User:Contribution/JI intervals approximated by 23edt
Jump to navigation
Jump to search
23edt divides the tritave in 23 equal steps and the octave in 14.511384 equal steps of 82.693696 cents each. Its 31-limit patent val is <15 23 34 41 50 54 59 62 66 70 72|.
| Factorization | Ratio | Value (¢) | FJS | Nearest degree |
Value (¢) | Error (¢) | Error (%) | Consistency | Consistent degree |
Value (¢) | Error (¢) | Error (%) |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
1/1
|
0
|
P1
|
0
|
0
|
0
|
0
|
CONSISTENT
|
0
|
0
|
0
|
0
| |
3-5⋅51⋅72
|
245/243
|
14.190522
|
m25,7,7
|
0
|
0
|
-14.190522
|
-17.160344
|
INCONSISTENT
|
1
|
82.693696
|
68.503173
|
82.839656
|
34⋅7-1⋅11-1
|
81/77
|
87.676155
|
A17,11
|
1
|
82.693696
|
-4.982459
|
-6.025198
|
CONSISTENT
|
1
|
82.693696
|
-4.982459
|
-6.025198
|
3-3⋅291
|
29/27
|
123.712192
|
m229
|
1
|
82.693696
|
-41.018496
|
-49.602930
|
CONSISTENT
|
1
|
82.693696
|
-41.018496
|
-49.602930
|
33⋅5-2
|
27/25
|
133.237575
|
m25,5
|
2
|
165.387391
|
32.149817
|
38.878195
|
INCONSISTENT
|
1
|
82.693696
|
-50.543879
|
-61.121805
|
3-2⋅5-1⋅72
|
49/45
|
147.428097
|
d37,75
|
2
|
165.387391
|
17.959294
|
21.717852
|
CONSISTENT
|
2
|
165.387391
|
17.959294
|
21.717852
|
3-4⋅71⋅131
|
91/81
|
201.533565
|
d37,13
|
2
|
165.387391
|
-36.146173
|
-43.710918
|
INCONSISTENT
|
3
|
248.081087
|
46.547522
|
56.289082
|
3-3⋅311
|
31/27
|
239.170570
|
M231
|
3
|
248.081087
|
8.910517
|
10.775328
|
CONSISTENT
|
3
|
248.081087
|
8.910517
|
10.775328
|
31⋅51⋅13-1
|
15/13
|
247.741053
|
A2513
|
3
|
248.081087
|
0.340034
|
0.411197
|
CONSISTENT
|
3
|
248.081087
|
0.340034
|
0.411197
|
33⋅23-1
|
27/23
|
277.590655
|
m323
|
3
|
248.081087
|
-29.509568
|
-35.685391
|
CONSISTENT
|
3
|
248.081087
|
-29.509568
|
-35.685391
|
11-1⋅131
|
13/11
|
289.209719
|
m31311
|
3
|
248.081087
|
-41.128632
|
-49.736116
|
INCONSISTENT
|
4
|
330.774783
|
41.565063
|
50.263884
|
3-1⋅52⋅7-1
|
25/21
|
301.846520
|
A25,57
|
4
|
330.774783
|
28.928262
|
34.982428
|
CONSISTENT
|
4
|
330.774783
|
28.928262
|
34.982428
|
3-2⋅111
|
11/9
|
347.407941
|
m311
|
4
|
330.774783
|
-16.633158
|
-20.114179
|
CONSISTENT
|
4
|
330.774783
|
-16.633158
|
-20.114179
|
34⋅5-1⋅13-1
|
81/65
|
380.978628
|
M35,13
|
5
|
413.468478
|
32.489851
|
39.289392
|
INCONSISTENT
|
4
|
330.774783
|
-50.203845
|
-60.710608
|
32⋅7-1
|
9/7
|
435.084095
|
M37
|
5
|
413.468478
|
-21.615617
|
-26.139377
|
CONSISTENT
|
5
|
413.468478
|
-21.615617
|
-26.139377
|
3-3⋅51⋅71
|
35/27
|
449.274618
|
P45,7
|
5
|
413.468478
|
-35.806139
|
-43.299721
|
INCONSISTENT
|
6
|
496.162174
|
46.887556
|
56.700279
|
31⋅51⋅11-1
|
15/11
|
536.950772
|
A4511
|
6
|
496.162174
|
-40.788598
|
-49.324919
|
INCONSISTENT
|
7
|
578.855870
|
41.905097
|
50.675081
|
35⋅5-2⋅7-1
|
243/175
|
568.321670
|
P45,5,7
|
7
|
578.855870
|
10.534200
|
12.738818
|
INCONSISTENT
|
6
|
496.162174
|
-72.159496
|
-87.261182
|
5-1⋅71
|
7/5
|
582.512193
|
d575
|
7
|
578.855870
|
-3.656323
|
-4.421525
|
CONSISTENT
|
7
|
578.855870
|
-3.656323
|
-4.421525
|
3-5⋅73
|
343/243
|
