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{{Harmonics in equal|311|columns=18}}
{{Harmonics in equal|311|start=19|columns=18}}
{{Harmonics in equal|311|start=37|columns=18}}
{{Harmonics in equal|388|columns=18}}
{{Harmonics in equal|388|start=19|columns=18}}
{{Harmonics in equal|388|start=37|columns=18}}
= User:Overthink/Sandbox (size comparison) =
= User:Overthink/Sandbox (size comparison) =
{{Harmonics in equal|10257|columns=18}}
{{Harmonics in equal|10257|columns=18}}

Revision as of 00:20, 20 October 2025

Approximation of prime harmonics in 311edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61
Error Absolute (¢) +0.00 +0.30 -0.46 -0.34 +0.45 +0.63 -0.78 -0.41 +0.66 +0.65 +0.95 -0.54 -0.77 +1.67 -1.84 -1.48 +1.92 -1.77
Relative (%) +0.0 +7.7 -12.0 -8.7 +11.7 +16.3 -20.1 -10.5 +17.2 +16.8 +24.5 -14.0 -19.9 +43.2 -47.7 -38.3 +49.8 -45.9
Steps
(reduced) 		311
(0) 		493
(182) 		722
(100) 		873
(251) 		1076
(143) 		1151
(218) 		1271
(27) 		1321
(77) 		1407
(163) 		1511
(267) 		1541
(297) 		1620
(65) 		1666
(111) 		1688
(133) 		1727
(172) 		1781
(226) 		1830
(275) 		1844
(289)
Approximation of prime harmonics in 311edo
Harmonic 67 71 73 79 83 89 97 101 103 107 109 113 127 131 137 139 149 151
Error Absolute (¢) +1.72 +1.65 -0.14 -1.84 +1.40 +0.18 +1.65 +1.14 +1.92 +1.56 +0.37 -0.29 -1.86 -1.52 -1.88 +0.04 -0.62 -0.56
Relative (%) +44.6 +42.9 -3.5 -47.6 +36.3 +4.7 +42.7 +29.6 +49.8 +40.4 +9.5 -7.6 -48.1 -39.5 -48.8 +0.9 -16.1 -14.4
Steps
(reduced) 		1887
(21) 		1913
(47) 		1925
(59) 		1960
(94) 		1983
(117) 		2014
(148) 		2053
(187) 		2071
(205) 		2080
(214) 		2097
(231) 		2105
(239) 		2121
(255) 		2173
(307) 		2187
(10) 		2207
(30) 		2214
(37) 		2245
(68) 		2251
(74)
Approximation of prime harmonics in 311edo
Harmonic 157 163 167 173 179 181 191 193 197 199 211 223 227 229 233 239 241 251
Error Absolute (¢) +1.44 -1.75 -1.28 -0.65 -1.80 -1.74 +1.62 -0.98 -1.77 +0.04 -1.01 -0.31 -0.22 +0.03 +0.92 -0.65 +0.35 -0.58
Relative (%) +37.3 -45.4 -33.2 -16.9 -46.7 -45.2 +42.0 -25.4 -45.8 +1.0 -26.2 -8.0 -5.7 +0.8 +23.8 -17.0 +9.1 -15.0
Steps
(reduced) 		2269
(92) 		2285
(108) 		2296
(119) 		2312
(135) 		2327
(150) 		2332
(155) 		2357
(180) 		2361
(184) 		2370
(193) 		2375
(198) 		2401
(224) 		2426
(249) 		2434
(257) 		2438
(261) 		2446
(269) 		2457
(280) 		2461
(284) 		2479
(302)
Approximation of prime harmonics in 388edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61
Error Absolute (¢) +0.00 +0.11 +0.28 -0.78 -0.80 +0.71 +0.20 -0.61 -0.44 +0.32 -0.71 -0.83 +0.83 -1.21 -0.56 -1.34 -1.44 -0.39
Relative (%) +0.0 +3.5 +9.2 -25.4 -25.9 +22.9 +6.4 -19.6 -14.2 +10.3 -22.8 -26.8 +27.0 -39.1 -18.0 -43.3 -46.6 -12.6
Steps
(reduced) 		388
(0) 		615
(227) 		901
(125) 		1089
(313) 		1342
(178) 		1436
(272) 		1586
(34) 		1648
(96) 		1755
(203) 		1885
(333) 		1922
(370) 		2021
(81) 		2079
(139) 		2105
(165) 		2155
(215) 		2222
(282) 		2282
(342) 		2301
(361)
Approximation of prime harmonics in 388edo
Harmonic 67 71 73 79 83 89 97 101 103 107 109 113 127 131 137 139 149 151
Error Absolute (¢) +1.11 -0.32 +1.08 +0.41 +1.50 +1.28 +0.72 -1.19 -1.12 +0.96 -0.17 -0.71 +1.21 +0.10 -0.11 -0.46 -0.12 +1.54
Relative (%) +35.7 -10.2 +34.8 +13.3 +48.5 +41.5 +23.4 -38.6 -36.2 +31.1 -5.6 -22.9 +39.0 +3.2 -3.6 -14.9 -3.7 +49.9
Steps
(reduced) 		2354
(26) 		2386
(58) 		2402
(74) 		2446
(118) 		2474
(146) 		2513
(185) 		2561
(233) 		2583
(255) 		2594
(266) 		2616
(288) 		2626
(298) 		2646
(318) 		2712
(384) 		2729
(13) 		2754
(38) 		2762
(46) 		2801
(85) 		2809
(93)
Approximation of prime harmonics in 388edo
Harmonic 157 163 167 173 179 181 191 193 197 199 211 223 227 229 233 239 241 251
Error Absolute (¢) -0.97 -0.95 +0.38 +1.13 +0.86 +0.18 -0.13 +0.39 -1.10 -0.03 +0.66 +0.78 +0.93 +1.20 -0.94 +1.43 -0.62 +0.13
Relative (%) -31.3 -30.7 +12.3 +36.4 +27.9 +6.0 -4.2 +12.7 -35.6 -1.0 +21.4 +25.1 +29.9 +38.9 -30.4 +46.4 -20.1 +4.1
Steps
(reduced) 		2830
(114) 		2851
(135) 		2865
(149) 		2885
(169) 		2904
(188) 		2910
(194) 		2940
(224) 		2946
(230) 		2957
(241) 		2963
(247) 		2996
(280) 		3027
(311) 		3037
(321) 		3042
(326) 		3051
(335) 		3066
(350) 		3070
(354) 		3093
(377)

