1125edo: Difference between revisions

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Created page with "1125edo divides the octave into parts of 1.066 cents each. Its divisors are {{EDOs|1, 3, 5, 9, 15, 25, 45, 75, 125, 225, 375}}. ==Theory== {{harmonics in equal|1125}} In the..."
 
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1125edo divides the octave into parts of 1.066 cents each.
{{Infobox ET}}
{{ED intro}}


Its divisors are  {{EDOs|1, 3, 5, 9, 15, 25, 45, 75, 125, 225, 375}}.
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]]. It [[Tempering out|tempers out]] [[2401/2400]], [[4375/4374]], and [[250047/250000]] in the 7-limit, supporting [[ennealimmal]].
==Theory==
 
{{harmonics in equal|1125}}
=== Prime harmonics ===
In the 11-limit, 1125edo tempers out [[2401/2400]], [[4375/4374]], and [[250047/250000]].
{{Harmonics in equal|1125}}
 
=== Subsets and supersets ===
Snce 1125 factors into {{factorization|1125}}, 1125edo has subset edos {{EDOs| 3, 5, 9, 15, 25, 45, 75, 125, 225, 375 }}.

Latest revision as of 17:42, 20 February 2025

← 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

1125 equal divisions of the octave (abbreviated 1125edo or 1125ed2), also called 1125-tone equal temperament (1125tet) or 1125 equal temperament (1125et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 1125 equal parts of about 1.07 ¢ each. Each step represents a frequency ratio of 21/1125, or the 1125th root of 2.

1125edo is a good 13-limit system, distinctly consistent to the 15-odd-limit, and the no-11 or no-17 29-odd-limit. It 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.