User:Aura/Archangelic EDO checks: Difference between revisions

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{{Infobox ET|2667518edo}}
{{Infobox ET|2667518edo}}
{{Harmonics in equal|2667518}}
{{Harmonics in equal|2667518}}
== 15X ==
{{Infobox ET|2858055edo}}
{{Harmonics in equal|2858055}}
== 16X ==
{{Infobox ET|3048592edo}}
{{Harmonics in equal|3048592}}
== 17X ==
{{Infobox ET|3239129edo}}
{{Harmonics in equal|3239129}}
== 18X ==
{{Infobox ET|3429666edo}}
{{Harmonics in equal|3429666}}
== 19X ==
{{Infobox ET|3620203edo}}
{{Harmonics in equal|3620203}}
== 20X ==
{{Infobox ET|3810740edo}}
{{Harmonics in equal|3810740}}
== 21X ==
{{Infobox ET|4001277edo}}
{{Harmonics in equal|4001277}}
== 22X ==
{{Infobox ET|4191814edo}}
{{Harmonics in equal|4191814}}
== 23X ==
{{Infobox ET|4382351edo}}
{{Harmonics in equal|4382351}}
== 24X ==
{{Infobox ET|4572888edo}}
{{Harmonics in equal|4572888}}
== 25X ==
{{Infobox ET|4763425edo}}
{{Harmonics in equal|4763425}}
== 26X ==
{{Infobox ET|4953962edo}}
{{Harmonics in equal|4953962}}
== 27X ==
{{Infobox ET|5144499edo}}
{{Harmonics in equal|5144499}}
== 28X ==
{{Infobox ET|5335036edo}}
{{Harmonics in equal|5335036}}

Revision as of 16:48, 22 December 2022

This page is dedicated to collecting data on EDOs tempering out the Archangelic comma.

1X

← 190536edo 190537edo 190538edo →
Prime factorization 190537 (prime)
Step size 0.00629799 ¢ 
Fifth 111457\190537 (701.955 ¢)
(convergent)
Semitones (A1:m2) 18051:14326 (113.7 ¢ : 90.22 ¢)
Consistency limit 11
Distinct consistency limit 11
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)

2X

← 381073edo 381074edo 381075edo →
Prime factorization 2 × 190537
Step size 0.00314899 ¢ 
Fifth 222914\381074 (701.955 ¢) (→ 111457\190537)
Semitones (A1:m2) 36102:28652 (113.7 ¢ : 90.22 ¢)
Consistency limit 15
Distinct consistency limit 15
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)

3X

← 571610edo 571611edo 571612edo →
Prime factorization 3 × 190537
Step size 0.00209933 ¢ 
Fifth 334371\571611 (701.955 ¢) (→ 111457\190537)
Semitones (A1:m2) 54153:42978 (113.7 ¢ : 90.22 ¢)
Consistency limit 9
Distinct consistency limit 9
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)

4X

← 762147edo 762148edo 762149edo →
Prime factorization 22 × 190537
Step size 0.0015745 ¢ 
Fifth 445828\762148 (701.955 ¢) (→ 111457\190537)
Semitones (A1:m2) 72204:57304 (113.7 ¢ : 90.22 ¢)
Consistency limit 17
Distinct consistency limit 17
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)

5X

← 952684edo 952685edo 952686edo →
Prime factorization 5 × 190537
Step size 0.0012596 ¢ 
Fifth 557285\952685 (701.955 ¢) (→ 111457\190537)
Semitones (A1:m2) 90255:71630 (113.7 ¢ : 90.22 ¢)
Consistency limit 11
Distinct consistency limit 11
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)

6X

← 1143221edo 1143222edo 1143223edo →
Prime factorization 2 × 3 × 190537
Step size 0.00104966 ¢ 
Fifth 668742\1143222 (701.955 ¢) (→ 111457\190537)
Semitones (A1:m2) 108306:85956 (113.7 ¢ : 90.22 ¢)
Consistency limit 15
Distinct consistency limit 15
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)

7X

← 1333758edo 1333759edo 1333760edo →
Prime factorization 7 × 190537
Step size 0.000899713 ¢ 
Fifth 780199\1333759 (701.955 ¢) (→ 111457\190537)
Semitones (A1:m2) 126357:100282 (113.7 ¢ : 90.22 ¢)
Consistency limit 5
Distinct consistency limit 5
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)

8X

← 1524295edo 1524296edo 1524297edo →
Prime factorization 23 × 190537
Step size 0.000787249 ¢ 
Fifth 891656\1524296 (701.955 ¢) (→ 111457\190537)
Semitones (A1:m2) 144408:114608 (113.7 ¢ : 90.22 ¢)
Consistency limit 11
Distinct consistency limit 11
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)

9X

← 1714832edo 1714833edo 1714834edo →
Prime factorization 32 × 190537
Step size 0.000699777 ¢ 
Fifth 1003113\1714833 (701.955 ¢) (→ 111457\190537)
Semitones (A1:m2) 162459:128934 (113.7 ¢ : 90.22 ¢)
Consistency limit 11
Distinct consistency limit 11
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)

10X

← 1905369edo 1905370edo 1905371edo →
Prime factorization 2 × 5 × 190537
Step size 0.000629799 ¢ 
Fifth 1114570\1905370 (701.955 ¢) (→ 111457\190537)
Semitones (A1:m2) 180510:143260 (113.7 ¢ : 90.22 ¢)
Consistency limit 17
Distinct consistency limit 17
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)

11X

← 2095906edo 2095907edo 2095908edo →
Prime factorization 11 × 190537
Step size 0.000572544 ¢ 
Fifth 1226027\2095907 (701.955 ¢) (→ 111457\190537)
Semitones (A1:m2) 198561:157586 (113.7 ¢ : 90.22 ¢)
Consistency limit 5
Distinct consistency limit 5
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)

12X

← 2286443edo 2286444edo 2286445edo →
Prime factorization 22 × 3 × 190537
Step size 0.000524832 ¢ 
Fifth 1337484\2286444 (701.955 ¢) (→ 111457\190537)
Semitones (A1:m2) 216612:171912 (113.7 ¢ : 90.22 ¢)
Consistency limit 11
Distinct consistency limit 11
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)

13X

← 2476980edo 2476981edo 2476982edo →
Prime factorization 13 × 190537
Step size 0.000484461 ¢ 
Fifth 1448941\2476981 (701.955 ¢) (→ 111457\190537)
Semitones (A1:m2) 234663:186238 (113.7 ¢ : 90.22 ¢)
Consistency limit 9
Distinct consistency limit 9
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)

14X

← 2667517edo 2667518edo 2667519edo →
Prime factorization 2 × 7 × 190537
Step size 0.000449856 ¢ 
Fifth 1560398\2667518 (701.955 ¢) (→ 111457\190537)
Semitones (A1:m2) 252714:200564 (113.7 ¢ : 90.22 ¢)
Consistency limit 11
Distinct consistency limit 11
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)
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