173edo

 ← 172edo 173edo 174edo →
Prime factorization 173 (prime)
Step size 6.93642¢
Fifth 101\173 (700.578¢)
Semitones (A1:m2) 15:14 (104¢ : 97.11¢)
Consistency limit 3
Distinct consistency limit 3

173 equal divisions of the octave (abbreviated 173edo or 173ed2), also called 173-tone equal temperament (173tet) or 173 equal temperament (173et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 173 equal parts of about 6.94 ¢ each. Each step represents a frequency ratio of 21/173, or the 173rd root of 2.

173edo is inconsistent to the 5-odd-limit. Two mappings are to be considered for the 5-limit: 173 274 402] (patent val) and 173 274 401] (173c).

Using the patent val, it tempers out the unicorn comma, 1594323/1562500 and the escapade comma, 4294967296/4271484375 in the 5-limit; 1728/1715, 3136/3125, and 413343/409600 in the 7-limit; 176/175, 540/539, 1331/1323, and 264627/262144 in the 11-limit, supporting the 11-limit semisept temperament; 676/675, 847/845, 1188/1183, and 1287/1280 in the 13-limit.

Using the 173e val, 173 271 402 486 599], it tempers out 441/440, 1944/1925, 4000/3993, and 5632/5625 in the 11-limit; 364/363, 676/675, 1001/1000, and 3159/3125 in the 13-limit. Using the 173ef val, 173 271 402 486 599 641], 144/143, 351/350, 640/637, and 847/845 are tempered out in the 13-limit.

Using the 173d val, 173 271 402 485], it tempers out 126/125, 10976/10935, and 28824005/28311552 in the 7-limit; 385/384, 1617/1600, 12005/11979, and 14641/14580 in the 11-limit; 196/195, 351/350, 676/675, 1287/1280, and 10648/10647 in the 13-limit, supporting the camahueto temperament.

Using the 173c val, it tempers out the amity comma, 1600000/1594323 and 35595703125/34359738368 in the 5-limit; 2430/2401, 4000/3969, and 234375/229376 in the 7-limit, supporting the 7-limit hamity temperament. Using the alternative 173cd val, 173 271 401 485] it tempers out 225/224, 84035/82944, and 1250000/1240029 in the 7-limit, supporting the 7-limit septimin temperament; 441/440, 1375/1372, 4000/3993, and 26411/26244 in the 11-limit; 325/324, 729/728, 847/845, and 1875/1859 in the 13-limit.

Odd harmonics

Approximation of prime harmonics in 173edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) +0.00 -1.38 +2.13 +2.27 -3.34 -1.22 -0.91 +0.75 +2.94 -2.99 -0.53
Relative (%) +0.0 -19.9 +30.6 +32.8 -48.2 -17.6 -13.1 +10.9 +42.4 -43.1 -7.6
Steps
(reduced)
173
(0)
274
(101)
402
(56)
486
(140)
598
(79)
640
(121)
707
(15)
735
(43)
783
(91)
840
(148)
857
(165)

Subsets and supersets

173edo is the 40th prime edo.