1015edo

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← 1014edo1015edo1016edo →
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 1015-tone equal temperament (1015tet), 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 of 1015edo 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 +24 -47 -47 -32 +5 -49 +23 +35 -20 -42
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.