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User:Aura/Archangelic EDO checks

< User:Aura
Revision as of 14:54, 22 December 2022 by Aura (talk | contribs) (Created page with "This page is dedicated to collecting data on EDOs tempering out the Archangelic comma. {{Harmonics in equal|190537}} {{Harmonics in equal|381074}} {{Harmonics in equal|...")
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This page is dedicated to collecting data on EDOs tempering out the Archangelic comma.


Approximation of prime harmonics in 190537edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) +0.00000 +0.00000 -0.00134 +0.00010 +0.00175 +0.00200 +0.00058 -0.00230 +0.00048 -0.00079 +0.00187
Relative (%) +0.0 +0.0 -21.3 +1.5 +27.8 +31.7 +9.3 -36.5 +7.6 -12.5 +29.8
Steps
(reduced) 		190537
(0) 		301994
(111457) 		442413
(61339) 		534905
(153831) 		659150
(87539) 		705071
(133460) 		778813
(16665) 		809387
(47239) 		861906
(99758) 		925625
(163477) 		943958
(181810)


Approximation of prime harmonics in 381074edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) +0.00000 +0.00000 -0.00134 +0.00010 -0.00140 -0.00115 +0.00058 +0.00085 +0.00048 -0.00079 -0.00127
Relative (%) +0.0 +0.0 -42.7 +3.0 -44.5 -36.5 +18.5 +27.1 +15.1 -25.0 -40.5
Steps
(reduced) 		381074
(0) 		603988
(222914) 		884826
(122678) 		1069810
(307662) 		1318299
(175077) 		1410141
(266919) 		1557626
(33330) 		1618775
(94479) 		1723812
(199516) 		1851250
(326954) 		1887915
(363619)


Approximation of prime harmonics in 571611edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) +0.000000 +0.000000 +0.000755 +0.000096 -0.000351 -0.000100 +0.000583 -0.000197 +0.000476 -0.000786 -0.000225
Relative (%) +0.0 +0.0 +36.0 +4.6 -16.7 -4.8 +27.8 -9.4 +22.7 -37.5 -10.7
Steps
(reduced) 		571611
(0) 		905982
(334371) 		1327240
(184018) 		1604715
(461493) 		1977449
(262616) 		2115212
(400379) 		2336439
(49995) 		2428162
(141718) 		2585718
(299274) 		2776875
(490431) 		2831873
(545429)


Approximation of prime harmonics in 762148edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) +0.000000 +0.000000 +0.000230 +0.000096 +0.000174 +0.000425 +0.000583 -0.000722 +0.000476 -0.000786 +0.000300
Relative (%) +0.0 +0.0 +14.6 +6.1 +11.1 +27.0 +37.0 -45.9 +30.2 -49.9 +19.0
Steps
(reduced) 		762148
(0) 		1207976
(445828) 		1769653
(245357) 		2139620
(615324) 		2636599
(350155) 		2820283
(533839) 		3115252
(66660) 		3237549
(188957) 		3447624
(399032) 		3702500
(653908) 		3775831
(727239)


Approximation of prime harmonics in 952685edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) +0.000000 +0.000000 -0.000084 +0.000096 +0.000489 -0.000520 +0.000583 +0.000223 +0.000476 +0.000473 +0.000615
Relative (%) +0.0 +0.0 -6.7 +7.6 +38.8 -41.3 +46.3 +17.7 +37.8 +37.6 +48.8
Steps
(reduced) 		952685
(0) 		1509970
(557285) 		2212066
(306696) 		2674525
(769155) 		3295749
(437694) 		3525353
(667298) 		3894065
(83325) 		4046937
(236197) 		4309530
(498790) 		4628126
(817386) 		4719789
(909049)


