# 185edo

 ← 184edo 185edo 186edo →
Prime factorization 5 × 37
Step size 6.48649¢
Fifth 108\185 (700.541¢)
Semitones (A1:m2) 16:15 (103.8¢ : 97.3¢)
Consistency limit 3
Distinct consistency limit 3

185 equal divisions of the octave (abbreviated 185edo or 185ed2), also called 185-tone equal temperament (185tet) or 185 equal temperament (185et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 185 equal parts of about 6.49 ¢ each. Each step represents a frequency ratio of 21/185, or the 185th root of 2.

## Theory

The patent val of 185edo tempers out 126/125, 1029/1024, 6144/6125 in the 7-limit, and 243/242 in the 11-limit, making it useful for various purposes. It is an excellent tuning for starling, the 7-limit planar temperament tempering out 126/125; valentine, which also tempers out 1029/1024; and cuckoo, tempering out 126/125 and 243/242.

Using the 185c val, it tempers out 225/224 and 1029/1024 in the 7-limit, 243/242, 385/384, 441/440, and 540/539 in the 11-limit, providing a great alternative to 72edo for miracle. With the 185cf val 185 293 429 519 640 684], it makes for an excellent tuning of 13-limit manna. Meanwhile the 185cff val 185 293 429 519 640 686] is a first-class tuning of 13-limit miraculous.

### Odd harmonics

Approximation of odd harmonics in 185edo
Harmonic 3 5 7 9 11 13 15 17 19 21 23
Error Absolute (¢) -1.41 +2.88 -2.34 -2.83 +0.03 +2.72 +1.46 -1.17 +0.87 +2.73 +0.91
Relative (%) -21.8 +44.3 -36.1 -43.6 +0.5 +41.9 +22.5 -18.1 +13.3 +42.1 +14.1
Steps
(reduced)
293
(108)
430
(60)
519
(149)
586
(31)
640
(85)
685
(130)
723
(168)
756
(16)
786
(46)
813
(73)
837
(97)

### Subsets and supersets

Since 185 factors into 5 × 37, 185edo contains 5edo and 37edo as its subsets.