263edo

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263edo

264edo →

Prime factorization	263 (prime)
Step size	4.56274 ¢
Fifth	154\263 (702.662 ¢)
Semitones (A1:m2)	26:19 (118.6 ¢ : 86.69 ¢)
Consistency limit	5
Distinct consistency limit	5

Theory

263et tempers out 393216/390625 (Würschmidt comma) and |50 -33 1> in the 5-limit. Using the patent val, it tempers out 4375/4374, 50421/50000, and 458752/455625 in the 7-limit; 441/440, 3388/3375, 16384/16335, and 26411/26244 in the 11-limit; 364/363, 2080/2079, 2197/2187, and 3584/3575 in the 13-limit; 595/594, 833/832, 936/935, and 1156/1155 in the 17-limit.

Using the 263d val, it tempers out 5120/5103, 16875/16807, and 1959552/1953125 in the 7-limit; 540/539, 1375/1372, 16384/16335, and 43923/43750 in the 11-limit; 351/350, 1001/1000, 1573/1568, 2197/2187, and 4225/4224 in the 13-limit.

Using the 263df val, it tempers out 352/351, 640/637, 729/728, and 3584/3575 in the 13-limit.

Prime harmonics

Approximation of prime harmonics in 263edo

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+0.00	+0.71	+1.52	-1.53	+0.77	-0.98	-0.01	-0.94	+1.38	+1.60	+0.21
	Relative (%)	+0.0	+15.5	+33.3	-33.4	+16.9	-21.6	-0.3	-20.5	+30.3	+35.1	+4.6
Steps (reduced)		263 (0)	417 (154)	611 (85)	738 (212)	910 (121)	973 (184)	1075 (23)	1117 (65)	1190 (138)	1278 (226)	1303 (251)

Subsets and supersets

263edo is the 56th prime EDO. It is accurate for the 17th harmonic, as the denominator of a convergent to log₂17, after 80 and before 343.

Regular temperament properties

Subgroup	Comma List	Mapping	Optimal 8ve Stretch (¢)	Tuning Error
				Absolute (¢)	Relative (%)
2.3	[417 -263⟩	⟨263 417]	-0.2229	0.2229	4.89
2.3.5	393216/390625, [50 -33 1⟩	⟨263 417 611]	-0.3666	0.2728	5.98

Rank-2 temperaments

Table of rank-2 temperaments by generator

Periods per 8ve	Generator (reduced)	Cents (reduced)	Associated ratio	Temperaments
1	40\263	182.51	10/9	Minortone
1	85\263	387.83	5/4	Würschmidt