# 1015edo

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 ← 1014edo 1015edo 1016edo →
Prime factorization 5 × 7 × 29
Step size 1.18227¢
Fifth 594\1015 (702.266¢)
Semitones (A1:m2) 98:75 (115.9¢ : 88.67¢)
Consistency limit 5
Distinct consistency limit 5

1015 equal divisions of the octave (abbreviated 1015edo or 1015ed2), also called 1015-tone equal temperament (1015tet) or 1015 equal temperament (1015et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 1015 equal parts of about 1.18 ¢ each. Each step represents a frequency ratio of 21/1015, or the 1015th root of 2.

1015edo is consistent in the 5-odd-limit, where it tunes quintosec. It also tunes the 2.3.5.11 subgroup natural extension for quintosec tempering out 5632/5625 and 26214400/26198073, despite not being consistent. The patent val also tempers out 3025/3024 and tunes the ganesha temperament in the 11-limit.

Aside from the patent val, there is a number of other mappings to be considered. For example, 1015edo is an excellent 2.5/3.9/7.13 subgroup tuning. 1015d val tunes supermajor.

### Odd harmonics

Approximation of odd harmonics in 1015edo
Harmonic 3 5 7 9 11 13 15 17 19 21 23
Error Absolute (¢) +0.311 +0.287 -0.550 -0.560 -0.382 +0.063 -0.584 +0.266 +0.418 -0.239 -0.491
Relative (%) +26.3 +24.3 -46.5 -47.4 -32.3 +5.4 -49.4 +22.5 +35.4 -20.2 -41.5
Steps
(reduced)
1609
(594)
2357
(327)
2849
(819)
3217
(172)
3511
(466)
3756
(711)
3965
(920)
4149
(89)
4312
(252)
4458
(398)
4591
(531)

### Subsets and supersets

Since 1015 factors as 5 × 7 × 29, 1015edo has subset edos 1, 5, 7, 29, 35, 145, 203.