User:Overthink/Sandbox

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Revision as of 05:56, 30 September 2025 by Overthink (talk | contribs) (test)
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Approximation of prime harmonics in 10257edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61
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 +0.0500
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 +42.7
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) 		60832
(9547)
Approximation of odd harmonics in 10195edo
Harmonic 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35
Error Absolute (¢) +0.0362 -0.0067 +0.0020 -0.0454 +0.0111 +0.0020 +0.0295 +0.0372 +0.0446 +0.0381 +0.0336 -0.0134 -0.0092 -0.0137 -0.0037 +0.0473 -0.0048
Relative (%) +30.7 -5.7 +1.7 -38.5 +9.5 +1.7 +25.0 +31.6 +37.9 +32.4 +28.6 -11.4 -7.8 -11.6 -3.1 +40.2 -4.0
Steps
(reduced) 		16159
(5964) 		23672
(3282) 		28621
(8231) 		32317
(1732) 		35269
(4684) 		37726
(7141) 		39831
(9246) 		41672
(892) 		43308
(2528) 		44780
(4000) 		46118
(5338) 		47344
(6564) 		48476
(7696) 		49527
(8747) 		50508
(9728) 		51428
(453) 		52293
(1318)

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)

--Overthink (talk) 04:41, 29 September 2025 (UTC)

How

far

can

this

even
go
= ? =

oh this is the limit

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