The fifteen characters, it has been noticed, form two diatonic octaves. It will appear on a little further examination that the scheme must have been constructed with a view to these two octaves. The successive notes are not expressed by the letters of the alphabet in their usual order (as is done in the case of the vocal notes). The highest note is represented by the first letter, [Greek: A]: and then the remaining fourteen notes are taken in pairs, each with its octave: and each of the pairs of notes is represented by two successive letters--the two forms of lambda counting as one such pair of letters. Thus: The higher and lower _e_ are denoted by [Greek: b] and [Greek: g] " " " _c_ " " [Greek: d] " [Greek: e] " " " _g_ " " [Symbol: digamma] " [Greek: z] " " " _a_ " " [Greek: ê] " [Greek: th] " " " _b_ " " [Greek: i] " [Greek: k] " " " _d_ " " [Greek: l^1] " [Greek: l^2] " " " _f_ " " [Greek: m] " [Greek: n] On this plan the alphabetical order of the letters serves as a series of links connecting the highest and lowest notes of every one of the seven octaves that can be taken on the scale. It is evident that the scheme cannot have grown up by degrees, but is the work of an inventor who contrived it for the practical requirements of the music of his time. Two questions now arise, which it is impossible to separate. What is the scale or System for which the notation was originally devised? And how and when was the notation adapted to exhibit the several keys in which any such System might be set?