1125edo: Difference between revisions

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Adopt template: EDO intro; cleanup
Expand on theory; adopt template: Factorization
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{{EDO intro|1125}}
{{EDO intro|1125}}


The equal temperament [[Tempering out|tempers out]] [[2401/2400]], [[4375/4374]], and [[250047/250000]] in the 7-limit, supporting [[ennealimmal]].  
1125edo is a good 13-limit system, [[consistency|distinctly consistent]] to the [[15-odd-limit]], and the no-11 or no-17 [[29-odd-limit]]. The equal temperament [[Tempering out|tempers out]] [[2401/2400]], [[4375/4374]], and [[250047/250000]] in the 7-limit, supporting [[ennealimmal]].  


=== Prime harmonics ===
=== Prime harmonics ===
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=== Subsets and supersets ===
=== Subsets and supersets ===
Snce 1125 factors into 3<sup>2</sup> × 5<sup>3</sup>, 1125edo has subset edos {{EDOs| 3, 5, 9, 15, 25, 45, 75, 125, 225, 375 }}.
Snce 1125 factors into {{factorization|1125}}, 1125edo has subset edos {{EDOs| 3, 5, 9, 15, 25, 45, 75, 125, 225, 375 }}.

Revision as of 10:26, 31 October 2023

← 1124edo 1125edo 1126edo →
Prime factorization 32 × 53
Step size 1.06667 ¢ 
Fifth 658\1125 (701.867 ¢)
Semitones (A1:m2) 106:85 (113.1 ¢ : 90.67 ¢)
Consistency limit 15
Distinct consistency limit 15

Template:EDO intro

1125edo is a good 13-limit system, distinctly consistent to the 15-odd-limit, and the no-11 or no-17 29-odd-limit. The equal temperament tempers out 2401/2400, 4375/4374, and 250047/250000 in the 7-limit, supporting ennealimmal.

Prime harmonics

Approximation of prime harmonics in 1125edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) +0.000 -0.088 -0.180 -0.293 +0.149 +0.006 -0.422 +0.087 -0.008 -0.244 -0.502
Relative (%) +0.0 -8.3 -16.9 -27.4 +13.9 +0.5 -39.6 +8.2 -0.7 -22.9 -47.1
Steps
(reduced)
1125
(0)
1783
(658)
2612
(362)
3158
(908)
3892
(517)
4163
(788)
4598
(98)
4779
(279)
5089
(589)
5465
(965)
5573
(1073)

Subsets and supersets

Snce 1125 factors into 32 × 53, 1125edo has subset edos 3, 5, 9, 15, 25, 45, 75, 125, 225, 375.