2053edo

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2053edo

2054edo →

Prime factorization	2053 (prime)
Step size	0.58451 ¢
Fifth	1201\2053 (701.997 ¢)
Semitones (A1:m2)	195:154 (114 ¢ : 90.01 ¢)
Consistency limit	5
Distinct consistency limit	5

Theory

2053edo is consistent to the 5-odd-limit, its harmonic 7 is exactly between its steps. The equal temperament is strong in the 2.3.5.13.19.23.31 subgroup, tempering out 359424/359375, 22816/22815, 96876/96875, 497705/497664, 4784000/4782969 and 369664/369603. Using the 2.3.5.13.19.37 subgroup, it tempers out 7696/7695.

Prime harmonics

Approximation of prime harmonics in 2053edo

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+0.000	+0.042	+0.048	-0.292	-0.125	-0.002	+0.256	+0.003	+0.074	-0.254	+0.020
	Relative (%)	+0.0	+7.2	+8.2	-50.0	-21.3	-0.3	+43.9	+0.5	+12.7	-43.5	+3.5
Steps (reduced)		2053 (0)	3254 (1201)	4767 (661)	5763 (1657)	7102 (943)	7597 (1438)	8392 (180)	8721 (509)	9287 (1075)	9973 (1761)	10171 (1959)

Subsets and supersets

2053edo is the 310th prime edo. 4106edo, which doubles it, gives a good correction to the harmonic 7.

Regular temperament properties

Subgroup	Comma List	Mapping	Optimal 8ve Stretch (¢)	Tuning Error
				Absolute (¢)	Relative (%)
2.3	[3254 -2053⟩	[⟨2053 3254]]	-0.0133	0.0133	2.28
2.3.5	[37 25 -33⟩, [93 -66 5⟩	[⟨2053 3254 4767]]	-0.0157	0.0114	1.95

Rank-2 temperaments

Table of rank-2 temperaments by generator

Periods per 8ve	Generator*	Cents*	Associated Ratio*	Temperaments
1	959\2053	560.546	864/625	Whoosh

* Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if it is distinct