User:Overthink/Sandbox: Difference between revisions

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{{Harmonics in equal|43|columns=30}}
{{Harmonics in equal|43|columns=30}}
{{Harmonics in equal|44|columns=30}}
{{Harmonics in equal|45|columns=30}}
{{Harmonics in equal|46|columns=30}}

Revision as of 10:40, 24 December 2025

Approximation of prime harmonics in 43edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97 101 103 107 109 113
Error Absolute (¢) +0.0 -4.3 +4.4 +7.9 +6.8 -3.3 +6.7 +9.5 +13.6 +3.0 -0.8 -0.2 -10.5 -9.2 +4.3 -8.4 +1.3 -0.6 +4.4 -12.3 -4.5 -1.7 -3.5 -12.7 +5.7 -8.5 +13.4 +3.3 -0.9 -7.5
Relative (%) +0.0 -15.3 +15.7 +28.4 +24.4 -11.9 +23.9 +33.9 +48.7 +10.7 -3.0 -0.6 -37.5 -32.9 +15.3 -30.1 +4.6 -2.2 +15.8 -43.9 -16.2 -6.3 -12.7 -45.7 +20.4 -30.3 +48.0 +11.7 -3.2 -26.8
Steps
(reduced) 		43
(0) 		68
(25) 		100
(14) 		121
(35) 		149
(20) 		159
(30) 		176
(4) 		183
(11) 		195
(23) 		209
(37) 		213
(41) 		224
(9) 		230
(15) 		233
(18) 		239
(24) 		246
(31) 		253
(38) 		255
(40) 		261
(3) 		264
(6) 		266
(8) 		271
(13) 		274
(16) 		278
(20) 		284
(26) 		286
(28) 		288
(30) 		290
(32) 		291
(33) 		293
(35)
Approximation of odd harmonics in 44edo
Harmonic 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53 55 57 59 61
Error Absolute (¢) +7.1 -4.5 +13.0 -13.0 -5.9 +4.9 +2.6 +4.1 +2.5 -7.1 -1.0 -9.0 -5.9 +6.8 +0.4 +1.3 +8.5 -5.9 +12.1 +7.3 +6.7 +9.8 -11.0 -1.3 +11.3 -0.8 -10.4 +9.6 +4.5 +1.3
Relative (%) +26.2 -16.5 +47.6 -47.7 -21.5 +18.1 +9.7 +15.2 +9.1 -26.2 -3.7 -33.0 -21.5 +24.9 +1.5 +4.7 +31.2 -21.6 +44.2 +26.8 +24.4 +35.8 -40.2 -4.7 +41.3 -2.9 -38.0 +35.3 +16.4 +4.8
Steps
(reduced) 		70
(26) 		102
(14) 		124
(36) 		139
(7) 		152
(20) 		163
(31) 		172
(40) 		180
(4) 		187
(11) 		193
(17) 		199
(23) 		204
(28) 		209
(33) 		214
(38) 		218
(42) 		222
(2) 		226
(6) 		229
(9) 		233
(13) 		236
(16) 		239
(19) 		242
(22) 		244
(24) 		247
(27) 		250
(30) 		252
(32) 		254
(34) 		257
(37) 		259
(39) 		261
(41)
Approximation of odd harmonics in 45edo
Harmonic 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53 55 57 59 61
Error Absolute (¢) -8.6 -13.0 -8.8 +9.4 +8.7 +12.8 +5.1 +1.7 -4.2 +9.2 +11.7 +0.7 +0.8 +10.4 +1.6 +0.1 +4.9 -11.3 +4.2 -2.4 -4.9 -3.6 +1.2 +9.0 -6.9 +6.5 -4.3 -12.8 +7.5 +3.1
Relative (%) -32.3 -48.7 -33.1 +35.3 +32.6 +48.0 +19.0 +6.4 -15.7 +34.6 +44.0 +2.6 +3.0 +39.1 +6.1 +0.2 +18.2 -42.5 +15.7 -9.0 -18.2 -13.3 +4.4 +33.8 -25.9 +24.4 -16.1 -48.0 +28.1 +11.7
Steps
(reduced) 		71
(26) 		104
(14) 		126
(36) 		143
(8) 		156
(21) 		167
(32) 		176
(41) 		184
(4) 		191
(11) 		198
(18) 		204
(24) 		209
(29) 		214
(34) 		219
(39) 		223
(43) 		227
(2) 		231
(6) 		234
(9) 		238
(13) 		241
(16) 		244
(19) 		247
(22) 		250
(25) 		253
(28) 		255
(30) 		258
(33) 		260
(35) 		262
(37) 		265
(40) 		267
(42)
Approximation of prime harmonics in 46edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97 101 103 107 109 113
Error Absolute (¢) +0.0 +2.4 +5.0 -3.6 -3.5 -5.7 -0.6 -10.6 -2.2 -12.2 +2.8 +9.5 -11.7 +10.2 +12.8 -12.6 +10.4 +4.9 -1.0 +2.9 +7.0 +0.7 -6.6 +3.0 +10.5 -7.2 +11.0 -2.8 -8.8 +7.1
Relative (%) +0.0 +9.2 +19.1 -13.8 -13.4 -22.0 -2.3 -40.5 -8.4 -46.7 +10.7 +36.5 -44.7 +39.2 +48.9 -48.4 +39.8 +18.6 -4.0 +11.2 +26.8 +2.6 -25.2 +11.6 +40.4 -27.8 +42.1 -10.7 -33.6 +27.2
Steps
(reduced) 		46
(0) 		73
(27) 		107
(15) 		129
(37) 		159
(21) 		170
(32) 		188
(4) 		195
(11) 		208
(24) 		223
(39) 		228
(44) 		240
(10) 		246
(16) 		250
(20) 		256
(26) 		263
(33) 		271
(41) 		273
(43) 		279
(3) 		283
(7) 		285
(9) 		290
(14) 		293
(17) 		298
(22) 		304
(28) 		306
(30) 		308
(32) 		310
(34) 		311
(35) 		314
(38)
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