412edo
| ← 411edo | 412edo | 413edo → |
Theory
412edo has a very accurate perfect fifth, but it is not quite accurate beyond that. The equal temperament tempers out [32 -7 -9⟩ (escapade comma) and [-69 45 -1⟩ (counterschisma) in the 5-limit; 6144/6125, 118098/117649, 2460375/2458624, 49009212/48828125, and notably the nanisma in the 7-limit. It supports nanic and counterschismic.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.00 | -0.01 | +1.06 | +1.08 | -0.83 | +1.22 | -0.10 | -0.43 | +0.85 | -1.42 | -0.38 |
| Relative (%) | +0.0 | -0.5 | +36.6 | +37.0 | -28.6 | +41.9 | -3.5 | -14.6 | +29.2 | -48.8 | -12.9 | |
| Steps (reduced) |
412 (0) |
653 (241) |
957 (133) |
1157 (333) |
1425 (189) |
1525 (289) |
1684 (36) |
1750 (102) |
1864 (216) |
2001 (353) |
2041 (393) | |
Subsets and supersets
412 factors into 22 × 103, with subset edos 2, 4, 103, and 206. 1236edo, which triples it, gives a good correction to harmonics 5, 7, and 11.
Regular temperament properties
Template:Comma basis begin |- | 2.3 | [-653 412⟩ | [⟨412 653]] | +0.0042 | 0.0042 | 0.14 |- | 2.3.5 | [32 -7 -9⟩, [-5 31 -19⟩ | [⟨412 653 957]] | −0.1501 | 0.2182 | 7.49 |- | 2.3.5.7 | 6144/6125, 2460375/2458624, 49009212/48828125 | [⟨412 653 957 1157]] | −0.2085 | 0.2143 | 7.36 Template:Comma basis end
Rank-2 temperaments
Template:Rank-2 begin
|-
| 1
| 9\412
| 26.21
| 49/48
| Sfourth (5-limit)
|-
| 1
| 19\412
| 55.34
| 16875/16384
| Escapade (5-limit)
|-
| 1
| 171\412
| 498.06
| 4/3
| Counterschismic
Nanic
|-
| 2
| 19\412
| 55.34
| 16875/16384
| Septisuperfourth (7-limit)
Template:Rank-2 end
Template:Orf