User:Contribution/JI intervals approximated by 13edt
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13edt divides the tritave in 13 equal steps and the octave in 8.202087 equal steps of 146.304231 cents each. Its 31-limit patent val is <8 13 19 23 28 30 34 35 37 40 41|.
| 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
|
-9.699325
|
CONSISTENT
|
0
|
0
|
-14.190522
|
-9.699325
|
34⋅7-1⋅11-1
|
81/77
|
87.676155
|
A17,11
|
1
|
146.304231
|
58.628076
|
40.072714
|
CONSISTENT
|
1
|
146.304231
|
58.628076
|
40.072714
|
3-3⋅291
|
29/27
|
123.712192
|
m229
|
1
|
146.304231
|
22.592039
|
15.441822
|
CONSISTENT
|
1
|
146.304231
|
22.592039
|
15.441822
|
33⋅5-2
|
27/25
|
133.237575
|
m25,5
|
1
|
146.304231
|
13.066656
|
8.931154
|
CONSISTENT
|
1
|
146.304231
|
13.066656
|
8.931154
|
3-2⋅5-1⋅72
|
49/45
|
147.428097
|
d37,75
|
1
|
146.304231
|
-1.123867
|
-0.768171
|
CONSISTENT
|
1
|
146.304231
|
-1.123867
|
-0.768171
|
3-4⋅71⋅131
|
91/81
|
201.533565
|
d37,13
|
1
|
146.304231
|
-55.229334
|
-37.749649
|
CONSISTENT
|
1
|
146.304231
|
-55.229334
|
-37.749649
|
3-3⋅311
|
31/27
|
239.170570
|
M231
|
2
|
292.608462
|
53.437892
|
36.525186
|
CONSISTENT
|
2
|
292.608462
|
53.437892
|
36.525186
|
31⋅51⋅13-1
|
15/13
|
247.741053
|
A2513
|
2
|
292.608462
|
44.867409
|
30.667198
|
CONSISTENT
|
2
|
292.608462
|
44.867409
|
30.667198
|
33⋅23-1
|
27/23
|
277.590655
|
m323
|
2
|
292.608462
|
15.017806
|
10.264779
|
CONSISTENT
|
2
|
292.608462
|
15.017806
|
10.264779
|
11-1⋅131
|
13/11
|
289.209719
|
m31311
|
2
|
292.608462
|
3.398742
|
2.323065
|
CONSISTENT
|
2
|
292.608462
|
3.398742
|
2.323065
|
3-1⋅52⋅7-1
|
25/21
|
301.846520
|
A25,57
|
2
|
292.608462
|
-9.238059
|
-6.314280
|
CONSISTENT
|
2
|
292.608462
|
-9.238059
|
-6.314280
|
3-2⋅111
|
11/9
|
347.407941
|
m311
|
2
|
292.608462
|
-54.799479
|
-37.455840
|
CONSISTENT
|
2
|
292.608462
|
-54.799479
|
-37.455840
|
34⋅5-1⋅13-1
|
81/65
|
380.978628
|
M35,13
|
3
|
438.912693
|
57.934065
|
39.598352
|
CONSISTENT
|
3
|
438.912693
|
57.934065
|
39.598352
|
32⋅7-1
|
9/7
|
435.084095
|
M37
|
3
|
438.912693
|
3.828597
|
2.616874
|
CONSISTENT
|
3
|
438.912693
|
3.828597
|
2.616874
|
3-3⋅51⋅71
|
35/27
|
449.274618
|
P45,7
|
3
|
438.912693
|
-10.361925
|
-7.082451
|
CONSISTENT
|
3
|
438.912693
|
-10.361925
|
-7.082451
|
31⋅51⋅11-1
|
15/11
|
536.950772
|
A4511
|
4
|
585.216923
|
48.266151
|
32.990263
|
CONSISTENT
|
4
|
585.216923
|
48.266151
|
32.990263
|
35⋅5-2⋅7-1
|
243/175
|
568.321670
|
P45,5,7
|
4
|
585.216923
|
16.895253
|
11.548028
|
CONSISTENT
|
4
|
585.216923
|
16.895253
|
11.548028
|
5-1⋅71
|
7/5
|
582.512193
|
d575
|
4
|
585.216923
|
2.704731
|
1.848703
|
CONSISTENT
|
4
|
585.216923
|
2.704731
|
1.848703
|
3-5⋅73
|
343/243
|
596.702715
|
d67,7,7
|
4
|
585.216923
|
-11.485792
|
-7.850622
|
CONSISTENT
|
4
|
585.216923
|
-11.485792
|
-7.850622
|
33⋅19-1
|
27/19
|
608.351986
|
A419
|
4
|
585.216923
|
-23.135063
|
-15.812983
|
