Preface.

A certain Spartan, wishing to cut the redundant strings from a Lyre, pointed out that there was another among the Spartans who used a Lyre with the same number of strings; upon saying this, he was dismissed. Thus, since history is varied on this point and it is not sufficiently certain—though it matters much—whether authors are speaking of the strings of the Lyre or the Cithara both are types of ancient Greek stringed instruments similar to harps when they write that he was condemned; and since he even earned praise for adding strings to the Cithara, as he is proclaimed by all professors of this art to have made an eleven-stringed instrument Hendecachordum out of a nine-stringed one Enneachordo along with Hestiaeus of Colophon, this point may be deliberately omitted, and let us come to the matter itself.

Those who cry out that we have introduced a "new" commentary on the Twelve Modes original: "XII Modis"—truly, they show themselves to have been only very lightly engaged in the reading of ancient authors. Indeed, they are content with the usage of these few centuries, in which eight or nine modes sufficed for the singing of the Psalms. But we must bring forward authors—few indeed, but those to whom credit is deservedly given.

Plato, although he frequently mentions the Modes, calls them "Harmonies" original: "Harmonías". Certainly, in the third book of the Republic, he names six principal Modes; if we give to each of these its own plagal a "plagal" mode is a variation of a scale starting a fourth lower; original: "plagios" version, who could deny that there are twelve Modes? From the same author, and from his no less learned disciple Aristotle, it is clear enough that in that era, knowledge of the Modes was in very frequent use among all the learned. We have not read Aristoxenus ourselves, but all admit he was the author of the twelve Modes, having even added a nomenclature for them, which we have determined should be followed in the second book of these Commentaries. I pass over here innumerable Greeks, some of whom have even been translated into Latin.

Among the Roman writers, Boëthius—the true light of this art—established seven species of the Diapason the octave, from which twelve (or if you prefer, fourteen) Modes are easily gathered through arithmetic and harmonic division. For in more than one place, he admits that the eighth species is the same as the first, and was added by Ptolemy to complete the maximum system of the double octave original: "δὶς διὰ πασῶν". Otherwise, there would be sixteen, but we, along with Aristoxenus, set them at twelve (excluding two "bastard" modes). Martianus Capella shows us fifteen, of which we shall speak in the proper place. The Roman Church uses nine intonations in the singing of the Psalms, but its chants nevertheless contain thirteen Modes, as we shall show in the same second book with examples taken from the Church Choir. Georgius Valla was satisfied to review everyone's opinion and pile up whatever he had read written anywhere about musicians. Thus, he himself has more than twelve.

It is established, therefore, that this assertion of ours concerning the Twelve Modes is not a new thing, but a proper restoration of antiquity. But let the reader not believe this until I have shown the matter itself with firm arguments through mathematical ratios, and the precepts through the clearest examples—which we are fully persuaded we have done in the two subsequent books. Furthermore, I often tend to marvel that, while in our age no one uses the Chromatic or Enharmonic two of the three "genera" of Greek music, involving semi-tones and quarter-tones—two types of melody frequent among the ancients—nevertheless all...