277edo

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277edo

278edo →

Prime factorization	277 (prime)
Step size	4.33213 ¢
Fifth	162\277 (701.805 ¢)
Semitones (A1:m2)	26:21 (112.6 ¢ : 90.97 ¢)
Consistency limit	5
Distinct consistency limit	5

Theory

277et tempers out 32805/32768 (schisma) and |-11 -37 30> in the 5-limit.

Using the patent val, it tempers out 4375/4374, 65625/65536, and 829440/823543 in the 7-limit; 540/539, 6250/6237, 15488/15435, and 35937/35840 in the 11-limit; 625/624, 729/728, 1573/1568, 2080/2079, and 2200/2197 in the 13-limit.

Using the 277d val, it tempers out 1029/1024, 10976/10935, and 48828125/48771072 in the 7-limit; 385/384, 441/440, 19712/19683, and 234375/234256 in the 11-limit; 625/624, 847/845, 1001/1000, and 1575/1573 in the 13-limit.

The patent val supports the pontiac, and the 277d val supports the guiron and the widefourth.

Prime harmonics

Approximation of prime harmonics in 277edo

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+0.00	-0.15	-0.75	+1.57	-1.14	-0.09	-0.98	+1.40	-0.12	+1.47	-1.35
	Relative (%)	+0.0	-3.5	-17.4	+36.3	-26.3	-2.2	-22.7	+32.4	-2.7	+33.9	-31.2
Steps (reduced)		277 (0)	439 (162)	643 (89)	778 (224)	958 (127)	1025 (194)	1132 (24)	1177 (69)	1253 (145)	1346 (238)	1372 (264)

Subsets and supersets

277edo is the 59th prime EDO.

Regular temperament properties

Subgroup	Comma List	Mapping	Optimal 8ve Stretch (¢)	Tuning Error
				Absolute (¢)	Relative (%)
2.3	[-439 277⟩	⟨277 439]	0.0473	0.0473	1.09
2.3.5	32805/32768, [-11 -37 30⟩	⟨277 439 643]	0.1398	0.1364	3.15

Rank-2 temperaments

Table of rank-2 temperaments by generator

Periods per 8ve	Generator (reduced)	Cents (reduced)	Associated ratio	Temperaments
1	115\277	498.19	4/3	Helmholtz