Chapter 4: Systems Based on Numbers

Section 6: Mathematical Functions

Musical chords [from sine sums]

In a so-called equal temperament scale the 12 standard musical notes that make up an octave have a progression of frequencies 2n/12. Most schemes for musical tuning use rational approximations to these numbers. Until the past century, and since at least the 1300s, diminished fifth or tritone chords that consist of two notes (such as C and G♭) with frequency ratio 2 have generally been avoided as sounding discordant. (See also page 1079.)

Image Source Notebooks:

From Stephen Wolfram: A New Kind of Science [citation]