596.702715
|
d67,7,7
|
7
|
578.855870
|
-17.846845
|
-21.581869
|
INCONSISTENT
|
8
|
661.549566
|
64.846850
|
78.418131
|
33⋅19-1
|
27/19
|
608.351986
|
A419
|
7
|
578.855870
|
-29.496117
|
-35.669124
|
CONSISTENT
|
7
|
578.855870
|
-29.496117
|
-35.669124
|
35⋅13-2
|
243/169
|
628.719681
|
AA413,13
|
8
|
661.549566
|
32.829885
|
39.700590
|
INCONSISTENT
|
7
|
578.855870
|
-49.863811
|
-60.299410
|
3-2⋅131
|
13/9
|
636.617660
|
d513
|
8
|
661.549566
|
24.931905
|
30.149705
|
CONSISTENT
|
8
|
661.549566
|
24.931905
|
30.149705
|
34⋅5-1⋅11-1
|
81/55
|
670.188347
|
P55,11
|
8
|
661.549566
|
-8.638782
|
-10.446723
|
CONSISTENT
|
8
|
661.549566
|
-8.638782
|
-10.446723
|
3-4⋅112
|
121/81
|
694.815881
|
d511,11
|
8
|
661.549566
|
-33.266316
|
-40.228358
|
CONSISTENT
|
8
|
661.549566
|
-33.266316
|
-40.228358
|
3-4⋅53
|
125/81
|
751.121138
|
A55,5,5
|
9
|
744.243261
|
-6.877877
|
-8.317293
|
INCONSISTENT
|
10
|
826.936957
|
75.815819
|
91.682707
|
7-1⋅111
|
11/7
|
782.492036
|
P5117
|
9
|
744.243261
|
-38.248775
|
-46.253556
|
CONSISTENT
|
9
|
744.243261
|
-38.248775
|
-46.253556
|
33⋅17-1
|
27/17
|
800.909593
|
A517
|
10
|
826.936957
|
26.027364
|
31.474423
|
CONSISTENT
|
10
|
826.936957
|
26.027364
|
31.474423
|
31⋅71⋅13-1
|
21/13
|
830.253246
|
M6713
|
10
|
826.936957
|
-3.316289
|
-4.010328
|
CONSISTENT
|
10
|
826.936957
|
-3.316289
|
-4.010328
|
34⋅7-2
|
81/49
|
870.168191
|
A57,7
|
11
|
909.630653
|
39.462462
|
47.721246
|
INCONSISTENT
|
10
|
826.936957
|
-43.231234
|
-52.278754
|
3-1⋅51
|
5/3
|
884.358713
|
M65
|
11
|
909.630653
|
25.271940
|
30.560902
|
CONSISTENT
|
11
|
909.630653
|
25.271940
|
30.560902
|
35⋅11-1⋅13-1
|
243/143
|
917.929400
|
A611,13
|
11
|
909.630653
|
-8.298748
|
-10.035526
|
CONSISTENT
|
11
|
909.630653
|
-8.298748
|
-10.035526
|
3-4⋅111⋅131
|
143/81
|
984.025601
|
d711,13
|
12
|
992.324348
|
8.298748
|
10.035526
|
CONSISTENT
|
12
|
992.324348
|
8.298748
|
10.035526
|
32⋅5-1
|
9/5
|
1017.596288
|
m75
|
12
|
992.324348
|
-25.271940
|
-30.560902
|
CONSISTENT
|
12
|
992.324348
|
-25.271940
|
-30.560902
|
3-3⋅72
|
49/27
|
1031.786810
|
d87,7
|
12
|
992.324348
|
-39.462462
|
-47.721246
|
INCONSISTENT
|
13
|
1075.018044
|
43.231234
|
52.278754
|
7-1⋅131
|
13/7
|
1071.701755
|
m7137
|
13
|
1075.018044
|
3.316289
|
4.010328
|
CONSISTENT
|
13
|
1075.018044
|
3.316289
|
4.010328
|
3-2⋅171
|
17/9
|
1101.045408
|
d817
|
13
|
1075.018044
|
-26.027364
|
-31.474423
|
CONSISTENT
|
13
|
1075.018044
|
-26.027364
|
-31.474423
|
31⋅71⋅11-1
|
21/11
|
1119.462965
|
P8711
|
14
|
1157.711740
|
38.248775
|
46.253556
|
CONSISTENT
|
14
|
1157.711740
|
38.248775
|
46.253556
|
35⋅5-3
|
243/125
|
1150.833863
|
d85,5,5
|
14
|
1157.711740
|
6.877877
|
8.317293
|
INCONSISTENT
|
13
|
1075.018044
|
-75.815819
|
-91.682707
|
35⋅11-2
|
243/121
|
1207.139120
|
cA111,11
|
15
|
1240.405435
|
33.266316
|
40.228358
|
CONSISTENT
|
15
|
1240.405435
|
33.266316
|
40.228358
|
3-3⋅51⋅111
|
55/27
|
1231.766654
|
P85,11
|
15
|
1240.405435
|
8.638782
|
10.446723
|
CONSISTENT
|
15
|
1240.405435
|
8.638782
