Nicomachus Quotes

11 Sourced Quotes

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 [perfect fourth] is the ratio of 4 : 3, the diapente [perfect fifth] that of 3 : 2, and the diapason [perfect octave] the double ratio [2 : 1]; and the most perfect, the di-diapason [fifteenth], is the quadruple ratio [4 : 1].

Nicomachus
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.

Nicomachus
Since of quantity, one kind is viewed by itself, having no relation to anything else, as 'even,' 'odd,' 'perfect,' and the like, and the other is relative to something else, and is conceived of together with its relationship to another thing, like' double,', greater,' 'smaller,' 'half,' 'one and one-half times,' 'one and one-third times,' and so forth, it is clear that two scientific methods will lay hold of and deal with the whole investigation of quantity: arithmetic, [with] absolute quantity; and music, [with] relative quantity.

Nicomachus
If geometry exists, arithmetic must also needs be implied... But on the contrary 3, 4, and the rest might be 5 without the figures existing to which they give names. Hence arithmetic abolishes geometry along with itself, but is not abolished by it, and while it is implied by geometry, it does not itself imply geometry.

Nicomachus
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...

Nicomachus
Scientific number, being set over such things as these, should be harmoniously constituted, in accordance with itself; not by any other but by itself.

Nicomachus
Everything that is harmoniously constituted is knit together out of opposites...

Nicomachus
Every number is at once half the sum of the two on either side of itself...

Nicomachus
All that has by nature, with systematic method, been arranged in the universe, seems both in part and as a whole to have been determined and ordered in accordance with number, by the forethought and the mind of him that created all things; for the pattern was fixed, like a preliminary sketch, by the domination of number preëxistent in the mind of the world-creating God, number conceptual only and immaterial in every way, but at the same time the true and the eternal essence, so that with reference to it, as to an artistic plan, should be created all these things: time, motion, the heavens, the stars, all sorts of revolutions.

Nicomachus
Some... agreeing with Philolaus, 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...

Nicomachus
Two other sciences in the same way will accurately treat of 'size': geometry, the part that abides and is at rest, [and] astronomy, that which moves and revolves.

Nicomachus