88edo

← 87edo

88edo

89edo →

Prime factorization	23 × 11
Step size	13.6364 ¢
Fifth	51\88 (695.455 ¢)
Semitones (A1:m2)	5:9 (68.18 ¢ : 122.7 ¢)
Dual sharp fifth	52\88 (709.091 ¢) (→ 13\22)
Dual flat fifth	51\88 (695.455 ¢)
Dual major 2nd	15\88 (204.545 ¢)
Consistency limit	7
Distinct consistency limit	7

Theory

Using two different approximations to the perfect fifth (one of 51 steps and one of 52 steps), it is compatible with both meantone temperament and the particular variety of superpyth temperament(s) supported by 22 equal temperament, respectively. The meantone fifth is 0.0384 cents flatter than that of Lucy Tuning and, thus, audibly indistinguishable from it. It also gives the optimal patent val for the 11-limit mothra and euterpe temperaments.

Odd harmonics

Approximation of odd harmonics in 88edo

Harmonic		3	5	7	9	11	13	15	17	19	21	23
Error	Absolute (¢)	-6.50	-4.50	-0.64	+0.64	-5.86	+4.93	+2.64	+4.14	+2.49	+6.49	-1.00
	Relative (%)	-47.7	-33.0	-4.7	+4.7	-43.0	+36.1	+19.4	+30.3	+18.2	+47.6	-7.3
Steps (reduced)		139 (51)	204 (28)	247 (71)	279 (15)	304 (40)	326 (62)	344 (80)	360 (8)	374 (22)	387 (35)	398 (46)