# 445edo

 ← 444edo 445edo 446edo →
Prime factorization 5 × 89
Step size 2.69663¢
Fifth 260\445 (701.124¢) (→52\89)
Semitones (A1:m2) 40:35 (107.9¢ : 94.38¢)
Consistency limit 7
Distinct consistency limit 7

445 equal divisions of the octave (abbreviated 445edo or 445ed2), also called 445-tone equal temperament (445tet) or 445 equal temperament (445et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 445 equal parts of about 2.7 ¢ each. Each step represents a frequency ratio of 21/445, or the 445th root of 2.

## Theory

445edo is enfactored in the 3-limit with the same tuning as 89edo, but the approximation to some of the higher harmonics are improved. It is consistent to the 7-odd-limit with harmonics 3, 5, 7 all tuned flat, and it allows an extension to the 11-limit. The equal temperament tempers out 2401/2400, 7381125/7340032, 33756345/33554432, 43046721/42875000, and 48828125/48771072 in the 7-limit; 3025/3024, 8019/8000, 24057/24010, 35937/35840, 41503/41472, 137781/137500, 151263/151250, and 234375/234256 in the 11-limit. It notably supports neptune.

### Odd harmonics

Approximation of odd harmonics in 445edo
Harmonic 3 5 7 9 11 13 15 17 19 21 23
Error Absolute (¢) -0.83 -0.70 -0.74 +1.03 -1.21 +0.82 +1.17 +0.21 -0.88 +1.13 +0.04
Relative (%) -30.8 -25.8 -27.3 +38.3 -44.7 +30.4 +43.4 +7.9 -32.8 +41.9 +1.5
Steps
(reduced)
705
(260)
1033
(143)
1249
(359)
1411
(76)
1539
(204)
1647
(312)
1739
(404)
1819
(39)
1890
(110)
1955
(175)
2013
(233)

### Subsets and supersets

Since 445 factors into 5 × 89, 445edo has 5edo and 89edo as its subsets.

## Regular temperament properties

Subgroup Comma List Mapping Optimal
8ve Stretch (¢)
Tuning Error
Absolute (¢) Relative (%)
2.3.5 [-28 25 -5, [-29 -11 20 [445 705 1033]] +0.2748 0.2149 7.97
2.3.5.7 2401/2400, 7381125/7340032, 43046721/42875000 [445 705 1033 1249]] +0.2716 0.1862 6.90
2.3.5.7.11 2401/2400, 3025/3024, 8019/8000, 234375/234256 [445 705 1033 1249 1539]] +0.2870 0.1694 6.28

### Rank-2 temperaments

Table of rank-2 temperaments by generator
Periods
per 8ve
Generator* Cents* Associated
Ratio*
Temperaments
1 13\445 35.06 1990656/1953125 Gammic (5-limit)
1 42\445 113.26 16/15 Misneb
1 216\445 582.47 7/5 Neptune (7-limit)
5 185\445
(7\445)
498.88
(18.88)
4/3
(81/80)
Pental (5-limit)

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