1911edo

← 1910edo

1911edo

1912edo →

Prime factorization	3 × 72 × 13
Step size	0.627943 ¢
Fifth	1118\1911 (702.041 ¢) (→ 86\147)
Semitones (A1:m2)	182:143 (114.3 ¢ : 89.8 ¢)
Consistency limit	11
Distinct consistency limit	11

Theory

1911edo is consistent in the 11-limit and tempers out the aluminium comma in the 5-limit. It provides the optimal patent val for the protactinium temperament in the 17-limit. However as may stem from consistency only in the 11-limit, the 13th harmonic has a large relative error. As such, 1911edo is best considered as a 2.3.5.7.11.17.19 subgroup tuning.

Odd harmonics

Approximation of prime harmonics in 1911edo

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+0.000	+0.086	-0.128	+0.091	+0.016	+0.289	-0.089	+0.132	+0.297	+0.250	-0.295
	Relative (%)	+0.0	+13.7	-20.5	+14.5	+2.6	+46.0	-14.1	+21.1	+47.3	+39.8	-46.9
Steps (reduced)		1911 (0)	3029 (1118)	4437 (615)	5365 (1543)	6611 (878)	7072 (1339)	7811 (167)	8118 (474)	8645 (1001)	9284 (1640)	9467 (1823)

Subsets and supersets

Since 1911 factors into 3 × 7² × 13, 1911edo has subset edos 3, 7, 13, 21, 39, 49, 91, 147, 273, 637.

Regular temperament properties

Rank-2 temperaments

Periods per 8ve	Generator*	Cents*	Associated Ratio	Temperaments
13	793\1911 (58\1911)	497.959 (36.421)	4/3 (?)	Aluminium
91	793\1911 (16\1911)	497.959 (10.047)	4/3 (176/175)	Protactinium

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