User:Overthink/Sandbox (size comparison)

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

← 3731edo 3732edo 3733edo →
Prime factorization 22 × 3 × 311
Step size 0.321543 ¢ 
Fifth 2183\3732 (701.929 ¢)
Semitones (A1:m2) 353:281 (113.5 ¢ : 90.35 ¢)
Consistency limit 9
Distinct consistency limit 9
Approximation of odd harmonics in 3732edo
Harmonic 3 5 7 9 11 13 15 17 19 21 23
Error Absolute (¢) -0.026 -0.140 -0.016 -0.051 +0.129 -0.013 +0.156 -0.132 -0.085 -0.041 +0.021
Relative (%) -8.0 -43.6 -4.9 -16.0 +40.1 -4.1 +48.4 -41.1 -26.5 -12.9 +6.7
Steps
(reduced) 		5915
(2183) 		8665
(1201) 		10477
(3013) 		11830
(634) 		12911
(1715) 		13810
(2614) 		14581
(3385) 		15254
(326) 		15853
(925) 		16392
(1464) 		16882
(1954)
Approximation of prime harmonics in 9999edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31 37 41 43 47
Error Absolute (¢) +0.0000 -0.0048 +0.0049 +0.0310 +0.0172 +0.0364 +0.0551 -0.0033 -0.0115 +0.0058 -0.0011 -0.0389 -0.0195 -0.0266 -0.0401
Relative (%) +0.0 -4.0 +4.1 +25.8 +14.3 +30.3 +45.9 -2.7 -9.6 +4.8 -0.9 -32.4 -16.2 -22.1 -33.4
Steps
(reduced) 		9999
(0) 		15848
(5849) 		23217
(3219) 		28071
(8073) 		34591
(4594) 		37001
(7004) 		40871
(875) 		42475
(2479) 		45231
(5235) 		48575
(8579) 		49537
(9541) 		52089
(2094) 		53570
(3575) 		54257
(4262) 		55540
(5545)
Approximation of prime harmonics in 10158edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) +0.0000 -0.0058 -0.0172 -0.0131 +0.0111 -0.0079 -0.0529 -0.0529 -0.0404 -0.0438 +0.0324
Relative (%) +0.0 -4.9 -14.6 -11.1 +9.4 -6.7 -44.8 -44.8 -34.2 -37.1 +27.4
Steps
(reduced) 		10158
(0) 		16100
(5942) 		23586
(3270) 		28517
(8201) 		35141
(4667) 		37589
(7115) 		41520
(888) 		43150
(2518) 		45950
(5318) 		49347
(8715) 		50325
(9693)
Approximation of prime harmonics in 7464edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31 37 41 43 47
Error Absolute (¢) +0.0000 -0.0257 +0.0207 -0.0156 -0.0318 -0.0132 +0.0285 +0.0754 +0.0215 +0.0048 -0.0195 -0.0579 +0.0373 +0.0579 -0.0725
Relative (%) +0.0 -16.0 +12.9 -9.7 -19.8 -8.2 +17.7 +46.9 +13.4 +3.0 -12.1 -36.0 +23.2 +36.0 -45.1
Steps
(reduced) 		7464
(0) 		11830
(4366) 		17331
(2403) 		20954
(6026) 		25821
(3429) 		27620
(5228) 		30509
(653) 		31707
(1851) 		33764
(3908) 		36260
(6404) 		36978
(7122) 		38883
(1563) 		39989
(2669) 		40502
(3182) 		41459
(4139)
← 4047edo 4048edo 4049edo →
Prime factorization 24 × 11 × 23
Step size 0.296443 ¢ 
Fifth 2368\4048 (701.976 ¢) (→ 148\253)
Semitones (A1:m2) 384:304 (113.8 ¢ : 90.12 ¢)
Consistency limit 11
Distinct consistency limit 11
Approximation of prime harmonics in 4048edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) +0.000 +0.021 -0.049 -0.051 +0.065 -0.113 -0.015 +0.115 -0.112 -0.032 +0.123
Relative (%) +0.0 +7.2 -16.5 -17.3 +22.1 -38.0 -5.0 +38.9 -37.9 -10.7 +41.3
Steps
(reduced) 		4048
(0) 		6416
(2368) 		9399
(1303) 		11364
(3268) 		14004
(1860) 		14979
(2835) 		16546
(354) 		17196
(1004) 		18311
(2119) 		19665
(3473) 		20055
(3863)
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