2573edo

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2573edo

2574edo →

Prime factorization	31 × 83
Step size	0.466382 ¢
Fifth	1505\2573 (701.904 ¢)
Semitones (A1:m2)	243:194 (113.3 ¢ : 90.48 ¢)
Consistency limit	17
Distinct consistency limit	17

2573 equal divisions of the octave (abbreviated 2573edo or 2573ed2), also called 2573-tone equal temperament (2573tet) or 2573 equal temperament (2573et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 2573 equal parts of about 0.466 ¢ each. Each step represents a frequency ratio of 2^1/2573, or the 2573rd root of 2.

2573edo is consistent in the 17-odd-limit, being a mostly flat system. It tunes the 217 & 1178 temperament, for which it provides the optimal patent val in the 7, 11, 13, 17, and 19-limits (though it is not consistent to the 19-limit).

Prime harmonics

Approximation of prime harmonics in 2573edo

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+0.000	-0.051	-0.150	-0.151	-0.055	-0.108	-0.020	+0.038	-0.058	+0.194	-0.069
	Relative (%)	+0.0	-10.9	-32.1	-32.4	-11.8	-23.1	-4.2	+8.3	-12.5	+41.5	-14.7
Steps (reduced)		2573 (0)	4078 (1505)	5974 (828)	7223 (2077)	8901 (1182)	9521 (1802)	10517 (225)	10930 (638)	11639 (1347)	12500 (2208)	12747 (2455)

Subsets and supersets

2573edo has 31edo and 83edo as subsets.