Everything that is harmoniously constituted is knit together out of op — Nicomachus

"The ancients, who under the leadership of Pythagoras first made science systematic, defined philosophy as the love of wisdom... [Οἱ παλαιοὶ καὶ πρώτοι μεθοδεύσαντες ἐπιστήμην κατάρξαντος Πυθαγόρου ὡρίζοντο φιλοσοφίαν εἶναι φιλίαν σοφίας...] This wisdom he defined as the knowledge, or science, of the truth in real things, conceiving science to be a steadfast and firm apprehension of the underlying substance. and real things to be those which continue uniformly and the same in the universe and never depart even briefly from their existence; these real things would be things immaterial..."

"And once more is this true in the case of music; not only because the absolute is prior to the relative, as great to greater and rich to richer and man to father, but also because the musical harmonies, diatessaron, diapente, and diapason, are named for numbers; similarly all of their harmonic ratios are arithmetical ones, for the diatessaron [] is the ratio of 4 : 3, the diapente [] that of 3 : 2, and the diapason [perfect ] the double ratio [2 : 1]; and the most perfect, the di-diapason [], is the quadruple ratio [4 : 1]."

"Number is limited multitude or a combination of units or a flow of quantity made up of units; and the first division of number is even and odd."

"The even is that which can be divided into two equal parts without a unit intervening in the middle; and the odd is that which cannot..."

"Some... agreeing with , believe that the proportion is called harmonic because it attends upon all geometric harmony, and they say that geometric harmony is the cube because it is harmonized in all three dimensions, being the product of a number thrice multiplied together. For in every cube this proportion is mirrored; there are in every cube 12 sides, 8 angles and 6 faces; hence 8, the [harmonic] mean between 6 and 12, is according to harmonic proportion..."

"Boetius wrote mathematical texts which were considered authoritative in the Western world for more than a thousand years. ...His "institutio arithmetica," a superficial translation of Nicomachus, did provide some Pythagorean number theory which was absorbed in medieval instruction as part of the ancient and : arithmetic, geometry, astronomy, and music."