The C. F. Abdy Williams´s book about the Story of Musical Notation.
An excerpt from the INTRODUCTORY SKETCH:
THE representation of musical sounds in writing, called musical notation, or simply notation, from nota, a mark or sign, is a thing so commonplace, so universal, and apparently so simple, that we are apt to overlook the fact that our stave, with its variously shaped "notes" and all that goes to convey a composer's thoughts to the world, are the outcome of centuries of experiments and gradual improvements. Whether the Egyptians, the Hebrews, Chaldeans, and other Semitic nations, which had arrived at a certain degree of musical culture, noted their music is not known; it may be presumed that they did, but up to the present nothing has been discovered of the nature of a musical semeiography.
It cannot be said that these nations were not yet sufficiently advanced to be able to invent a means of writing down the various sounds of voices and instruments: the fact remains that, as far as we know at present, the Greeks were the only ancient European nation that did so, and they made use of letters of the alphabet for this purpose, as did the Hindus before them, and the Western Europeans after them; the Persians Other used numbers, and a kind of stave of nine lines, between which the numbers were placed, while the Chinese used special signs for their pentatonic scale.
The history of our present notation begins with that of the Greeks, who arranged their alphabet in groups of three letters to each tone, thus showing the semitones and quarter-tones. The knowledge of this arrangement passed away until rediscovered in the nineteenth century by the labours of Bellermann, Fortlage, and others, who have explained the notation tables given by Alypius, Aristides, Nicomachus, Ptolemy, Gaudentius, and later writers. The tables, arranged according to tropes and modes, show successions of letters, apparently taken at haphazard, to indicate the seven notes of the three kinds of scale, the diatonic, chromatic, and enharmonic.
The Greeks also used a system of time-signs, two of which have survived to the present day in the long (-) and short (u) signs placed over vowels in Latin grammars, and they had means of representing accent, so that their notation was as complete as the mediaeval tablatures, of which we shall speak later, or the modern tonic sol-fa.
The first use of Latin letters for representing musical sounds is found in the writings of Boethius, about A.D. 500; though it is a mistake to speak of the "Boethian notation," since he never used the letters to indicate musical melodies….