# 385edo

 ← 384edo 385edo 386edo →
Prime factorization 5 × 7 × 11
Step size 3.11688¢
Fifth 225\385 (701.299¢) (→45\77)
Semitones (A1:m2) 35:30 (109.1¢ : 93.51¢)
Consistency limit 7
Distinct consistency limit 7

385 equal divisions of the octave (abbreviated 385edo or 385ed2), also called 385-tone equal temperament (385tet) or 385 equal temperament (385et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 385 equal parts of about 3.12 ¢ each. Each step represents a frequency ratio of 21/385, or the 385th root of 2.

## Theory

385edo has a reasonable approximation to the 11-limit, and perhaps beyond. The equal temperament tempers out 19683/19600, 589824/588245, and 703125/702464 in the 7-limit; 540/539, 8019/8000, 43923/43904, 151263/151250, 160083/160000, 166698/166375, and 172032/171875 in the 11-limit. It supports hemipental and provides the optimal patent val for the 7-limit version thereof. Using the patent val, it tempers out 1575/1573, 1716/1715, 2200/2197, 4096/4095, 6656/6655 and 10648/10647 in the 13-limit; and 936/935, 1275/1274, 1377/1375, and 2601/2600 in the 17-limit.

### Prime harmonics

Approximation of prime harmonics in 385edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) +0.00 -0.66 +0.18 +0.52 +0.37 +1.03 +1.02 -1.41 +1.34 -1.01 -1.14
Relative (%) +0.0 -21.1 +5.8 +16.8 +11.9 +33.1 +32.7 -45.2 +42.9 -32.3 -36.6
Steps
(reduced)
385
(0)
610
(225)
894
(124)
1081
(311)
1332
(177)
1425
(270)
1574
(34)
1635
(95)
1742
(202)
1870
(330)
1907
(367)

### Subsets and supersets

Since 385 factors into 5 × 7 × 11, 385edo has subset edos 5, 7, 11, 35, 55, and 77.

## Regular temperament properties

Subgroup Comma List Mapping Optimal
8ve Stretch (¢)
Tuning Error
Absolute (¢) Relative (%)
2.3 [-122 77 [385 610]] +0.2070 0.2071 6.64
2.3.5 [-28 25 -5, [38 -2 -15 [385 610 894]] +0.1122 0.2158 6.92
2.3.5.7 19683/19600, 589824/588245, 703125/702464 [385 610 894 1081]] +0.0374 0.2274 7.30
2.3.5.7.11 540/539, 8019/8000, 151263/151250, 172032/171875 [385 610 894 1081 1332]] +0.0085 0.2114 6.78
2.3.5.7.11.13 540/539, 1575/1573, 2200/2197, 4096/4095, 8019/8000 [385 610 894 1081 1332 1425]] -0.0394 0.2207 7.08
2.3.5.7.11.13.17 540/539, 936/935, 1377/1375, 1575/1573, 2200/2197, 4096/4095 [385 610 894 1081 1332 1425 1574]] -0.0693 0.2171 6.97

### Rank-2 temperaments

Table of rank-2 temperaments by generator
Periods
per 8ve
Generator* Cents* Associated
Ratio*
Temperaments
1 62\385 193.25 262144/234375 Luna
1 162/385 504.94 4/3 Countermeantone
5 80\385
(3\385)
249.35
(9.35)
81/70
(176/175)
Hemipental
5 160\385
(6\385)
498.70
(18.70)
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