1407edo

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← 1406edo1407edo1408edo →
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

1407 equal divisions of the octave (abbreviated 1407edo or 1407ed2), also called 1407-tone equal temperament (1407tet) or 1407 equal temperament (1407et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 1407 equal parts of about 0.853 ¢ each. Each step represents a frequency ratio of 21/1407, or the 1407th root of 2.

Theory

1407edo is excellent in the 7-limit, in which it supports the 441 & 966 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.

Prime harmonics

Approximation of prime harmonics in 1407edo
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 (%) +0.0 -4.2 +4.7 +5.2 -42.0 +48.1 -6.0 +16.6 +34.8 -17.9 +44.6
Steps
(reduced)
1407
(0)
2230
(823)
3267
(453)
3950
(1136)
4867
(646)
5207
(986)
5751
(123)
5977
(349)
6365
(737)
6835
(1207)
6971
(1343)

Subsets and supersets

Since 1407 factors into 3 × 7 × 67, 1407edo has subset edos 3, 7, 21, 67, 201, and 469.

Regular temperament properties

Rank-2 temperaments

Table of rank-2 temperaments by generator
Periods
per 8ve
Generator* Cents* 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

* octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if it is distinct