# User:Aura/Archangelic EDO checks

This page is dedicated to collecting data on EDOs tempering out the Archangelic comma. For continuation, see here.

## 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 37
Error absolute (¢) +0.00000 +0.00000 -0.00134 +0.00010 +0.00175 +0.00200 +0.00058 -0.00230 +0.00048 -0.00079 +0.00187 +0.00242
relative (%) +0 +0 -21 +2 +28 +32 +9 -36 +8 -12 +30 +38
Steps
(reduced)
190537
(0)
301994
(111457)
442413
(61339)
534905
(153831)
659150
(87539)
705071
(133460)
778813
(16665)
809387
(47239)
861906
(99758)
925625
(163477)
943958
(181810)
992594
(39909)

## 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 37
Error absolute (¢) +0.00000 +0.00000 -0.00134 +0.00010 -0.00140 -0.00115 +0.00058 +0.00085 +0.00048 -0.00079 -0.00127 -0.00073
relative (%) +0 +0 -43 +3 -44 -37 +19 +27 +15 -25 -40 -23
Steps
(reduced)
381074
(0)
603988
(222914)
884826
(122678)
1069810
(307662)
1318299
(175077)
1410141
(266919)
1557626
(33330)
1618775
(94479)
1723812
(199516)
1851250
(326954)
1887915
(363619)
1985187
(79817)

## 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 37
Error absolute (¢) +0.000000 +0.000000 +0.000755 +0.000096 -0.000351 -0.000100 +0.000583 -0.000197 +0.000476 -0.000786 -0.000225 +0.000320
relative (%) +0 +0 +36 +5 -17 -5 +28 -9 +23 -37 -11 +15
Steps
(reduced)
571611
(0)
905982
(334371)
1327240
(184018)
1604715
(461493)
1977449
(262616)
2115212
(400379)
2336439
(49995)
2428162
(141718)
2585718
(299274)
2776875
(490431)
2831873
(545429)
2977781
(119726)

## 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 37
Error absolute (¢) +0.000000 +0.000000 +0.000230 +0.000096 +0.000174 +0.000425 +0.000583 -0.000722 +0.000476 -0.000786 +0.000300 -0.000730
relative (%) +0 +0 +15 +6 +11 +27 +37 -46 +30 -50 +19 -46
Steps
(reduced)
762148
(0)
1207976
(445828)
1769653
(245357)
2139620
(615324)
2636599
(350155)
2820283
(533839)
3115252
(66660)
3237549
(188957)
3447624
(399032)
3702500
(653908)
3775831
(727239)
3970374
(159634)

## 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 37
Error absolute (¢) +0.000000 +0.000000 -0.000084 +0.000096 +0.000489 -0.000520 +0.000583 +0.000223 +0.000476 +0.000473 +0.000615 -0.000100
relative (%) +0 +0 -7 +8 +39 -41 +46 +18 +38 +38 +49 -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)
4962968
(199543)

## 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 37
Error absolute (¢) +0.000000 +0.000000 -0.000294 +0.000096 -0.000351 -0.000100 -0.000466 -0.000197 +0.000476 +0.000263 -0.000225 +0.000320
relative (%) +0 +0 -28 +9 -33 -10 -44 -19 +45 +25 -21 +30
Steps
(reduced)
1143222
(0)
1811964
(668742)
2654479
(368035)
3209430
(922986)
3954898
(525232)
4230424
(800758)
4672877
(99989)
4856324
(283436)
5171436
(598548)
5553751
(980863)
5663746
(1090858)
5955562
(239452)

## 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 37
Error absolute (¢) +0.000000 +0.000000 -0.000444 +0.000096 -0.000051 +0.000200 -0.000316 +0.000403 -0.000424 +0.000113 +0.000075 -0.000280
relative (%) +0 +0 -49 +11 -6 +22 -35 +45 -47 +13 +8 -31
Steps
(reduced)
1333759
(0)
2113958
(780199)
3096892
(429374)
3744335
(1076817)
4614048
(612771)
4935495
(934218)
5451690
(116654)
5665712
(330676)
6033341
(698305)
6479376
(1144340)
6607704
(1272668)
6948155
(279360)

