616edo: Difference between revisions
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Adopt template: EDO intro; +prime error table; +subsets and supersets; -redundant categories |
Rework on theory; adopt template: Factorization |
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{{EDO intro|616}} | {{EDO intro|616}} | ||
The equal temperament [[tempering out|tempers out]] [[2401/2400]], 48828125/48771072, and 129140163/128450560 in the 7-limit; [[9801/9800]], 46656/46585, 117649/117612, and 1265625/1261568 in the 11-limit. | 616edo is [[consistent]] to the [[7-odd-limit]], but it tends heavily flat in the first few [[harmonic]]s. The equal temperament [[tempering out|tempers out]] [[2401/2400]], 48828125/48771072, and 129140163/128450560 in the 7-limit; [[9801/9800]], 46656/46585, 117649/117612, and 1265625/1261568 in the 11-limit. Alternatively, the 2.9.15.21.11 [[subgroup]] may be worth considering. Finally, as every third step of [[1848edo]], it provides an excellent tuning for the [[K*N subgroups|3*616]] 2.5/3.7/3.11 [[subgroup]], approximating [[6/5]], [[7/6]], [[7/5]], and [[11/8]] within 0.057 cents. | ||
=== Odd harmonics === | === Odd harmonics === | ||
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=== Subsets and supersets === | === Subsets and supersets === | ||
Since 616 factors into | Since 616 factors into {{factorization|616}}, 616edo has subset edos {{EDOs| 2, 4, 7, 8, 11, 14, 22, 28, 44, 56, 77, 88, 154, 308 }}. | ||
Revision as of 13:17, 2 November 2023
| ← 615edo | 616edo | 617edo → |
616edo is consistent to the 7-odd-limit, but it tends heavily flat in the first few harmonics. The equal temperament tempers out 2401/2400, 48828125/48771072, and 129140163/128450560 in the 7-limit; 9801/9800, 46656/46585, 117649/117612, and 1265625/1261568 in the 11-limit. Alternatively, the 2.9.15.21.11 subgroup may be worth considering. Finally, as every third step of 1848edo, it provides an excellent tuning for the 3*616 2.5/3.7/3.11 subgroup, approximating 6/5, 7/6, 7/5, and 11/8 within 0.057 cents.
Odd harmonics
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -0.656 | -0.599 | -0.644 | +0.635 | -0.019 | -0.917 | +0.692 | +0.239 | +0.539 | +0.648 | +0.946 |
| Relative (%) | -33.7 | -30.8 | -33.1 | +32.6 | -1.0 | -47.1 | +35.5 | +12.3 | +27.7 | +33.2 | +48.6 | |
| Steps (reduced) |
976 (360) |
1430 (198) |
1729 (497) |
1953 (105) |
2131 (283) |
2279 (431) |
2407 (559) |
2518 (54) |
2617 (153) |
2706 (242) |
2787 (323) | |
Subsets and supersets
Since 616 factors into 23 × 7 × 11, 616edo has subset edos 2, 4, 7, 8, 11, 14, 22, 28, 44, 56, 77, 88, 154, 308.