870edo: Difference between revisions

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{{EDO intro|870}}
{{EDO intro|870}}


870edo is notably strong in the subgroup of ''Fermat primes'', 2.3.5.17.
870edo is notably strong in the [[subgroup]] of {{w|Fermat prime|Fermat primes}}, 2.3.5.17.


=== Odd harmonics ===
=== Odd harmonics ===
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=== Subsets and supersets ===
=== Subsets and supersets ===
Since 870 factors into {{factorization|870}}, 870edo has subset edos {{EDOs|1, 2, 3, 5, 6, 10, 15, 29, 30, 58, 87, 145, 174, 290, and 435}}.  
Since 870 factors into {{factorization|870}}, 870edo has subset edos {{EDOs| 2, 3, 5, 6, 10, 15, 29, 30, 58, 87, 145, 174, 290, and 435 }}.  


{{Stub}}
{{Stub}}

Revision as of 10:22, 13 July 2024

← 869edo 870edo 871edo →
Prime factorization 2 × 3 × 5 × 29
Step size 1.37931 ¢ 
Fifth 509\870 (702.069 ¢)
Semitones (A1:m2) 83:65 (114.5 ¢ : 89.66 ¢)
Consistency limit 7
Distinct consistency limit 7

Template:EDO intro

870edo is notably strong in the subgroup of Fermat primes, 2.3.5.17.

Odd harmonics

Approximation of prime harmonics in 870edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) +0.000 +0.114 -0.107 -0.550 +0.406 -0.528 -0.128 +0.418 -0.688 -0.612 -0.208
Relative (%) +0.0 +8.3 -7.7 -39.9 +29.4 -38.3 -9.3 +30.3 -49.9 -44.3 -15.1
Steps
(reduced)
870
(0)
1379
(509)
2020
(280)
2442
(702)
3010
(400)
3219
(609)
3556
(76)
3696
(216)
3935
(455)
4226
(746)
4310
(830)

Subsets and supersets

Since 870 factors into 2 × 3 × 5 × 29, 870edo has subset edos 2, 3, 5, 6, 10, 15, 29, 30, 58, 87, 145, 174, 290, and 435.

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