1330edo

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← 1329edo1330edo1331edo →
Prime factorization 2 × 5 × 7 × 19
Step size 0.902256¢ 
Fifth 778\1330 (701.955¢) (→389\665)
Semitones (A1:m2) 126:100 (113.7¢ : 90.23¢)
Consistency limit 11
Distinct consistency limit 11

1330 equal divisions of the octave (abbreviated 1330edo or 1330ed2), also called 1330-tone equal temperament (1330tet) or 1330 equal temperament (1330et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 1330 equal parts of about 0.902 ¢ each. Each step represents a frequency ratio of 21/1330, or the 1330th root of 2.

1330edo is enfactored in the 7-limit and has the same tuning as 665edo. It corrects 665edo's approximation of harmonic 11, only to be consistent up to the 11-odd-limit, unfortunately. It tempers out 3025/3024, 9801/9800, and 234375/234256, supporting hemienneadecal, though 1178edo is a better tuning for that purpose.

Prime harmonics

Approximation of prime harmonics in 1330edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) +0.000 -0.000 -0.148 +0.197 -0.040 +0.375 -0.294 +0.231 -0.304 -0.104 -0.073
Relative (%) +0.0 -0.0 -16.4 +21.8 -4.4 +41.5 -32.6 +25.6 -33.7 -11.5 -8.1
Steps
(reduced)
1330
(0)
2108
(778)
3088
(428)
3734
(1074)
4601
(611)
4922
(932)
5436
(116)
5650
(330)
6016
(696)
6461
(1141)
6589
(1269)

Subsets and supersets

Since 1330 factors into 2 × 5 × 7 × 19, it has subset edos 2, 5, 7, 19, 35, 70, 95, 133, 190, 266, and 665. A step of 1330edo is exactly 24 imps (24\31920).