1506edo: Difference between revisions
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The 1506 division divides the octave into 1506 parts of 0.7968 | The 1506 division divides the octave into 1506 parts of 0.7968 [[cent]]s each. It is a very strong 13- and 17-limit system, since it is the first past 494 with a lower 13-limit [[Tenney-Euclidean temperament measures #TE simple badness|relative error]], and likewise the first with a lower 17-limit relative error. Like 494 it is distinctly [[consistent]] through the 17-odd-limit. It tends sharp, all of the odd primes to 17 being tuned sharply. A basis for the 13 limit commas is {4096/4095, 6656/6655, 9801/9800, 105644/105625, 371293/371250}, and for the 17-limit commas, {4096/4095, 4914/4913, 5832/5831, 6656/6655, 9801/9800, 28561/28560, 105644/105625}. | ||
=== Prime harmonics === | |||
{{Harmonics in equal|1506|columns=11}} | |||
[[Category:Equal divisions of the octave|####]] <!-- 4-digit number --> | [[Category:Equal divisions of the octave|####]] <!-- 4-digit number --> | ||
Revision as of 09:20, 29 October 2022
| ← 1505edo | 1506edo | 1507edo → |
The 1506 division divides the octave into 1506 parts of 0.7968 cents each. It is a very strong 13- and 17-limit system, since it is the first past 494 with a lower 13-limit relative error, and likewise the first with a lower 17-limit relative error. Like 494 it is distinctly consistent through the 17-odd-limit. It tends sharp, all of the odd primes to 17 being tuned sharply. A basis for the 13 limit commas is {4096/4095, 6656/6655, 9801/9800, 105644/105625, 371293/371250}, and for the 17-limit commas, {4096/4095, 4914/4913, 5832/5831, 6656/6655, 9801/9800, 28561/28560, 105644/105625}.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.000 | +0.037 | +0.140 | +0.098 | +0.076 | +0.110 | +0.224 | -0.302 | -0.386 | -0.095 | -0.016 |
| Relative (%) | +0.0 | +4.6 | +17.6 | +12.3 | +9.6 | +13.8 | +28.1 | -37.9 | -48.4 | -11.9 | -2.0 | |
| Steps (reduced) |
1506 (0) |
2387 (881) |
3497 (485) |
4228 (1216) |
5210 (692) |
5573 (1055) |
6156 (132) |
6397 (373) |
6812 (788) |
7316 (1292) |
7461 (1437) | |