# 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

1911 equal divisions of the octave (abbreviated 1911edo or 1911ed2), also called 1911-tone equal temperament (1911tet) or 1911 equal temperament (1911et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 1911 equal parts of about 0.628 ¢ each. Each step represents a frequency ratio of 21/1911, or the 1911th root of 2.

## Theory

1911edo is consistent in the 11-odd-limit. The equal temperament tempers out the aluminium comma in the 5-limit, and 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

Table of rank-2 temperaments by generator
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