Here begin the Chapters of the second book on Music

Introduction. Chapter 1.

What Pythagoras established philosophy to be. Chapter 2.

¶ On the division of quantity and which branch of discipline it should be assigned to. 3.
¶ On the effects of relative quantity. 4.
¶ Why multiplicity excels all other types. 5.
¶ What square numbers are and a speculation concerning them. 6.
¶ That all inequality proceeds from equality, and its demonstration. 7.
¶ Rules for finding any continuous proportions of the superparticular type. 8.
¶ On smaller proportions which are measured by others. 9.
¶ Which proportions are created from multiples and multiplied superparticulars. 10.
¶ Which superparticulars are produced by multiples. 11.
¶ On the arithmetic, geometric, and harmonic means means: also called "medieties"; the mathematical ways of finding a middle value between two numbers. 12.
¶ On continuous and disjoint means. 13.
¶ Why the means arranged above were so named. 14.
¶ In what way the aforementioned means proceeded from equality. 15.
¶ On the harmonic mean and a richer speculation concerning it. 16.
¶ In what way the aforementioned means may be placed interchangeably between two terms. 17.
¶ On the measures or modes of consonances according to Nicomachus Nicomachus of Gerasa was a mathematician whose work heavily influenced Boethius. 18.
¶ On the order of consonances according to the opinion of Eubulides and Hippasus. 19. Of Seon. 20.
¶ The opinion of Nicomachus: which consonances are opposed to which. 21.
¶ What must be established first so that the diapason diapason: the interval of an octave may be demonstrated in the multiple genus. 21. The original manuscript repeats the number 21
¶ Demonstration by the "impossible" that the diapason is in the multiple genus. 22.
¶ Demonstration that the diapente diapente: the interval of a fifth, the diatesseron diatesseron: the interval of a fourth, and the tone are in the superparticular genus original: superparticulari; a ratio where the larger number contains the smaller number plus one part of it, like 3:2 or 4:3. 23.
¶ Demonstration that the diapente and diatesseron are in the greatest superparticulars. 24.

in the greatest superparticulars. 24. The text repeats the end of the previous column's entry at the top of the new column
¶ That the diapente is in a sesquialtera sesquialtera: a 3:2 ratio and the diatesseron in a sesquitertia sesquitertia: a 4:3 ratio; and that the tone is in a sesquioctave sesquioctave: a 9:8 ratio. 25.
¶ That the diapason and diapente combined are in a triple proportion; and the double diapason is in a quadruple proportion. 26.
¶ That the diapason and diatesseron together are not a consonance according to the Pythagoreans. 27.
¶ On the semitone: in which smallest numbers it consists. 28.
¶ Demonstration that one part? to another? does not consist of a half-tone. 29. The OCR for chapters 29-30 is compressed/unclear
¶ On the larger part of the tone and its smallest numbers. 31.
¶ By which proportions the diapente and diapason are shown; and that the diapason does not consist of six full tones. 32.

Introduction. 1.

The previous volume organized all the things which I have now proposed to demonstrate diligently. Therefore, before I come to offering the proofs by their proper reasons, let me set down a few things by which the mind of the Christian listener may be prepared to grasp the things that are to be said.

What Pythagoras established philosophy to be. 2.

Pythagoras was the first of all to name the study of wisdom "philosophy" original: phiam, an abbreviation for philosophiam. He defined it as the knowledge and discipline of those things which are properly and truly said "to be." He believed that those things "are" which neither increase by extension nor decrease by diminution, nor are changed by any accidents accidents: in philosophy, these are non-essential qualities that can change without changing the nature of the object. These things are forms, magnitudes, qualities, relations, and the rest which, when studied by themselves, are immutable; but when they are joined to bodies, they are altered and transformed into the many-shaped variations of changing things.

On the differences of quantity and which branch of philosophy it is assigned to. Chapter 3.

According to Pythagoras, all quantity is either continuous or discrete. That which is continuous is called "magnitude," while that which is discrete is called "multitude."