Approximation of prime harmonics in 1143222edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) +0.000000 +0.000000 -0.000294 +0.000096 -0.000351 -0.000100 -0.000466 -0.000197 +0.000476 +0.000263 -0.000225
Relative (%) +0.0 +0.0 -28.0 +9.1 -33.4 -9.5 -44.4 -18.8 +45.3 +25.1 -21.4
Steps
(reduced) 		1143222
(0) 		1811964
(668742) 		2654479
(368035) 		3209430
(922986) 		3954898
(525232) 		4230424
(800758) 		4672877
(99989) 		4856324
(283436) 		5171436
(598548) 		5553751
(980863) 		5663746
(1090858)


Approximation of prime harmonics in 1333759edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) +0.000000 +0.000000 -0.000444 +0.000096 -0.000051 +0.000200 -0.000316 +0.000403 -0.000424 +0.000113 +0.000075
Relative (%) +0.0 +0.0 -49.4 +10.7 -5.6 +22.2 -35.2 +44.8 -47.1 +12.6 +8.3
Steps
(reduced) 		1333759
(0) 		2113958
(780199) 		3096892
(429374) 		3744335
(1076817) 		4614048
(612771) 		4935495
(934218) 		5451690
(116654) 		5665712
(330676) 		6033341
(698305) 		6479376
(1144340) 		6607704
(1272668)


Approximation of prime harmonics in 1524296edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) +0.000000 +0.000000 +0.000230 +0.000096 +0.000174 -0.000363 -0.000204 +0.000065 -0.000311 +0.000001 +0.000300
Relative (%) +0.0 +0.0 +29.3 +12.2 +22.1 -46.1 -25.9 +8.3 -39.5 +0.1 +38.1
Steps
(reduced) 		1524296
(0) 		2415952
(891656) 		3539306
(490714) 		4279240
(1230648) 		5273198
(700310) 		5640565
(1067677) 		6230503
(133319) 		6475099
(377915) 		6895247
(798063) 		7405001
(1307817) 		7551662
(1454478)


Approximation of prime harmonics in 1714833edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) +0.000000 +0.000000 +0.000055 +0.000096 +0.000349 -0.000100 -0.000116 -0.000197 -0.000224 -0.000087 -0.000225
Relative (%) +0.0 +0.0 +7.9 +13.7 +49.9 -14.3 -16.6 -28.2 -32.0 -12.4 -32.2
Steps
(reduced) 		1714833
(0) 		2717946
(1003113) 		3981719
(552053) 		4814145
(1384479) 		5932348
(787849) 		6345636
(1201137) 		7009316
(149984) 		7284486
(425154) 		7757153
(897821) 		8330626
(1471294) 		8495619
(1636287)


Approximation of prime harmonics in 1905370edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) +0.000000 +0.000000 -0.000084 +0.000096 -0.000141 +0.000110 -0.000047 +0.000223 -0.000154 -0.000157 -0.000015
Relative (%) +0.0 +0.0 -13.4 +15.2 -22.3 +17.4 -7.4 +35.4 -24.4 -24.9 -2.4
Steps
(reduced) 		1905370
(0) 		3019940
(1114570) 		4424132
(613392) 		5349050
(1538310) 		6591497
(875387) 		7050707
(1334597) 		7788129
(166649) 		8093874
(472394) 		8619059
(997579) 		9256251
(1634771) 		9439577
(1818097)


Approximation of prime harmonics in 2095907edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) +0.000000 +0.000000 -0.000199 +0.000096 +0.000031 +0.000282 +0.000011 -0.000006 -0.000097 -0.000214 +0.000157
Relative (%) +0.0 +0.0 -34.8 +16.7 +5.4 +49.2 +1.9 -1.1 -16.9 -37.4 +27.4
Steps
(reduced) 		2095907
(0) 		3321934
(1226027) 		4866545
(674731) 		5883955
(1692141) 		7250647
(962926) 		7755778
(1468057) 		8566942
(183314) 		8903261
(519633) 		9480965
(1097337) 		10181876
(1798248) 		10383535
(1999907)


