451edo

Theory

451 = 11 × 41, and 451edo shares its fifth with 41edo. Unlike 41, however, 451 is only consistent to the 7-odd-limit, though it has a reasonable approximation up to the 13-limit using the patent val. The equal temperament tempers out 2401/2400, 65625/65536, 703125/702464, 2100875/2097152, and 390625000/387420489 in the 7-limit; 6250/6237, 42592/42525, 42875/42768, 43923/43904 in the 11-limit; and 625/624, 2080/2079, 2200/2197, 4096/4095, 4225/4224, 4459/4455, and 17303/17280 in the 13-limit. It supports tertiaseptal, tertiseptisix, and hemermacomp.

Approximation of prime harmonics in 451edo
Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+0.00	+0.48	-0.50	-0.31	-0.54	+0.27	-1.19	+0.49	-0.34	+0.13	-0.91
Error	Relative (%)	+0.0	+18.2	-19.0	-11.7	-20.4	+10.2	-44.6	+18.5	-12.6	+5.1	-34.3
Steps (reduced)		451 (0)	715 (264)	1047 (145)	1266 (364)	1560 (207)	1669 (316)	1843 (39)	1916 (112)	2040 (236)	2191 (387)	2234 (430)

Since 451 factors into 11 × 41, 451edo has 11edo and 41edo as its subsets.

Subgroup	Comma List	Mapping	Optimal 8ve Stretch (¢)	Tuning Error
Subgroup	Comma List	Mapping	Optimal 8ve Stretch (¢)	Absolute (¢)	Relative (%)
2.3.5	[3 -18 11⟩, [-59 5 22⟩	[⟨451 715 1047]]	-0.0294	0.2144	8.06
2.3.5.7	2401/2400, 65625/65536, 390625000/387420489	[⟨451 715 1047 126 6]]	+0.0057	0.1953	7.34
2.3.5.7.11	2401/2400, 6250/6237, 42592/42525, 43923/43904	[⟨451 715 1047 1266 1560]]	+0.0359	0.1849	6.95
2.3.5.7.11.13	625/624, 2080/2079, 2200/2197, 2401/2400, 17303/17280	[⟨451 715 1047 1266 1560 1669]]	+0.0177	0.1736	6.52

Table of rank-2 temperaments by generator
Periods per 8ve	Generator*	Cents*	Associated Ratio*	Temperaments
1	29\451	77.16	256/245	Tertiaseptal

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