of professional players (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. The poet Ion, the contemporary of Sophocles, was the author of an epigram on a certain ten-stringed lyre, which seems to have had a scale closely approaching that of the Lesser Perfect System [11]. A little later we hear of the comic poet Pherecrates attacking the musician Timotheus for various innovations tending to the loss of primitive simplicity, in particular the use of twelve strings [12]. According to a tradition mentioned by Pausanias, the Spartans condemned Timotheus because in his cithara he had added four strings to the ancient seven. The offending instrument was hung up in the Scias (the place of meeting of the Spartan assembly), and apparently was seen there by Pausanias himself (Paus. iii. 12, 8).

A similar or still more rapid development took place in the flute (aulos). The flute-player Pronomus of Thebes, who was said to have been one of the instructors of Alcibiades, invented a flute on which it was possible to play in all the modes. 'Up to his time,' says Pausanias (ix. 12, 5), 'flute-players had three forms of flute: with one they played Dorian music; a different set of flutes served for the Phrygian mode (harmonia); and the so-called Lydian was played on another kind again. Pronomus was the first who devised flutes fitted for every sort of mode, and played melodies different in mode on the same flute.' The use of the new invention soon became general, since in Plato's time the flute was the instrument most distinguished by the multiplicity of its notes: cp. Rep. p. 399 ti de? aulopoious Ê aulÊtas paradexei eis tÊn polin? Ê ou touto polychordotaton? Plato may have had the invention of Pronomus in mind when he wrote these words.

With regard to the order in which the new notes obtained a place in the schemes of theoretical musicians we have no trustworthy information. The name proslambanomenos, applied to the lowest note of the Perfect System, points to a time when it was the last new addition to the scale. Plutarch in his work on the Timaeus of Plato (peri tÊs en TimaiÔ psychogonias) speaks of the Proslambanomenos as having been added in comparatively recent times (p. 1029 c hoi de neÔteroi ton proslambanomenon tonÔ diapheronta tÊs hypatÊs epi to bary taxantes to men holon diastÊma dis dia pasÔn epoiÊsan). The rest of the Perfect System he ascribes to 'the ancients' (tous palaious ismen hypatas men dyo, treis de nÊtas, mian de mesÊn kai mian paramesÊn tithemenous). An earlier addition—perhaps the first made to the primitive octave—was a note called HyperhypatÊ, which was a tone below the old HypatÊ, in the place afterwards occupied on the Diatonic scale by Lichanos HypatÔn. It naturally disappeared when the tetrachord HypatÔn came into use. It is only mentioned by one author, Thrasyllus (quoted by Theon Smyrnaeus, cc. 35-36 [13]).

The notes of the Perfect System, with the intervals of the scale which they formed, are fully set out in the two treatises that pass under the name of the geometer Euclid, viz. the Introductio Harmonica and the Sectio Canonis. Unfortunately the authorship of both these works is doubtful [14]. All that we can say is that if the Perfect System was elaborated in the brief interval between the time of Aristotle and that of Euclid, the materials for it must have already existed in musical practice.