# 1065edo

 ← 1064edo 1065edo 1066edo →
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 1.13 ¢ 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 (%) +0.0 +1.5 +14.7 +16.7 -29.5 +3.2 -14.8 -4.3 +40.7 +25.0 -21.9
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.