1407edo
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Prime factorization
3 × 7 × 67
Step size
0.852878¢
Fifth
823\1407 (701.919¢)
Semitones (A1:m2)
133:106 (113.4¢ : 90.41¢)
Consistency limit
11
Distinct consistency limit
11
| ← 1406edo | 1407edo | 1408edo → |
1407 equal divisions of the octave (1407edo), or 1407-tone equal temperament (1407tet), 1407 equal temperament (1407et) when viewed from a regular temperament perspective, is the tuning system that divides the octave into 1407 equal parts of about 0.853 ¢ each.
Theory
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | absolute (¢) | +0.000 | -0.036 | +0.040 | +0.044 | -0.358 | +0.411 | -0.051 | +0.142 | +0.297 | -0.153 | +0.380 |
| relative (%) | +0 | -4 | +5 | +5 | -42 | +48 | -6 | +17 | +35 | -18 | +45 | |
| Steps (reduced) |
1407 (0) |
2230 (823) |
3267 (453) |
3950 (1136) |
4867 (646) |
5207 (986) |
5751 (123) |
5977 (349) |
6365 (737) |
6835 (1207) |
6971 (1343) | |
1407edo is excellent in the 7-limit, in which it supports the 441 & 1407 akjayland temperament with period 21. Just like 441edo, it tempers out the akjaysma and the landscape comma. However, unlike 441edo it does not temper out the tritrizo comma, since 1407 is not divisible by 9.
It tunes the pure bastille temperament in the 1407eff val and the marvelous bastille temperament in the patent val in the 13-limit.
1407's divisors are 1, 3, 7, 21, 67, 201, 469.
Regular temperament properties
Rank-2 temperaments
| Periods per 8ve |
Generator (Reduced) |
Cents (Reduced) |
Associated Ratio |
Temperaments |
|---|---|---|---|---|
| 1 | 814\1407 | 694.243 | [381 0 -159 -4⟩ | Bastille (2.5.7) / pure bastille (1407eff) / marvelous bastille (1407) |
| 3 | 292\1407 | 249.040 | 1536/1331 | Tribilo |
| 7 | 10\1407 | 8.529 | 1029/1024 | Nitrogen |
| 21 | 686\1407 (16\1407) |
585.074 (13.646) |
91875/65536 (126/125) |
Akjayland |