1337edo: Difference between revisions

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.

Approximation of odd harmonics in 1337edo
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
Error	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)

Since 1337 factors into 7 × 191, 1337edo contains 7edo and 191edo as subsets.

@@ Line 2: / Line 2: @@
 {{EDO intro|1337}}
-In the 7-limit on the [[patent val]], 1337edo supports [[tertiaseptal]]. In the 11-limit on the patent val, it supports [[hemitert]].
+edo 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 ===
@@ Line 8: / Line 8: @@
 === Subsets and supersets ===
-Since 1337 factors as 7 × 191, 1337edo contains [[7edo]] and [[191edo]] as its subsets.
+Since 1337 factors into {{factorization|1337}}, 1337edo contains [[7edo]] and [[191edo]] as subsets.

Revision as of 09:30, 31 October 2023