## 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 37
Error absolute (¢) +0.000000 +0.000000 +0.000230 +0.000096 +0.000174 -0.000363 -0.000204 +0.000065 -0.000311 +0.000001 +0.000300 +0.000057
relative (%) +0 +0 +29 +12 +22 -46 -26 +8 -40 +0 +38 +7
Steps
(reduced)
1524296
(0)
2415952
(891656)
3539306
(490714)
4279240
(1230648)
5273198
(700310)
5640565
(1067677)
6230503
(133319)
6475099
(377915)
6895247
(798063)
7405001
(1307817)
7551662
(1454478)
7940749
(319269)

## 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 37
Error absolute (¢) +0.000000 +0.000000 +0.000055 +0.000096 +0.000349 -0.000100 -0.000116 -0.000197 -0.000224 -0.000087 -0.000225 +0.000320
relative (%) +0 +0 +8 +14 +50 -14 -17 -28 -32 -12 -32 +46
Steps
(reduced)
1714833
(0)
2717946
(1003113)
3981719
(552053)
4814145
(1384479)
5932348
(787849)
6345636
(1201137)
7009316
(149984)
7284486
(425154)
7757153
(897821)
8330626
(1471294)
8495619
(1636287)
8933343
(359178)

## 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 37
Error absolute (¢) +0.000000 +0.000000 -0.000084 +0.000096 -0.000141 +0.000110 -0.000047 +0.000223 -0.000154 -0.000157 -0.000015 -0.000100
relative (%) +0 +0 -13 +15 -22 +17 -7 +35 -24 -25 -2 -16
Steps
(reduced)
1905370
(0)
3019940
(1114570)
4424132
(613392)
5349050
(1538310)
6591497
(875387)
7050707
(1334597)
7788129
(166649)
8093874
(472394)
8619059
(997579)
9256251
(1634771)
9439577
(1818097)
9925936
(399086)

## 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 37
Error absolute (¢) +0.000000 +0.000000 -0.000199 +0.000096 +0.000031 +0.000282 +0.000011 -0.000006 -0.000097 -0.000214 +0.000157 +0.000129
relative (%) +0 +0 -35 +17 +5 +49 +2 -1 -17 -37 +27 +22
Steps
(reduced)
2095907
(0)
3321934
(1226027)
4866545
(674731)
5883955
(1692141)
7250647
(962926)
7755778
(1468057)
8566942
(183314)
8903261
(519633)
9480965
(1097337)
10181876
(1798248)
10383535
(1999907)
10918530
(438995)

## 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 37
Error absolute (¢) +0.000000 +0.000000 +0.000230 +0.000096 +0.000174 -0.000100 +0.000058 -0.000197 -0.000049 -0.000262 -0.000225 -0.000205
relative (%) +0 +0 +44 +18 +33 -19 +11 -38 -9 -50 -43 -39
Steps
(reduced)
2286444
(0)
3623928
(1337484)
5308959
(736071)
6418860
(1845972)
7909797
(1050465)
8460848
(1601516)
9345755
(199979)
9712648
(566872)
10342871
(1197095)
11107501
(1961725)
11327492
(2181716)
11911123
(478903)

## 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 37
Error absolute (¢) +0.000000 +0.000000 +0.000109 +0.000096 -0.000189 +0.000061 +0.000099 +0.000126 -0.000008 +0.000183 -0.000064 -0.000003
relative (%) +0 +0 +23 +20 -39 +13 +20 +26 -2 +38 -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)
12903717
(518812)

## 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 37
Error absolute (¢) +0.000000 +0.000000 +0.000005 +0.000096 -0.000051 +0.000200 +0.000133 -0.000047 +0.000026 +0.000113 +0.000075 +0.000170
relative (%) +0 +0 +1 +21 -11 +44 +30 -10 +6 +25 +17 +38
Steps
(reduced)
2667518
(0)
4227916
(1560398)
6193785
(858749)
7488670
(2153634)
9228096
(1225542)
9870990
(1868436)
10903381
(233309)
11331423
(661351)
12066683
(1396611)
12958752
(2288680)
13215408
(2545336)
13896311
(558721)