# 1944edo

← 1943edo | 1944edo | 1945edo → |

^{3}× 3^{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 2^{1/1944}, 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

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 2^{3} × 3^{5}, 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