1230edo

 ← 1229edo 1230edo 1231edo →
Prime factorization 2 × 3 × 5 × 41
Step size 0.97561¢
Fifth 720\1230 (702.439¢) (→24\41)
Semitones (A1:m2) 120:90 (117.1¢ : 87.8¢)
Dual sharp fifth 720\1230 (702.439¢) (→24\41)
Dual flat fifth 719\1230 (701.463¢)
Dual major 2nd 209\1230 (203.902¢)
Consistency limit 5
Distinct consistency limit 5

1230 equal divisions of the octave (abbreviated 1230edo or 1230ed2), also called 1230-tone equal temperament (1230tet) or 1230 equal temperament (1230et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 1230 equal parts of about 0.976 ¢ each. Each step represents a frequency ratio of 21/1230, or the 1230th root of 2.

1230edo is consistent to the 5-odd-limit, but harmonic 3 is about halfway between its steps. As every other step of 2460edo, it is excellent in approximating harmonics 5, 7, 9, 11, 19, and 23, making it suitable for a 2.9.5.7.11.19.23 subgroup interpretation, on which it is identical to 2460edo.

Odd harmonics

Approximation of odd harmonics in 1230edo
Harmonic 3 5 7 9 11 13 15 17 19 21 23
Error Absolute (¢) +0.484 +0.028 -0.045 -0.008 -0.098 +0.448 -0.464 +0.410 +0.048 +0.439 +0.018
Relative (%) +49.6 +2.8 -4.7 -0.8 -10.1 +45.9 -47.5 +42.1 +4.9 +45.0 +1.9
Steps
(reduced)
1950
(720)
2856
(396)
3453
(993)
3899
(209)
4255
(565)
4552
(862)
4805
(1115)
5028
(108)
5225
(305)
5403
(483)
5564
(644)

Miscellaneous properties

1230edo could be called a "highly Kartvelian edo" because it supports the largest number of scales dividing its patent val 4/3 and 3/2 into even parts relative to its size. See Kartvelian scales.

Subsets and supersets

Since 1230 factors into 2 × 3 × 5 × 41, 1230edo has subset edos 2, 3, 5, 6, 10, 15, 30, 41, 82, 123, 205, 246, 410, and 615. A step of 1230edo is exactly 2 minas (2\2460).