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User:Contribution/Exploring 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


Approximation of prime harmonics in 121-ED15
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) +1.1 -3.4 +3.4 +2.1 -5.5 +15.3 +15.8 +17.0 -3.8 -17.7 -16.9
Relative (%) +2.9 -8.8 +8.8 +5.4 -14.2 +39.4 +40.8 +43.8 -9.9 -45.6 -43.6
Steps
(reduced) 		31
(31) 		49
(49) 		72
(72) 		87
(87) 		107
(107) 		115
(115) 		127
(6) 		132
(11) 		140
(19) 		150
(29) 		153
(32)
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