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 [Greek: 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 ([Greek: peri tês en Timaiô psychogonias]) speaks of the Proslambanomenos as having been added in comparatively recent times (p. 1029 _c_ [Greek: 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' ([Greek: 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[1]). [Footnote 1: The term [Greek: hyperypatê] had all but disappeared from the text of Theon Smyrnaeus in the edition of Bullialdus (Paris, 1644), having been corrupted into [Greek: hypatê] or [Greek: parypatê] in every place except one (p. 141, 3). It has been restored from MSS. in the edition of Hiller (Teubner, Leipzig, 1878). The word occurs also in Aristides Quintilianus (p. 10 Meib.), where the plural [Greek: hyperypatai] is used for the notes below Hypatê, and in Boethius (_Mus._ i. 20). It may be worth noticing also that Thrasyllus uses the words [Greek: diezeugmenê] and [Greek: hyperbolaia] in the sense of [Greek: nêtê diezeugmenôn] and [Greek: nêtê hyperbolaiôn] (Theon Smyrn. _l. c._).] 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[1]. 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.