587edo: Difference between revisions
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{{Infobox ET}} | |||
{{ED intro}} | |||
587edo is [[consistent]] to the [[7-odd-limit]], but the error of [[harmonic]] [[3/1|3]] is quite large. With good approximations to harmonics [[5/1|5]], [[7/1|7]], [[9/1|9]], [[11/1|11]], and [[13/1|13]], it commends itself as a 2.9.5.7.11.13 [[subgroup]] tuning. | |||
Using the [[patent val]], however, the equal temperament [[tempering out|tempers out]] [[19683/19600]] and [[703125/702464]] in the 7-limit, providing the [[optimal patent val]] for the 19 & 183 temperament and the planar temperament [[cataharry]] tempering out 19683/19600. | |||
=== Odd harmonics === | |||
{{Harmonics in equal|587}} | |||
=== Subsets and supersets === | |||
587edo is the 107th [[prime edo]]. | |||
[[Category:Cataharry]] | |||
Latest revision as of 15:38, 20 February 2025
| ← 586edo | 587edo | 588edo → |
587 equal divisions of the octave (abbreviated 587edo or 587ed2), also called 587-tone equal temperament (587tet) or 587 equal temperament (587et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 587 equal parts of about 2.04 ¢ each. Each step represents a frequency ratio of 21/587, or the 587th root of 2.
587edo is consistent to the 7-odd-limit, but the error of harmonic 3 is quite large. With good approximations to harmonics 5, 7, 9, 11, and 13, it commends itself as a 2.9.5.7.11.13 subgroup tuning.
Using the patent val, however, the equal temperament tempers out 19683/19600 and 703125/702464 in the 7-limit, providing the optimal patent val for the 19 & 183 temperament and the planar temperament cataharry tempering out 19683/19600.
Odd harmonics
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -0.762 | +0.058 | +0.169 | +0.519 | +0.641 | -0.323 | -0.705 | -0.696 | +0.954 | -0.594 | -0.676 |
| Relative (%) | -37.3 | +2.8 | +8.3 | +25.4 | +31.4 | -15.8 | -34.5 | -34.1 | +46.7 | -29.0 | -33.1 | |
| Steps (reduced) |
930 (343) |
1363 (189) |
1648 (474) |
1861 (100) |
2031 (270) |
2172 (411) |
2293 (532) |
2399 (51) |
2494 (146) |
2578 (230) |
2655 (307) | |
Subsets and supersets
587edo is the 107th prime edo.