26edo

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26edo, or 26 equal divisions of the octave, is the equal tuning featuring steps of (1200/26) ~= 46.15 cents, 26 of which stack to the perfect octave 2/1.

Theory

JI approximation

26edo is characterized by a flat tuning of harmonics 3, 5, and 13 and slightly sharp but accurate tunings of 7 and 11. Although its primes 3, 5, and 13 are damaged, 26edo can be used as a 13-limit temperament as it is consistent to the 13-odd-limit. The accurate 7 combined with the flat 5 means that 7/5 and 10/7 are both mapped to the 600¢ half octave tritone, tempering out 50/49. The flat 13 means that 13/8 is tempered to the same interval as 8/5, tempering out 65/64, and the combination of the accurate 11 and flat 3 implies that 11/9 is tempered to the same interval as 16/13 and 5/4, so 144/143 and 45/44 are also tempered out.

26edo is an even EDO and contains the 600¢ half-octave tritone,

Approximation of prime harmonics in 26edo

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	0.0	-9.6	-17.1	+0.4	+2.5	-9.8	-12.6	-20.6	+17.9	-14.2	+8.8
	Relative (%)	0.0	-20.9	-37.0	+0.9	+5.5	-21.1	-27.4	-44.6	+38.7	-30.8	+19.1
Steps (reduced)		26 (0)	41 (15)	60 (8)	73 (21)	90 (12)	96 (18)	106 (2)	110 (6)	118 (14)	126 (22)	129 (25)

TODO:

• write about flattone
• write about usability in the 13-limit