21edo: Difference between revisions

Revision as of 23:11, 22 January 2026

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

Notable scales:

21edo is the first edo with a diasem scale: 323132313 (RH) or 313231323 (LH). Diasem provides basic 2.3.7 harmony, though 7/6 and 28/27 are not accurate at all in 21edo.
Slentonic (5L6s, sLsLsLsLsLs), interpreted as Slendric[11], generated by stacking the ~8/7 (4\21)
Oneirotonic (5L3s, LLsLLsLs), generated by stacking 8\21

Since 21edo's best fifth is from 7edo, 21edo is notated with CDEFGAB representing 7edo and up/down representing 1\21.

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
Error	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)

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

@@ Line 1: / Line 1: @@
 '''21edo''' is an equal division of the octave into 21 steps of 1200c/21 ~= 57.1c each.
+Notable scales:
+* 21edo is the first edo with a [[diasem]] scale: 323132313 (RH) or 313231323 (LH). Diasem provides basic 2.3.7 harmony, though 7/6 and 28/27 are not accurate at all in 21edo.
+* Slentonic (5L6s, sLsLsLsLsLs), interpreted as [[Slendric]][11], generated by stacking the ~8/7 (4\21)
+* Oneirotonic (5L3s, LLsLLsLs), generated by stacking 8\21
 == Basic theory ==
 === Intervals and notation ===