1337edo: Difference between revisions
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== | 1337edo is [[consistent]] to the [[13-odd-limit]], although the errors of [[harmonic]]s [[5/1|5]], [[7/1|7]], and [[13/1|13]] are quite large. The equal temperament [[tempering out|tempers out]] 2401/2400 ([[breedsma]]), 65625/65536 ([[horwell comma]]) and 703125/702464 ([[meter]]) in the 7-limit, so that it [[support]]s [[tertiaseptal]]. In the 11-limit it tempers out [[3025/3024]] and [[41503/41472]], so that it supports [[hemitert]]. | ||
=== Odd harmonics === | |||
{{Harmonics in equal|1337}} | {{Harmonics in equal|1337}} | ||
[[ | === Subsets and supersets === | ||
Since 1337 factors into {{factorization|1337}}, 1337edo contains [[7edo]] and [[191edo]] as subsets. | |||
Latest revision as of 23:06, 20 February 2025
| ← 1336edo | 1337edo | 1338edo → |
1337 equal divisions of the octave (abbreviated 1337edo or 1337ed2), also called 1337-tone equal temperament (1337tet) or 1337 equal temperament (1337et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 1337 equal parts of about 0.898 ¢ each. Each step represents a frequency ratio of 21/1337, or the 1337th root of 2.
1337edo is consistent to the 13-odd-limit, although the errors of harmonics 5, 7, and 13 are quite large. The equal temperament tempers out 2401/2400 (breedsma), 65625/65536 (horwell comma) and 703125/702464 (meter) in the 7-limit, so that it supports tertiaseptal. In the 11-limit it tempers out 3025/3024 and 41503/41472, so that it supports hemitert.
Odd harmonics
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -0.085 | -0.375 | -0.389 | -0.170 | -0.233 | -0.438 | +0.437 | +0.056 | -0.430 | +0.423 | -0.002 |
| Relative (%) | -9.5 | -41.8 | -43.4 | -19.0 | -26.0 | -48.8 | +48.7 | +6.2 | -47.9 | +47.2 | -0.2 | |
| Steps (reduced) |
2119 (782) |
3104 (430) |
3753 (1079) |
4238 (227) |
4625 (614) |
4947 (936) |
5224 (1213) |
5465 (117) |
5679 (331) |
5873 (525) |
6048 (700) | |
Subsets and supersets
Since 1337 factors into 7 × 191, 1337edo contains 7edo and 191edo as subsets.