CONSISTENT
|
4
|
585.216923
|
-23.135063
|
-15.812983
|
35⋅13-2
|
243/169
|
628.719681
|
AA413,13
|
4
|
585.216923
|
-43.502757
|
-29.734449
|
INCONSISTENT
|
5
|
731.521154
|
102.801473
|
70.265551
|
3-2⋅131
|
13/9
|
636.617660
|
d513
|
4
|
585.216923
|
-51.400737
|
-35.132775
|
CONSISTENT
|
4
|
585.216923
|
-51.400737
|
-35.132775
|
34⋅5-1⋅11-1
|
81/55
|
670.188347
|
P55,11
|
5
|
731.521154
|
61.332807
|
41.921417
|
CONSISTENT
|
5
|
731.521154
|
61.332807
|
41.921417
|
3-4⋅112
|
121/81
|
694.815881
|
d511,11
|
5
|
731.521154
|
36.705273
|
25.088320
|
INCONSISTENT
|
4
|
585.216923
|
-109.598958
|
-74.911680
|
3-4⋅53
|
125/81
|
751.121138
|
A55,5,5
|
5
|
731.521154
|
-19.599984
|
-13.396731
|
CONSISTENT
|
5
|
731.521154
|
-19.599984
|
-13.396731
|
7-1⋅111
|
11/7
|
782.492036
|
P5117
|
5
|
731.521154
|
-50.970882
|
-34.838966
|
CONSISTENT
|
5
|
731.521154
|
-50.970882
|
-34.838966
|
33⋅17-1
|
27/17
|
800.909593
|
A517
|
5
|
731.521154
|
-69.388439
|
-47.427500
|
CONSISTENT
|
5
|
731.521154
|
-69.388439
|
-47.427500
|
31⋅71⋅13-1
|
21/13
|
830.253246
|
M6713
|
6
|
877.825385
|
47.572139
|
32.515901
|
CONSISTENT
|
6
|
877.825385
|
47.572139
|
32.515901
|
34⋅7-2
|
81/49
|
870.168191
|
A57,7
|
6
|
877.825385
|
7.657194
|
5.233748
|
CONSISTENT
|
6
|
877.825385
|
7.657194
|
5.233748
|
3-1⋅51
|
5/3
|
884.358713
|
M65
|
6
|
877.825385
|
-6.533328
|
-4.465577
|
CONSISTENT
|
6
|
877.825385
|
-6.533328
|
-4.465577
|
35⋅11-1⋅13-1
|
243/143
|
917.929400
|
A611,13
|
6
|
877.825385
|
-40.104015
|
-27.411384
|
INCONSISTENT
|
7
|
1024.129616
|
106.200216
|
72.588616
|
3-4⋅111⋅131
|
143/81
|
984.025601
|
d711,13
|
7
|
1024.129616
|
40.104015
|
27.411384
|
INCONSISTENT
|
6
|
877.825385
|
-106.200216
|
-72.588616
|
32⋅5-1
|
9/5
|
1017.596288
|
m75
|
7
|
1024.129616
|
6.533328
|
4.465577
|
CONSISTENT
|
7
|
1024.129616
|
6.533328
|
4.465577
|
3-3⋅72
|
49/27
|
1031.786810
|
d87,7
|
7
|
1024.129616
|
-7.657194
|
-5.233748
|
CONSISTENT
|
7
|
1024.129616
|
-7.657194
|
-5.233748
|
7-1⋅131
|
13/7
|
1071.701755
|
m7137
|
7
|
1024.129616
|
-47.572139
|
-32.515901
|
CONSISTENT
|
7
|
1024.129616
|
-47.572139
|
-32.515901
|
3-2⋅171
|
17/9
|
1101.045408
|
d817
|
8
|
1170.433847
|
69.388439
|
47.427500
|
CONSISTENT
|
8
|
1170.433847
|
69.388439
|
47.427500
|
31⋅71⋅11-1
|
21/11
|
1119.462965
|
P8711
|
8
|
1170.433847
|
50.970882
|
34.838966
|
CONSISTENT
|
8
|
1170.433847
|
50.970882
|
34.838966
|
35⋅5-3
|
243/125
|
1150.833863
|
d85,5,5
|
8
|
1170.433847
|
19.599984
|
13.396731
|
CONSISTENT
|
8
|
1170.433847
|
19.599984
|
13.396731
|
35⋅11-2
|
243/121
|
1207.139120
|
cA111,11
|
8
|
1170.433847
|
-36.705273
|
-25.088320
|
INCONSISTENT
|
9
|
1316.738078
|
109.598958
|
74.911680
|
3-3⋅51⋅111
|
55/27
|
1231.766654
|
P85,11
|
8
|
1170.433847
|
-61.332807
|
-41.921417
|
CONSISTENT
|
8
|
1170.433847
|
-61.332807
|
-41.921417
|
33⋅13-1
|
27/13
|
1265.337341
|
cA113
|
9
|
1316.738078
|
51.400737
|
35.132775