Approximation of prime harmonics in 2286444edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) +0.000000 +0.000000 +0.000230 +0.000096 +0.000174 -0.000100 +0.000058 -0.000197 -0.000049 -0.000262 -0.000225
Relative (%) +0.0 +0.0 +43.9 +18.3 +33.2 -19.1 +11.1 -37.6 -9.3 -49.8 -42.9
Steps
(reduced) 		2286444
(0) 		3623928
(1337484) 		5308959
(736071) 		6418860
(1845972) 		7909797
(1050465) 		8460848
(1601516) 		9345755
(199979) 		9712648
(566872) 		10342871
(1197095) 		11107501
(1961725) 		11327492
(2181716)


Approximation of prime harmonics in 2476981edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) +0.000000 +0.000000 +0.000109 +0.000096 -0.000189 +0.000061 +0.000099 +0.000126 -0.000008 +0.000183 -0.000064
Relative (%) +0.0 +0.0 +22.6 +19.8 -39.0 +12.7 +20.4 +26.0 -1.7 +37.7 -13.1
Steps
(reduced) 		2476981
(0) 		3925922
(1448941) 		5751372
(797410) 		6953765
(1999803) 		8568946
(1138003) 		9165919
(1734976) 		10124568
(216644) 		10522036
(614112) 		11204777
(1296853) 		12033127
(2125203) 		12271450
(2363526)


Approximation of prime harmonics in 2667518edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) +0.000000 +0.000000 +0.000005 +0.000096 -0.000051 +0.000200 +0.000133 -0.000047 +0.000026 +0.000113 +0.000075
Relative (%) +0.0 +0.0 +1.2 +21.3 -11.2 +44.4 +29.7 -10.5 +5.8 +25.2 +16.7
Steps
(reduced) 		2667518
(0) 		4227916
(1560398) 		6193785
(858749) 		7488670
(2153634) 		9228096
(1225542) 		9870990
(1868436) 		10903381
(233309) 		11331423
(661351) 		12066683
(1396611) 		12958752
(2288680) 		13215408
(2545336)


Approximation of prime harmonics in 2858055edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) +0.000000 +0.000000 -0.000084 +0.000096 +0.000069 -0.000100 +0.000163 -0.000197 +0.000056 +0.000053 +0.000195
Relative (%) +0.0 +0.0 -20.1 +22.8 +16.5 -23.9 +38.9 -46.9 +13.4 +12.7 +46.4
Steps
(reduced) 		2858055
(0) 		4529910
(1671855) 		6636198
(920088) 		8023575
(2307465) 		9887246
(1313081) 		10576060
(2001895) 		11682194
(249974) 		12140810
(708590) 		12928589
(1496369) 		13884377
(2452157) 		14159366
(2727146)


Approximation of prime harmonics in 3048592edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) +0.000000 +0.000000 -0.000163 +0.000096 +0.000174 +0.000031 +0.000190 +0.000065 +0.000082 +0.000001 -0.000094
Relative (%) +0.0 +0.0 -41.5 +24.3 +44.3 +7.9 +48.2 +16.6 +20.9 +0.2 -23.8
Steps
(reduced) 		3048592
(0) 		4831904
(1783312) 		7078611
(981427) 		8558480
(2461296) 		10546396
(1400620) 		11281131
(2135355) 		12461007
(266639) 		12950198
(755830) 		13790495
(1596127) 		14810002
(2615634) 		15103323
(2908955)


Approximation of prime harmonics in 3239129edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) +0.000000 +0.000000 +0.000138 +0.000096 -0.000104 +0.000147 -0.000158 -0.000074 +0.000106 -0.000045 +0.000022
Relative (%) +0.0 +0.0 +37.2 +25.9 -27.9 +39.6 -42.6 -19.9 +28.5 -12.3 +5.9
Steps
(reduced) 		3239129
(0) 		5133898
(1894769) 		7521025
(1042767) 		9093385
(2615127) 		11205545
(1488158) 		11986202
(2268815) 		13239819
(283303) 		13759585
(803069) 		14652401
(1695885) 		15735627
(2779111) 		16047281
(3090765)


