1210edo

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← 1209edo1210edo1211edo →
Prime factorization 2 × 5 × 112
Step size 0.991736¢ 
Fifth 708\1210 (702.149¢) (→354\605)
Semitones (A1:m2) 116:90 (115¢ : 89.26¢)
Consistency limit 13
Distinct consistency limit 13

1210 equal divisions of the octave (abbreviated 1210edo or 1210ed2), also called 1210-tone equal temperament (1210tet) or 1210 equal temperament (1210et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 1210 equal parts of about 0.992 ¢ each. Each step represents a frequency ratio of 21/1210, or the 1210th root of 2.

1210edo is consistent in the 13-odd-limit, though it is a sharp system with high errors and with all odd harmonics upwards to 23 except 15 tending sharp. As such, the tuning system would benefit from octave compression. It can also be used as a 2.3.7.11.17.19-subgroup system for best accuracy.

1210edo provides the optimal patent val for the titanium temperament in the 11- and the 13-limit. Aside from this, in the 11-limit it provides the optimal patent val for decoid, baffin, as well as the rank-3 temperament zisa.

Odd harmonics

Approximation of odd harmonics in 1210edo
Harmonic 3 5 7 9 11 13 15 17 19 21 23
Error Absolute (¢) +0.194 +0.463 +0.100 +0.388 +0.087 +0.464 -0.335 +0.169 +0.008 +0.293 +0.486
Relative (%) +19.5 +46.7 +10.1 +39.1 +8.8 +46.8 -33.8 +17.0 +0.8 +29.6 +49.0
Steps
(reduced)
1918
(708)
2810
(390)
3397
(977)
3836
(206)
4186
(556)
4478
(848)
4727
(1097)
4946
(106)
5140
(300)
5315
(475)
5474
(634)

Subsets and supersets

Since 1210 factors as 2 × 5 × 112, 1210edo has subset edos 2, 5, 10, 11, 22, 55, 110, 121, 242, 605.