2964edo: Difference between revisions
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{{Infobox ET}} | {{Infobox ET}} | ||
{{ED intro}} | |||
In the 13-limit, 2964edo shares the same [[patent val]] with [[494edo]] except for the [[7/1|7th harmonic]], which is corrected to an extremely accurate result (absolute error 0.00000446 cents, relative error 0.0011%). 2964 is the denominator to a [[convergent]] to log<sub>2</sub>7. Bordering 2964edo's patent val 7/1 on either side are [[26edo]]'s sharp approximation and [[57edo]]'s flat approximation of 7/1, having nearly identical 0.4048{{c}} errors; 2964edo exactly divides the octave into 26 and into 57 equal steps, splitting the difference between 160\57 and 73\26, as 2964 is expressible as {{nowrap|26 × 57 × 2}}. | |||
In the 13-limit, 2964edo shares the same patent val | |||
=== Prime harmonics === | === Prime harmonics === | ||
{{Harmonics in equal|2964|columns=11|prec=3}} | {{Harmonics in equal|2964|columns=11|prec=3}} | ||
=== | === Subsets and supersets === | ||
Since 2964 | Since 2964 factors into {{factorization|2964}}, 2964edo has subset edos {{EDOs| 2, 3, 4, 6, 12, 13, 19, 26, 38, 39, 52, 57, 76, 78, 114, 156, 228, 247, 494, 741, 988, and 1482 }}. | ||
Latest revision as of 08:36, 9 November 2025
| ← 2963edo | 2964edo | 2965edo → |
2964 equal divisions of the octave (abbreviated 2964edo or 2964ed2), also called 2964-tone equal temperament (2964tet) or 2964 equal temperament (2964et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 2964 equal parts of about 0.405 ¢ each. Each step represents a frequency ratio of 21/2964, or the 2964th root of 2.
In the 13-limit, 2964edo shares the same patent val with 494edo except for the 7th harmonic, which is corrected to an extremely accurate result (absolute error 0.00000446 cents, relative error 0.0011%). 2964 is the denominator to a convergent to log27. Bordering 2964edo's patent val 7/1 on either side are 26edo's sharp approximation and 57edo's flat approximation of 7/1, having nearly identical 0.4048 ¢ errors; 2964edo exactly divides the octave into 26 and into 57 equal steps, splitting the difference between 160\57 and 73\26, as 2964 is expressible as 26 × 57 × 2.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.000 | +0.069 | -0.079 | +0.000 | +0.099 | -0.042 | -0.097 | +0.058 | +0.066 | -0.023 | -0.096 |
| Relative (%) | +0.0 | +17.1 | -19.5 | +0.0 | +24.5 | -10.3 | -24.0 | +14.3 | +16.2 | -5.6 | -23.8 | |
| Steps (reduced) |
2964 (0) |
4698 (1734) |
6882 (954) |
8321 (2393) |
10254 (1362) |
10968 (2076) |
12115 (259) |
12591 (735) |
13408 (1552) |
14399 (2543) |
14684 (2828) | |
Subsets and supersets
Since 2964 factors into 22 × 3 × 13 × 19, 2964edo has subset edos 2, 3, 4, 6, 12, 13, 19, 26, 38, 39, 52, 57, 76, 78, 114, 156, 228, 247, 494, 741, 988, and 1482.