173edo
| ← 172edo | 173edo | 174edo → |
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 6.936 ¢ each. Each step represents a frequency ratio of 21/173, or the 173rd root of 2.
173edo is only consistent in the 3-limit. Nonetheless, 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 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.
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 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.
Odd harmonics
| 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 | -20 | +31 | +33 | -48 | -18 | -13 | +11 | +42 | -43 | -8 | |
| 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.