696edo
| ← 695edo | 696edo | 697edo → |
696 equal divisions of the octave (abbreviated 696edo or 696ed2), also called 696-tone equal temperament (696tet) or 696 equal temperament (696et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 696 equal parts of about 1.72 ¢ each. Each step represents a frequency ratio of 21/696, or the 696th root of 2.
696edo is a strong 7-limit tuning, but unfortunately it is consistent only up to the 9-odd-limit. In the higher limits, it may be used as a 2.3.5.7.17.31 subgroup tuning. In the 5-limit, it supports the magnesium temperament which divides the octave in 12, as well as chromium temperament that divides it in 24.
Nonetheless despite inconsistency, it is a valuable xenharmonic system. It provides the optimal patent val for the octant temperament in the 13-limit, even if its approximation of 13 is almost half a step off. Likewise, 696edo tunes altierran and house temperaments in the 11-limit.
The 696cc val is also very close to the POTE tuning for the witcher temperament, while 696f tunes semiterm and the inaccurate 696d tunes pontic.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.000 | -0.231 | -0.107 | +0.140 | +0.406 | +0.852 | +0.217 | +0.763 | -0.688 | -0.267 | -0.208 |
| Relative (%) | +0.0 | -13.4 | -6.2 | +8.1 | +23.6 | +49.4 | +12.6 | +44.2 | -39.9 | -15.5 | -12.1 | |
| Steps (reduced) |
696 (0) |
1103 (407) |
1616 (224) |
1954 (562) |
2408 (320) |
2576 (488) |
2845 (61) |
2957 (173) |
3148 (364) |
3381 (597) |
3448 (664) | |