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Notes for: Systems Based on Numbers | 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.)


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* Number classification
* Mathematical functions
* Lissajous figures
* Two sine functions
* Differential equations [for sine sums]
* Musical chords [from sine sums]
* Three sine functions
* Substitution systems [and sine sums]
* Many sine functions
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From Stephen Wolfram: A New Kind of Science [citation] Previous note-----Next note