174edo
174 equal divisions of the octave (abbreviated 174edo or 174ed2), also called 174-tone equal temperament (174tet) or 174 equal temperament (174et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 174 equal parts of about 6.9 ¢ each. Each step represents a frequency ratio of 21/174, or the 174th root of 2.
| ← 173edo | 174edo | 175edo → |
174edo is closely related to 87edo, but the patent vals differ on the mapping for 17 and some higher primes. It is contorted in the 13-limit, tempering out 196/195, 245/243, 352/351, 364/363, and 625/624. Using the patent val, it tempers out 289/288 in the 17-limit; 361/360, 476/475, and 665/663 in the 19-limit; 391/390, 392/391, 460/459, 529/528, and 760/759 in the 23-limit; 1309/1305, 1450/1449, and 4147/4140 in the 29-limit; 496/495 and 1365/1364 in the 31-limit.
Odd harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.00 | +1.49 | -0.11 | -3.31 | +0.41 | +0.85 | -1.51 | -0.96 | -0.69 | -1.99 | -0.21 |
| Relative (%) | +0.0 | +21.7 | -1.5 | -48.0 | +5.9 | +12.3 | -21.9 | -13.9 | -10.0 | -28.9 | -3.0 | |
| Steps (reduced) |
174 (0) |
276 (102) |
404 (56) |
488 (140) |
602 (80) |
644 (122) |
711 (15) |
739 (43) |
787 (91) |
845 (149) |
862 (166) | |
Subsets and supersets
Since 174 factors into 2 × 3 × 29, 174edo has subset edos 2, 3, 6, 29, 58, and 87.