21edo

From Xenharmonic Reference
Revision as of 23:06, 22 January 2026 by Inthar (talk | contribs)

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