971edo: Difference between revisions
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971edo's fifth is only 0.00174 cents sharp of just, as it is the denominator of the first semiconvergent to log<sub>2</sub>(3/2) past 389\665. It is [[consistent]] to the 9-odd-limit, but there is a large relative delta in its approximation to harmonic 5. Skipping the harmonic, it is a good 2.3.7.11.13.17 subgroup system. | 971edo's fifth is only 0.00174 cents sharp of just, as it is the denominator of the first semiconvergent to log<sub>2</sub>(3/2) past 389\665. It is [[consistent]] to the 9-odd-limit, but there is a large relative delta in its approximation to harmonic 5. Skipping the harmonic, it is a good 2.3.7.11.13.17 subgroup system. | ||
Revision as of 06:55, 20 February 2025
| ← 970edo | 971edo | 972edo → |
(semiconvergent)
971 equal divisions of the octave (abbreviated 971edo or 971ed2), also called 971-tone equal temperament (971tet) or 971 equal temperament (971et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 971 equal parts of about 1.24 ¢ each. Each step represents a frequency ratio of 21/971, or the 971st root of 2.
971edo's fifth is only 0.00174 cents sharp of just, as it is the denominator of the first semiconvergent to log2(3/2) past 389\665. It is consistent to the 9-odd-limit, but there is a large relative delta in its approximation to harmonic 5. Skipping the harmonic, it is a good 2.3.7.11.13.17 subgroup system.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.000 | +0.002 | +0.504 | +0.072 | -0.134 | -0.157 | +0.091 | +0.324 | -0.468 | -0.123 | +0.587 |
| Relative (%) | +0.0 | +0.1 | +40.8 | +5.8 | -10.8 | -12.7 | +7.4 | +26.2 | -37.9 | -10.0 | +47.5 | |
| Steps (reduced) |
971 (0) |
1539 (568) |
2255 (313) |
2726 (784) |
3359 (446) |
3593 (680) |
3969 (85) |
4125 (241) |
4392 (508) |
4717 (833) |
4811 (927) | |
Subsets and supersets
971edo is the 164th prime edo.