1065edo

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← 1064edo1065edo1066edo →
Prime factorization 3 × 5 × 71
Step size 1.12676¢
Fifth 623\1065 (701.972¢)
Semitones (A1:m2) 101:80 (113.8¢ : 90.14¢)
Consistency limit 21
Distinct consistency limit 21
Special properties

1065 equal divisions of the octave (abbreviated 1065edo or 1065ed2), also called 1065-tone equal temperament (1065tet) or 1065 equal temperament (1065et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 1065 equal parts of about 1.127 ¢ each. Each step represents a frequency ratio of 21/1065, or the 1065th root of 2.

1065edo is consistent to the 21-odd-limit and is a zeta peak integer edo.

The equal temperament tempers out [54 -37 2 (monzisma) and [61 4 -29 (squarschmidt comma) in the 5-limit; 250047/250000 (landscape comma) in the 7-limit; 3025/3024, 102487/102400, 160083/160000, and 180224/180075 in the 11-limit; 1716/1715 and 4096/4095 in the 13-limit; 2601/2600 and 12376/12375 in the 17-limit; and 2376/2375, 2926/2925, 10830/10829, 14080/14079, and 14365/14364 in the 19-limit.

Prime harmonics

Approximation of prime harmonics in 1065edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error absolute (¢) +0.0000 +0.0168 +0.1652 +0.1882 -0.3320 +0.0357 -0.1667 -0.0482 +0.4580 +0.2820 -0.2468
relative (%) +0 +1 +15 +17 -29 +3 -15 -4 +41 +25 -22
Steps
(reduced)
1065
(0)
1688
(623)
2473
(343)
2990
(860)
3684
(489)
3941
(746)
4353
(93)
4524
(264)
4818
(558)
5174
(914)
5276
(1016)

Subsets and supersets

Since 1065 factors into 3 × 5 × 71, 1065edo has subset edos 3, 5, 15, 71, 213, and 355.