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

175et tempers out 225/224 and 1029/1024, so that it supports 7-limit miracle, and in fact provides an excellent alternative to 72edo for 7-limit miracle with improved 5 and 7 at the cost of a slightly flatter 3. In the 11-limit, it tempers out 243/242, 385/384, 441/440 and 540/539, and supports 11-limit miracle. In the 13-limit, the 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)

Subsets and supersets

Since 175 factors into 5² × 7, 175edo has subset edos 5, 7, 25, and 35.

Music

Gene Ward Smith

• Rachmaninoff Plays Blackjack (archived 2010) – detail | play – Blackjack in 175edo tuning