# 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

175 equal divisions of the octave (abbreviated 175edo or 175ed2), also called 175-tone equal temperament (175tet) or 175 equal temperament (175et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 175 equal parts of about 6.86 ¢ each. Each step represents a frequency ratio of 21/175, or the 175th root of 2.

## 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.

Gene Ward Smith