1944edo

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← 1943edo1944edo1945edo →
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