User:Contribution/Exploring 31-EDO

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Revision as of 20:22, 28 September 2025 by Contribution (talk | contribs) (Created page with "== 11-limit optimizations of 31-EDO == {{Harmonics in cet|38.743026608201324738|columns=11|intervals=prime|title=Approximation of prime harmonics in 11-limit Euler-product (σ = 1.0) optimization of 31-EDO}} {{Harmonics in cet|38.748558591979841975|columns=11|intervals=prime|title=Approximation of prime harmonics in 11-limit Tenney-Euclidian optimization of 31-EDO}}")
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11-limit optimizations of 31-EDO

Approximation of prime harmonics in 11-limit Euler-product (σ = 1.0) optimization of 31-EDO
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) +1.0 -3.5 +3.2 +1.8 -5.8 +14.9 +15.4 +16.6 -4.3 -18.1 -17.4
Relative (%) +2.7 -9.2 +8.2 +4.7 -15.0 +38.5 +39.8 +42.8 -11.0 -46.8 -44.8
Step 31 49 72 87 107 115 127 132 140 150 153


Approximation of prime harmonics in 11-limit Tenney-Euclidian optimization of 31-EDO
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) +1.2 -3.3 +3.6 +2.3 -5.2 +15.6 +16.1 +17.3 -3.5 -17.3 -16.5
Relative (%) +3.1 -8.5 +9.2 +5.9 -13.5 +40.1 +41.6 +44.6 -9.0 -44.6 -42.6
Step 31 49 72 87 107 115 127 132 140 150 153