Notes

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 2^(n/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\[Flat]) with frequency ratio Sqrt[2] have generally been avoided as sounding discordant. (See also page 1079.)

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