Approximation of prime harmonics in 3429666edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) +0.000000 +0.000000 +0.000055 +0.000096 -0.000001 -0.000100 -0.000116 +0.000153 +0.000126 -0.000087 +0.000125
Relative (%) +0.0 +0.0 +15.9 +27.4 -0.2 -28.6 -33.3 +43.7 +36.0 -24.8 +35.7
Steps
(reduced) 		3429666
(0) 		5435892
(2006226) 		7963438
(1104106) 		9628290
(2768958) 		11864695
(1575697) 		12691272
(2402274) 		14018632
(299968) 		14568973
(850309) 		15514307
(1795643) 		16661252
(2942588) 		16991239
(3272575)


Approximation of prime harmonics in 3620203edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) +0.000000 +0.000000 -0.000018 +0.000096 +0.000091 +0.000010 -0.000080 +0.000024 +0.000145 -0.000123 -0.000115
Relative (%) +0.0 +0.0 -5.5 +28.9 +27.6 +3.1 -24.0 +7.2 +43.6 -37.3 -34.5
Steps
(reduced) 		3620203
(0) 		5737886
(2117683) 		8405851
(1165445) 		10163195
(2922789) 		12523845
(1663236) 		13396343
(2535734) 		14797445
(316633) 		15378360
(897548) 		16376213
(1895401) 		17586877
(3106065) 		17935196
(3454384)


Approximation of prime harmonics in 3810740edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) +0.000000 +0.000000 -0.000084 +0.000096 -0.000141 +0.000110 -0.000047 -0.000092 -0.000154 -0.000157 -0.000015
Relative (%) +0.0 +0.0 -26.8 +30.4 -44.6 +34.8 -14.8 -29.3 -48.8 -49.7 -4.8
Steps
(reduced) 		3810740
(0) 		6039880
(2229140) 		8848264
(1226784) 		10698100
(3076620) 		13182994
(1750774) 		14101414
(2669194) 		15576258
(333298) 		16187747
(944787) 		17238118
(1995158) 		18512502
(3269542) 		18879154
(3636194)


Approximation of prime harmonics in 4001277edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) +0.000000 +0.000000 -0.000144 +0.000096 -0.000051 -0.000100 -0.000017 +0.000103 -0.000124 +0.000113 +0.000075
Relative (%) +0.0 +0.0 -48.2 +32.0 -16.9 -33.4 -5.5 +34.3 -41.3 +37.8 +25.0
Steps
(reduced) 		4001277
(0) 		6341874
(2340597) 		9290677
(1288123) 		11233005
(3230451) 		13842144
(1838313) 		14806484
(2802653) 		16355071
(349963) 		16997135
(992027) 		18100024
(2094916) 		19438128
(3433020) 		19823112
(3818004)


Approximation of prime harmonics in 4191814edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) +0.000000 +0.000000 +0.000087 +0.000096 +0.000031 -0.000005 +0.000011 -0.000006 -0.000097 +0.000072 -0.000130
Relative (%) +0.0 +0.0 +30.5 +33.5 +10.9 -1.7 +3.8 -2.2 -33.7 +25.3 -45.3
Steps
(reduced) 		4191814
(0) 		6643868
(2452054) 		9733091
(1349463) 		11767910
(3384282) 		14501294
(1925852) 		15511555
(2936113) 		17133884
(366628) 		17806522
(1039266) 		18961930
(2194674) 		20363753
(3596497) 		20767069
(3999813)