|
CONSISTENT
|
9
|
1316.738078
|
51.400737
|
35.132775
|
3-4⋅132
|
169/81
|
1273.235320
|
cd213,13
|
9
|
1316.738078
|
43.502757
|
29.734449
|
INCONSISTENT
|
8
|
1170.433847
|
-102.801473
|
-70.265551
|
3-2⋅191
|
19/9
|
1293.603014
|
cm219
|
9
|
1316.738078
|
23.135063
|
15.812983
|
CONSISTENT
|
9
|
1316.738078
|
23.135063
|
15.812983
|
31⋅51⋅7-1
|
15/7
|
1319.442808
|
cA157
|
9
|
1316.738078
|
-2.704731
|
-1.848703
|
CONSISTENT
|
9
|
1316.738078
|
-2.704731
|
-1.848703
|
3-4⋅52⋅71
|
175/81
|
1333.633331
|
cM25,5,7
|
9
|
1316.738078
|
-16.895253
|
-11.548028
|
CONSISTENT
|
9
|
1316.738078
|
-16.895253
|
-11.548028
|
5-1⋅111
|
11/5
|
1365.004228
|
cm2115
|
9
|
1316.738078
|
-48.266151
|
-32.990263
|
CONSISTENT
|
9
|
1316.738078
|
-48.266151
|
-32.990263
|
34⋅5-1⋅7-1
|
81/35
|
1452.680383
|
cM25,7
|
10
|
1463.042308
|
10.361925
|
7.082451
|
CONSISTENT
|
10
|
1463.042308
|
10.361925
|
7.082451
|
3-1⋅71
|
7/3
|
1466.870906
|
cm37
|
10
|
1463.042308
|
-3.828597
|
-2.616874
|
CONSISTENT
|
10
|
1463.042308
|
-3.828597
|
-2.616874
|
3-3⋅51⋅131
|
65/27
|
1520.976373
|
cm35,13
|
10
|
1463.042308
|
-57.934065
|
-39.598352
|
CONSISTENT
|
10
|
1463.042308
|
-57.934065
|
-39.598352
|
33⋅11-1
|
27/11
|
1554.547060
|
cM311
|
11
|
1609.346539
|
54.799479
|
37.455840
|
CONSISTENT
|
11
|
1609.346539
|
54.799479
|
37.455840
|
32⋅5-2⋅71
|
63/25
|
1600.108480
|
cd475,5
|
11
|
1609.346539
|
9.238059
|
6.314280
|
CONSISTENT
|
11
|
1609.346539
|
9.238059
|
6.314280
|
31⋅111⋅13-1
|
33/13
|
1612.745281
|
cM31113
|
11
|
1609.346539
|
-3.398742
|
-2.323065
|
CONSISTENT
|
11
|
1609.346539
|
-3.398742
|
-2.323065
|
3-2⋅231
|
23/9
|
1624.364346
|
cM323
|
11
|
1609.346539
|
-15.017806
|
-10.264779
|
CONSISTENT
|
11
|
1609.346539
|
-15.017806
|
-10.264779
|
5-1⋅131
|
13/5
|
1654.213948
|
cd4135
|
11
|
1609.346539
|
-44.867409
|
-30.667198
|
CONSISTENT
|
11
|
1609.346539
|
-44.867409
|
-30.667198
|
34⋅31-1
|
81/31
|
1662.784431
|
cP431
|
11
|
1609.346539
|
-53.437892
|
-36.525186
|
CONSISTENT
|
11
|
1609.346539
|
-53.437892
|
-36.525186
|
35⋅7-1⋅13-1
|
243/91
|
1700.421436
|
cA37,13
|
12
|
1755.650770
|
55.229334
|
37.749649
|
CONSISTENT
|
12
|
1755.650770
|
55.229334
|
37.749649
|
33⋅51⋅7-2
|
135/49
|
1754.526904
|
cA357,7
|
12
|
1755.650770
|
1.123867
|
0.768171
|
CONSISTENT
|
12
|
1755.650770
|
1.123867
|
0.768171
|
3-2⋅52
|
25/9
|
1768.717426
|
cA45,5
|
12
|
1755.650770
|
-13.066656
|
-8.931154
|
CONSISTENT
|
12
|
1755.650770
|
-13.066656
|
-8.931154
|
34⋅29-1
|
81/29
|
1778.242809
|
cA429
|
12
|
1755.650770
|
-22.592039
|
-15.441822
|
CONSISTENT
|
12
|
1755.650770
|
-22.592039
|
-15.441822
|
3-3⋅71⋅111
|
77/27
|
1814.278846
|
cd57,11
|
12
|
1755.650770
|
-58.628076
|
-40.072714
|
CONSISTENT
|
12
|
1755.650770
|
-58.628076
|
-40.072714
|
31
|
3/1
|
1901.955001
|
cP5
|
13
|
1901.955001
|
0
|
0
|
CONSISTENT
|
13
|
1901.955001
|
0
|
0
|
Main article: JI intervals approximated by various scales