21edo: Difference between revisions

From Xenharmonic Reference
Created page with "'''21edo''' is an equal division of the octave into 21 steps of 1200c/21 ~= 57.1c each. == Basic theory == === Intervals and notation === === Prime harmonic approximations === {{Harmonics in ED|21|31|0}} {{Cat|Edos}} ==== Edostep interpretations ==== 21edo's edostep has the following interpretations in the 2.3.5.7.23.29.31 subgroup: * 32/31 * 31/30 * 30/29 * 29/28 * 49/48 * 64/63"
 
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* 29/28
* 29/28
* 49/48
* 49/48
* 46/45
* 64/63
* 64/63

Revision as of 23:04, 22 January 2026

21edo is an equal division of the octave into 21 steps of 1200c/21 ~= 57.1c each.

Basic theory

Intervals and notation

Prime harmonic approximations

Approximation of prime harmonics in 21edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) 0.0 -16.2 +13.7 +2.6 +20.1 +16.6 +9.3 -11.8 +0.3 -1.0 -2.2
Relative (%) 0.0 -28.4 +24.0 +4.6 +35.2 +29.1 +16.3 -20.6 +0.5 -1.8 -3.8
Steps

(reduced)

21

(0)

33

(12)

49

(7)

59

(17)

73

(10)

78

(15)

86

(2)

89

(5)

95

(11)

102

(18)

104

(20)

Edostep interpretations

21edo's edostep has the following interpretations in the 2.3.5.7.23.29.31 subgroup:

  • 32/31
  • 31/30
  • 30/29
  • 29/28
  • 49/48
  • 46/45
  • 64/63