# 1944edo

 ← 1943edo 1944edo 1945edo →
Prime factorization 23 × 35
Step size 0.617284¢
Fifth 1137\1944 (701.852¢) (→379\648)
Semitones (A1:m2) 183:147 (113¢ : 90.74¢)
Consistency limit 5
Distinct consistency limit 5

1944 equal divisions of the octave (abbreviated 1944edo or 1944ed2), also called 1944-tone equal temperament (1944tet) or 1944 equal temperament (1944et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 1944 equal parts of about 0.617 ¢ each. Each step represents a frequency ratio of 21/1944, or the 1944th root of 2.

## Theory

1944edo is consistent in the 5-odd-limit to which it provides good approximation, and a near-perfect 15/8, but it is only consistent that far since harmonic 7 is about halfway between its steps. In the 5-limit, it tempers out the luna comma, [38 -2 -15. In the 1944d val in the 7-limit, it is a landscape system tempering out 250047/250000, and as a consequence it tunes the 24th-octave chromium temperament, providing a tuning close to POTE tuning.

In higher limits, 1944edo is a tuning for the jamala temperament in the 2.5.11.13.19.41.47 subgroup, for which 1944edo provides good approximation (except for the 13th harmonic). Overall, the best subgroup for 1944edo is 2.3.5.11.17.19.29.31.41.47.

### Odd harmonics

Approximation of odd harmonics in 1944edo
Harmonic 3 5 7 9 11 13 15 17 19 21 23
Error Absolute (¢) -0.103 +0.106 -0.307 -0.206 -0.083 +0.213 +0.003 -0.017 +0.018 +0.207 +0.121
Relative (%) -16.7 +17.2 -49.8 -33.4 -13.5 +34.5 +0.5 -2.8 +2.9 +33.5 +19.6
Steps
(reduced)
3081
(1137)
4514
(626)
5457
(1569)
6162
(330)
6725
(893)
7194
(1362)
7595
(1763)
7946
(170)
8258
(482)
8539
(763)
8794
(1018)

### Subsets and supersets

Since 1944 factors into 23 × 35, 1944edo has subset edos 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 81, 108, 162, 216, 243, 324, 486, 648, and 972.

## Regular temperament properties

### Rank-2 temperaments

Periods
per 8ve
Generator* Cents* Associated
Ratio*
Temperaments
1 313\1944 193.210 262144/234375 Luna (5-limit)
24 944\1944
(53\1944)
582.716
(32.716)
7/5
(?)
Chromium (1944d)
72 892\1944
(1\1944)
550.617
(0.617)
73205/53248
(?)
Jamala

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