175edo

← 174edo

175edo

176edo →

Prime factorization	52 × 7
Step size	6.85714 ¢
Fifth	102\175 (699.429 ¢)
Semitones (A1:m2)	14:15 (96 ¢ : 102.9 ¢)
Dual sharp fifth	103\175 (706.286 ¢)
Dual flat fifth	102\175 (699.429 ¢)
Dual major 2nd	30\175 (205.714 ¢) (→ 6\35)
Consistency limit	7
Distinct consistency limit	7

Theory

175edo tempers out 1029/1024 and 225/224, so that it supports 7-limit miracle temperament, and in fact provides an excellent alternative^[why?] to 72edo for 7-limit miracle. In the 11-limit, it tempers out 243/242, 385/384, 441/440 and 540/439, and supports 11-limit miracle. In the 13-limit, 175f val, ⟨175 277 406 491 605 647] tempers out 351/350 just as 72 does, and provides a tuning for benediction temperament very close to the POTE tuning.

Odd harmonics

Approximation of odd harmonics in 175edo

Harmonic		3	5	7	9	11	13	15	17	19	21	23
Error	Absolute (¢)	-2.53	-2.31	-1.97	+1.80	-2.75	+2.90	+2.02	-2.10	-2.66	+2.36	+2.58
	Relative (%)	-36.8	-33.7	-28.7	+26.3	-40.1	+42.3	+29.4	-30.6	-38.7	+34.4	+37.7
Steps (reduced)		277 (102)	406 (56)	491 (141)	555 (30)	605 (80)	648 (123)	684 (159)	715 (15)	743 (43)	769 (69)	792 (92)

Music

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