185edo
| ← 184edo | 185edo | 186edo → |
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
| 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 (%) | -22 | +44 | -36 | -44 | +1 | +42 | +23 | -18 | +13 | +42 | +14 | |
| 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.