User:Overthink/Sandbox: Difference between revisions

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{{Harmonics in equal|311|columns=50}}
{{Harmonics in equal|10257|columns=17}}
{{Harmonics in equal|10257|columns=20}}
Compressed 49edo:
{{Harmonics in equal|138|7|columns=22}}
{{Harmonics in equal|127|6|columns=22}}
{{Harmonics in equal|114|5|columns=22}}

Revision as of 22:06, 22 September 2025

Approximation of prime harmonics in 10257edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59
Error Absolute (¢) +0.0000 +0.0046 -0.0019 -0.0046 -0.0456 -0.0480 -0.0124 +0.0009 -0.0205 -0.0364 -0.0224 -0.0425 -0.0481 -0.0231 -0.0489 -0.0328 -0.0316
Relative (%) +0.0 +4.0 -1.6 -3.9 -39.0 -41.0 -10.6 +0.7 -17.5 -31.1 -19.2 -36.3 -41.1 -19.8 -41.8 -28.0 -27.0
Steps
(reduced)
10257
(0)
16257
(6000)
23816
(3302)
28795
(8281)
35483
(4712)
37955
(7184)
41925
(897)
43571
(2543)
46398
(5370)
49828
(8800)
50815
(9787)
53433
(2148)
54952
(3667)
55657
(4372)
56973
(5688)
58751
(7466)
60338
(9053)

Compressed 49edo:

Approximation of harmonics in 138ed7
Harmonic 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
Error Absolute (¢) -3.8 +2.2 -7.6 -3.4 -1.7 +0.0 -11.5 +4.3 -7.2 -1.3 -5.5 +2.4 -3.8 -1.2 +9.1 +1.8 +0.5 +4.5 -11.0 +2.2 -5.1 -8.9
Relative (%) -15.7 +8.9 -31.3 -13.8 -6.8 +0.0 -47.0 +17.7 -29.5 -5.4 -22.5 +9.9 -15.7 -4.9 +37.4 +7.4 +2.1 +18.6 -45.1 +8.9 -21.0 -36.3
Steps
(reduced)
49
(49)
78
(78)
98
(98)
114
(114)
127
(127)
138
(0)
147
(9)
156
(18)
163
(25)
170
(32)
176
(38)
182
(44)
187
(49)
192
(54)
197
(59)
201
(63)
205
(67)
209
(71)
212
(74)
216
(78)
219
(81)
222
(84)
Approximation of harmonics in 127ed6
Harmonic 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
Error Absolute (¢) -3.2 +3.2 -6.4 -1.9 +0.0 +1.8 -9.5 +6.4 -5.1 +0.9 -3.2 +4.8 -1.4 +1.3 +11.7 +4.4 +3.2 +7.3 -8.2 +5.0 -2.3 -6.0
Relative (%) -13.0 +13.0 -26.1 -7.7 +0.0 +7.4 -39.1 +26.1 -20.7 +3.7 -13.0 +19.6 -5.7 +5.3 +47.9 +18.2 +13.0 +29.8 -33.8 +20.4 -9.3 -24.4
Steps
(reduced)
49
(49)
78
(78)
98
(98)
114
(114)
127
(0)
138
(11)
147
(20)
156
(29)
163
(36)
170
(43)
176
(49)
182
(55)
187
(60)
192
(65)
197
(70)
201
(74)
205
(78)
209
(82)
212
(85)
216
(89)
219
(92)
222
(95)
Approximation of harmonics in 114ed5
Harmonic 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
Error Absolute (¢) -2.4 +4.5 -4.7 +0.0 +2.1 +4.1 -7.1 +8.9 -2.4 +3.7 -0.3 +7.8 +1.7 +4.5 -9.5 +7.8 +6.6 +10.7 -4.7 +8.6 +1.3 -2.3
Relative (%) -9.7 +18.3 -19.4 +0.0 +8.6 +16.7 -29.1 +36.6 -9.7 +15.2 -1.1 +31.9 +7.0 +18.3 -38.9 +31.7 +26.9 +43.9 -19.4 +35.0 +5.5 -9.4
Steps
(reduced)
49
(49)
78
(78)
98
(98)
114
(0)
127
(13)
138
(24)
147
(33)
156
(42)
163
(49)
170
(56)
176
(62)
182
(68)
187
(73)
192
(78)
196
(82)
201
(87)
205
(91)
209
(95)
212
(98)
216
(102)
219
(105)
222
(108)