|
10.446723
|
33⋅13-1
|
27/13
|
1265.337341
|
cA113
|
15
|
1240.405435
|
-24.931905
|
-30.149705
|
CONSISTENT
|
15
|
1240.405435
|
-24.931905
|
-30.149705
|
3-4⋅132
|
169/81
|
1273.235320
|
cd213,13
|
15
|
1240.405435
|
-32.829885
|
-39.700590
|
INCONSISTENT
|
16
|
1323.099131
|
49.863811
|
60.299410
|
3-2⋅191
|
19/9
|
1293.603014
|
cm219
|
16
|
1323.099131
|
29.496117
|
35.669124
|
CONSISTENT
|
16
|
1323.099131
|
29.496117
|
35.669124
|
31⋅51⋅7-1
|
15/7
|
1319.442808
|
cA157
|
16
|
1323.099131
|
3.656323
|
4.421525
|
CONSISTENT
|
16
|
1323.099131
|
3.656323
|
4.421525
|
3-4⋅52⋅71
|
175/81
|
1333.633331
|
cM25,5,7
|
16
|
1323.099131
|
-10.534200
|
-12.738818
|
INCONSISTENT
|
17
|
1405.792827
|
72.159496
|
87.261182
|
5-1⋅111
|
11/5
|
1365.004228
|
cm2115
|
17
|
1405.792827
|
40.788598
|
49.324919
|
INCONSISTENT
|
16
|
1323.099131
|
-41.905097
|
-50.675081
|
34⋅5-1⋅7-1
|
81/35
|
1452.680383
|
cM25,7
|
18
|
1488.486522
|
35.806139
|
43.299721
|
INCONSISTENT
|
17
|
1405.792827
|
-46.887556
|
-56.700279
|
3-1⋅71
|
7/3
|
1466.870906
|
cm37
|
18
|
1488.486522
|
21.615617
|
26.139377
|
CONSISTENT
|
18
|
1488.486522
|
21.615617
|
26.139377
|
3-3⋅51⋅131
|
65/27
|
1520.976373
|
cm35,13
|
18
|
1488.486522
|
-32.489851
|
-39.289392
|
INCONSISTENT
|
19
|
1571.180218
|
50.203845
|
60.710608
|
33⋅11-1
|
27/11
|
1554.547060
|
cM311
|
19
|
1571.180218
|
16.633158
|
20.114179
|
CONSISTENT
|
19
|
1571.180218
|
16.633158
|
20.114179
|
32⋅5-2⋅71
|
63/25
|
1600.108480
|
cd475,5
|
19
|
1571.180218
|
-28.928262
|
-34.982428
|
CONSISTENT
|
19
|
1571.180218
|
-28.928262
|
-34.982428
|
31⋅111⋅13-1
|
33/13
|
1612.745281
|
cM31113
|
20
|
1653.873914
|
41.128632
|
49.736116
|
INCONSISTENT
|
19
|
1571.180218
|
-41.565063
|
-50.263884
|
3-2⋅231
|
23/9
|
1624.364346
|
cM323
|
20
|
1653.873914
|
29.509568
|
35.685391
|
CONSISTENT
|
20
|
1653.873914
|
29.509568
|
35.685391
|
5-1⋅131
|
13/5
|
1654.213948
|
cd4135
|
20
|
1653.873914
|
-0.340034
|
-0.411197
|
CONSISTENT
|
20
|
1653.873914
|
-0.340034
|
-0.411197
|
34⋅31-1
|
81/31
|
1662.784431
|
cP431
|
20
|
1653.873914
|
-8.910517
|
-10.775328
|
CONSISTENT
|
20
|
1653.873914
|
-8.910517
|
-10.775328
|
35⋅7-1⋅13-1
|
243/91
|
1700.421436
|
cA37,13
|
21
|
1736.567609
|
36.146173
|
43.710918
|
INCONSISTENT
|
20
|
1653.873914
|
-46.547522
|
-56.289082
|
33⋅51⋅7-2
|
135/49
|
1754.526904
|
cA357,7
|
21
|
1736.567609
|
-17.959294
|
-21.717852
|
CONSISTENT
|
21
|
1736.567609
|
-17.959294
|
-21.717852
|
3-2⋅52
|
25/9
|
1768.717426
|
cA45,5
|
21
|
1736.567609
|
-32.149817
|
-38.878195
|
INCONSISTENT
|
22
|
1819.261305
|
50.543879
|
61.121805
|
34⋅29-1
|
81/29
|
1778.242809
|
cA429
|
22
|
1819.261305
|
41.018496
|
49.602930
|
CONSISTENT
|
22
|
1819.261305
|
41.018496
|
49.602930
|
3-3⋅71⋅111
|
77/27
|
1814.278846
|
cd57,11
|
22
|
1819.261305
|
4.982459
|
6.025198
|
CONSISTENT
|
22
|
1819.261305
|
4.982459
|
6.025198
|
31
|
3/1
|
1901.955001
|
cP5
|
23
|
1901.955001
|
0
|
0
|
CONSISTENT
|
23
|
1901.955001
|
0
|
0
|
Main article: JI intervals approximated by various scales