Approximation of prime harmonics in 4382351edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) +0.000000 +0.000000 +0.000025 +0.000096 +0.000106 +0.000082 +0.000036 -0.000106 -0.000072 +0.000035 -0.000042
Relative (%) +0.0 +0.0 +9.1 +35.0 +38.7 +30.1 +13.0 -38.6 -26.2 +12.8 -15.5
Steps
(reduced) 		4382351
(0) 		6945862
(2563511) 		10175504
(1410802) 		12302815
(3538113) 		15160444
(2013391) 		16216626
(3069573) 		17912697
(383293) 		18615909
(1086505) 		19823836
(2294432) 		21289378
(3759974) 		21711027
(4181623)


Approximation of prime harmonics in 4572888edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) +0.000000 +0.000000 -0.000032 +0.000096 -0.000088 -0.000100 +0.000058 +0.000065 -0.000049 +0.000001 +0.000037
Relative (%) +0.0 +0.0 -12.2 +36.5 -33.6 -38.2 +22.3 +24.9 -18.6 +0.3 +14.3
Steps
(reduced) 		4572888
(0) 		7247856
(2674968) 		10617917
(1472141) 		12837720
(3691944) 		15819593
(2100929) 		16921696
(3203032) 		18691510
(399958) 		19425297
(1133745) 		20685742
(2394190) 		22215003
(3923451) 		22654985
(4363433)


Approximation of prime harmonics in 4763425edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) +0.000000 +0.000000 -0.000084 +0.000096 -0.000015 -0.000016 +0.000079 -0.000029 -0.000028 -0.000031 +0.000111
Relative (%) +0.0 +0.0 -33.5 +38.0 -5.8 -6.4 +31.5 -11.6 -11.1 -12.2 +44.0
Steps
(reduced) 		4763425
(0) 		7549850
(2786425) 		11060330
(1533480) 		13372625
(3845775) 		16478743
(2188468) 		17626767
(3336492) 		19470323
(416623) 		20234684
(1180984) 		21547648
(2493948) 		23140628
(4086928) 		23598943
(4545243)


Approximation of prime harmonics in 4953962edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) +0.000000 +0.000000 +0.000109 +0.000096 +0.000053 +0.000061 +0.000099 -0.000116 -0.000008 -0.000060 -0.000064
Relative (%) +0.0 +0.0 +45.1 +39.6 +22.0 +25.3 +40.8 -48.0 -3.5 -24.7 -26.2
Steps
(reduced) 		4953962
(0) 		7851844
(2897882) 		11502744
(1594820) 		13907530
(3999606) 		17137893
(2276007) 		18331838
(3469952) 		20249136
(433288) 		21044071
(1228223) 		22409554
(2593706) 		24066253
(4250405) 		24542900
(4727052)


Approximation of prime harmonics in 5144499edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) +0.000000 +0.000000 +0.000055 +0.000096 +0.000116 -0.000100 -0.000116 +0.000036 +0.000009 -0.000087 +0.000008
Relative (%) +0.0 +0.0 +23.8 +41.1 +49.7 -43.0 -49.9 +15.5 +4.1 -37.1 +3.5
Steps
(reduced) 		5144499
(0) 		8153838
(3009339) 		11945157
(1656159) 		14442435
(4153437) 		17797043
(2363546) 		19036908
(3603411) 		21027948
(449952) 		21853459
(1275463) 		23271460
(2693464) 		24991878
(4413882) 		25486858
(4908862)


Approximation of prime harmonics in 5335036edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) +0.0000000 +0.0000000 +0.0000055 +0.0000958 -0.0000506 -0.0000252 -0.0000915 -0.0000471 +0.0000261 -0.0001116 +0.0000749
Relative (%) +0.0 +0.0 +2.4 +42.6 -22.5 -11.2 -40.7 -21.0 +11.6 -49.6 +33.3
Steps
(reduced) 		5335036
(0) 		8455832
(3120796) 		12387570
(1717498) 		14977340
(4307268) 		18456192
(2451084) 		19741979
(3736871) 		21806761
(466617) 		22662846
(1322702) 		24133366
(2793222) 		25917503
(4577359) 		26430816
(5090672)
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