1260edo

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← 1259edo1260edo1261edo →
Prime factorization 22 × 32 × 5 × 7
Step size 0.952381¢
Fifth 737\1260 (701.905¢)
Semitones (A1:m2) 119:95 (113.3¢ : 90.48¢)
Consistency limit 5
Distinct consistency limit 5
Special properties

1260 equal divisions of the octave (abbreviated 1260edo), or 1260-tone equal temperament (1260tet), 1260 equal temperament (1260et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 1260 equal parts of about 0.952 ¢ each. Each step of 1260edo represents a frequency ratio of 21/1260, or the 1260th root of 2.

1260edo is the 16th highly composite edo, and the first one after 12edo which has a good (only 5% error) and also coprime perfect fifth, so that a circle of fifths goes through every step. Unfortunately, it is only consistent to the 5-odd-limit since the errors of both harmonics 5 and 7 are quite large and on the opposite side.

It tunes well the 2.3.7.11.17.29 subgroup. It tempers out the parakleisma in the 5-limit on the patent val, and in the 13-limit in the 1260cf val it provides an alternative extension to the oquatonic temperament.

One step of 1260edo bears the name triangular cent, although for unclear reasons. See Interval size measure #Octave-based fine measures

Prime harmonics

Approximation of prime harmonics in 1260edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error absolute (¢) +0.000 -0.050 +0.353 -0.254 +0.111 +0.425 -0.194 -0.370 +0.297 -0.053 -0.274
relative (%) +0 -5 +37 -27 +12 +45 -20 -39 +31 -6 -29
Steps
(reduced)
1260
(0)
1997
(737)
2926
(406)
3537
(1017)
4359
(579)
4663
(883)
5150
(110)
5352
(312)
5700
(660)
6121
(1081)
6242
(1202)

Subsets and supersets

Since 1260 factors into 22 × 32 × 5 × 7, 1260edo has subset edos 2, 3, 4, 5, 6, 7, 9, 10, 12, 14, 15, 18, 20, 21, 28, 30, 35, 36, 42, 45, 60, 63, 70, 84, 90, 105, 126, 140, 180, 210, 252, 315, 420, and 630.