640edo: Difference between revisions

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Adopt template: EDO intro; +prime error table; +subsets and supersets
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=== Subsets and supersets ===
=== Subsets and supersets ===
Since 640 factors into 2<sup>7</sup> × 5, 640edo has subset edos {{EDOs| 2, 4, 5, 8, 10, 16, 20, 32, 40, 64, 80, 128, 160, and 320 }}.  
Since 640 factors into {{factorization|640}}, 640edo has subset edos {{EDOs| 2, 4, 5, 8, 10, 16, 20, 32, 40, 64, 80, 128, 160, and 320 }}.  


[[Category:Albus]]
[[Category:Albus]]
[[Category:Hemipental]]
[[Category:Hemipental]]

Revision as of 13:01, 2 November 2023

← 639edo 640edo 641edo →
Prime factorization 27 × 5
Step size 1.875 ¢ 
Fifth 374\640 (701.25 ¢) (→ 187\320)
Semitones (A1:m2) 58:50 (108.8 ¢ : 93.75 ¢)
Dual sharp fifth 375\640 (703.125 ¢) (→ 75\128)
Dual flat fifth 374\640 (701.25 ¢) (→ 187\320)
Dual major 2nd 109\640 (204.375 ¢)
Consistency limit 5
Distinct consistency limit 5

Template:EDO intro

640edo is enfactored in the 5-limit, tempering out the vishnuzma, [23 6 -14, with the same tuning as 320edo. In the 7-limit it tempers out 19683/19600 and [16 2 -1 -6 and in the 11-limit it tempers out 540/539, 8019/8000 and [14 -1 -2 -4 1. It provides the optimal patent val for the rank-3 albus temperament tempering out 540/539 and 8019/8000, and hemipental, the 255 & 385 temperament.

Odd harmonics

Approximation of odd harmonics in 640edo
Harmonic 3 5 7 9 11 13 15 17 19 21 23
Error Absolute (¢) -0.705 -0.064 +0.549 +0.465 -0.068 -0.528 -0.769 +0.045 +0.612 -0.156 -0.149
Relative (%) -37.6 -3.4 +29.3 +24.8 -3.6 -28.1 -41.0 +2.4 +32.6 -8.3 -8.0
Steps
(reduced)
1014
(374)
1486
(206)
1797
(517)
2029
(109)
2214
(294)
2368
(448)
2500
(580)
2616
(56)
2719
(159)
2811
(251)
2895
(335)

Subsets and supersets

Since 640 factors into 27 × 5, 640edo has subset edos 2, 4, 5, 8, 10, 16, 20, 32, 40, 64, 80, 128, 160, and 320.