851edo: Difference between revisions

Revision as of 12:50, 15 July 2024

851edo is consistent to the 15-odd-limit or the no-17 no-23 25-odd-limit. As an equal temperament, it tempers out 2401/2400 (breedsma) and 33554432/33480783 (garischisma) in the 7-limit; 3025/3024 and 19712/19683 in the 11-limit; and 2080/2079, 4096/4095, and 4225/4224 in the 13-limit. It provides the optimal patent val for 13-limit newt, the 270 & 581 temperament, as well as neonewt, its no-17 19-limit extension.

Approximation of prime harmonics in 851edo
Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+0.000	+0.278	+0.055	-0.083	+0.033	-0.105	-0.608	+0.019	+0.633	-0.200	-0.030
Error	Relative (%)	+0.0	+19.7	+3.9	-5.9	+2.4	-7.4	-43.1	+1.4	+44.9	-14.2	-2.1
Steps (reduced)		851 (0)	1349 (498)	1976 (274)	2389 (687)	2944 (391)	3149 (596)	3478 (74)	3615 (211)	3850 (446)	4134 (730)	4216 (812)

Since 851 factors into 23 × 37, 851edo contains 23edo and 37edo as its subsets.

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 {{EDO intro}}
-edo is [[consistent]] to the [[15-odd-limit]] or the no-17 no-23 [[25-odd-limit]]. As an equal temperament, it [[tempering out|tempers out]] 2401/2400 ([[breedsma]]) and 33554432/33480783 ([[garischisma]]) in the 7-limit; [[3025/3024]] and [[19712/19683]] in the 11-limit; and [[2080/2079]], [[4096/4095]], and [[4225/4224]] in the 13-limit. It provides the [[optimal patent val]] for 13-limit [[newt]] and its no-17 19-limit extension neonewt.
+edo is [[consistent]] to the [[15-odd-limit]] or the no-17 no-23 [[25-odd-limit]]. As an equal temperament, it [[tempering out|tempers out]] 2401/2400 ([[breedsma]]) and 33554432/33480783 ([[garischisma]]) in the 7-limit; [[3025/3024]] and [[19712/19683]] in the 11-limit; and [[2080/2079]], [[4096/4095]], and [[4225/4224]] in the 13-limit. It provides the [[optimal patent val]] for 13-limit [[newt]], the 270 & 581 temperament, as well as neonewt, its no-17 19-limit extension.
 === Prime harmonics ===