351edo

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351edo

352edo →

Prime factorization	33 × 13
Step size	3.4188 ¢
Fifth	205\351 (700.855 ¢)
Semitones (A1:m2)	31:28 (106 ¢ : 95.73 ¢)
Consistency limit	7
Distinct consistency limit	7

Theory

351et tempers out 184528125/184473632, 26873856/26796875, 65625/65536, 235298/234375 and 40353607/40310784 in the 7-limit; 806736/805255, 1019215872/1019046875, 46656/46585, 1366875/1362944, 759375/758912, 117649/117612, 172032/171875, 441/440, 5788125/5767168, 24057/24010, 537109375/536870912, 422576/421875, 184877/184320, 275653125/275365888, 78408/78125, 41503/41472, 766656/765625, 35937/35840, 43923/43904, 246071287/246037500 and 1771561/1769472 in the 11-limit. It supports snape.

Odd harmonics

Approximation of odd harmonics in 351edo

Harmonic		3	5	7	9	11	13	15	17	19	21	23
Error	Absolute (¢)	-1.10	+0.01	-1.30	+1.22	-0.89	+0.50	-1.09	+1.03	-0.08	+1.01	+0.79
	Relative (%)	-32.2	+0.3	-38.2	+35.6	-26.0	+14.6	-31.9	+30.1	-2.3	+29.7	+23.0
Steps (reduced)		556 (205)	815 (113)	985 (283)	1113 (60)	1214 (161)	1299 (246)	1371 (318)	1435 (31)	1491 (87)	1542 (138)	1588 (184)

Subsets and supersets

351 factors into 3³ × 13 with subset edos 3, 9, 13, 27, 39, and 117.

Regular temperament properties

Subgroup	Comma List	Mapping	Optimal 8ve Stretch (¢)	Tuning Error
				2.3	[-556 351⟩	[⟨351 556]]	0.3471	0.3472	10.16
2.3.5	[-36 11 8⟩, [-11 26 -13⟩	[⟨351 556 815]]	0.2298	0.3284	9.61
2.3.5.7	19683/19600, 65625/65536, 235298/234375	[⟨351 556 815 985]]	0.2885	0.3021	8.84
2.3.5.7.11	441/440, 19683/19600, 41503/41472, 759375/758912	[⟨351 556 815 985 1214]]	0.2823	0.2705	7.91

Rank-2 temperaments

Table of rank-2 temperaments by generator

Periods per 8ve	Generator*	Cents*	Associated Ratio*	Temperaments
1	116\351	396.58	98304/78125	Squarschmidt

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