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Music Theory for Computer Musicians by Michael Hewitt

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Pythagorean Intonation

Another type of intonation is Pythagorean intonation, in which each note of the scale is tuned in pure fifths of ratio 3/2. Also used in traditional Chinese and Arabian music, it generates its own unique interval set, too. The 12-toned chromatic scale as tuned in equal temperament, just intonation, and Pythagorean intonation would appear as you see in Table 25.1.

Table 25.1. Twelve-Toned Chromatic Scale Tuned in Equal Temperament, Just Intonation, and Pythagorean Intonation
Equally TemperedJust IntonationPythagorean Intonation
NoteCentsRatioCentsRatioCents
C00001/100001/10000
Db010016/150112256/2430090
D02009/802049/80204
Eb03006/5031632/270294
E04005/4038681/640408
F05004/304984/30498
F#060045/320590729/5120612
G07003/20702 ...

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