User:Contribution/JI intervals approximated by 21edt
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21edt divides the tritave in 21 equal steps and the octave in 13.249525 equal steps of 90.569286 cents each. Its 31-limit patent val is <13 21 31 37 46 49 54 56 60 64 66|.
| 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
|
-15.668140
|
CONSISTENT
|
0
|
0
|
-14.190522
|
-15.668140
|
34⋅7-1⋅11-1
|
81/77
|
87.676155
|
A17,11
|
1
|
90.569286
|
2.893131
|
3.194384
|
CONSISTENT
|
1
|
90.569286
|
2.893131
|
3.194384
|
3-3⋅291
|
29/27
|
123.712192
|
m229
|
1
|
90.569286
|
-33.142906
|
-36.593979
|
CONSISTENT
|
1
|
90.569286
|
-33.142906
|
-36.593979
|
33⋅5-2
|
27/25
|
133.237575
|
m25,5
|
1
|
90.569286
|
-42.668289
|
-47.111213
|
CONSISTENT
|
1
|
90.569286
|
-42.668289
|
-47.111213
|
3-2⋅5-1⋅72
|
49/45
|
147.428097
|
d37,75
|
2
|
181.138572
|
33.710474
|
37.220647
|
INCONSISTENT
|
1
|
90.569286
|
-56.858812
|
-62.779353
|
3-4⋅71⋅131
|
91/81
|
201.533565
|
d37,13
|
2
|
181.138572
|
-20.394993
|
-22.518664
|
CONSISTENT
|
2
|
181.138572
|
-20.394993
|
-22.518664
|
3-3⋅311
|
31/27
|
239.170570
|
M231
|
3
|
271.707857
|
32.537287
|
35.925300
|
CONSISTENT
|
3
|
271.707857
|
32.537287
|
35.925300
|
31⋅51⋅13-1
|
15/13
|
247.741053
|
A2513
|
3
|
271.707857
|
23.966804
|
26.462397
|
CONSISTENT
|
3
|
271.707857
|
23.966804
|
26.462397
|
33⋅23-1
|
27/23
|
277.590655
|
m323
|
3
|
271.707857
|
-5.882798
|
-6.495357
|
CONSISTENT
|
3
|
271.707857
|
-5.882798
|
-6.495357
|
11-1⋅131
|
13/11
|
289.209719
|
m31311
|
3
|
271.707857
|
-17.501862
|
-19.324280
|
CONSISTENT
|
3
|
271.707857
|
-17.501862
|
-19.324280
|
3-1⋅52⋅7-1
|
25/21
|
301.846520
|
A25,57
|
3
|
271.707857
|
-30.138663
|
-33.276914
|
INCONSISTENT
|
4
|
362.277143
|
60.430623
|
66.723086
|
3-2⋅111
|
11/9
|
347.407941
|
m311
|
4
|
362.277143
|
14.869202
|
16.417489
|
CONSISTENT
|
4
|
362.277143
|
14.869202
|
16.417489
|
34⋅5-1⋅13-1
|
81/65
|
380.978628
|
M35,13
|
4
|
362.277143
|
-18.701485
|
-20.648816
|
CONSISTENT
|
4
|
362.277143
|
-18.701485
|
-20.648816
|
32⋅7-1
|
9/7
|
435.084095
|
M37
|
5
|
452.846429
|
17.762334
|
19.611873
|
CONSISTENT
|
5
|
452.846429
|
17.762334
|
19.611873
|
3-3⋅51⋅71
|
35/27
|
449.274618
|
P45,7
|
5
|
452.846429
|
3.571811
|
3.943733
|
CONSISTENT
|
5
|
452.846429
|
3.571811
|
3.943733
|
31⋅51⋅11-1
|
15/11
|
536.950772
|
A4511
|
6
|
543.415715
|
6.464942
|
7.138118
|
CONSISTENT
|
6
|
543.415715
|
6.464942
|
7.138118
|
35⋅5-2⋅7-1
|
243/175
|
568.321670
|
P45,5,7
|
6
|
543.415715
|
-24.905956
|
-27.499340
|
CONSISTENT
|
6
|
543.415715
|
-24.905956
|
-27.499340
|
5-1⋅71
|
7/5
|
582.512193
|
d575
|
6
|
543.415715
|
-39.096478
|
-43.167480
|
CONSISTENT
|
6
|
543.415715
|
-39.096478
|
-43.167480
|
3-5⋅73
|
343/243
|
596.702715
|
d67,7,7
|
7
|
633.985000
|
37.282285
|
41.164380
|
INCONSISTENT
|
6
|
543.415715
|
-53.287001
|
-58.835620
|
33⋅19-1
|
27/19
|
608.351986
|
A419
|
7
|
633.985000
|
25.633014
|
28.302104
|
CONSISTENT
|
7
|
633.985000
|
25.633014
|
28.302104
|
35⋅13-2
|
243/169
|
628.719681
|
AA413,13
|
7
|
633.985000
|
5.265320
|
5.813582
|
CONSISTENT
|
7
|
633.985000
|
5.265320
|
5.813582
|
3-2⋅131
|
13/9
|
636.617660
|
d513
|
7
|
633.985000
|
-2.632660
|
-2.906791
|
CONSISTENT
|
7
|
633.985000
|
-2.632660
|
-2.906791
|
34⋅5-1⋅11-1
|
81/55
|
670.188347
|
P55,11
|
7
|
633.985000
|
-36.203347
|
-39.973095
|
CONSISTENT
|
7
|
633.985000
|
-36.203347
|
-39.973095
|
3-4⋅112
|
121/81
|
694.815881
|
d511,11
|
8
|
724.554286
|
29.738405
|
32.834978
|
CONSISTENT
|
8
|
724.554286
|
29.738405
|
32.834978
|
3-4⋅53
|
125/81
|
751.121138
|
A55,5,5
|
8
|
724.554286
|
-26.566852
|
-29.333181
|
INCONSISTENT
|
9
|
815.123572
|
64.002434
|
70.666819
|
7-1⋅111
|
11/7
|
782.492036
|
P5117
|
9
|
815.123572
|
32.631536
|
36.029362
|
CONSISTENT
|
9
|
815.123572
|
32.631536
|
36.029362
|
33⋅17-1
|
27/17
|
800.909593
|
A517
|
9
|
815.123572
|
14.213979
|
15.694039
|
CONSISTENT
|
9
|
815.123572
|
14.213979
|
15.694039
|
31⋅71⋅13-1
|
21/13
|
830.253246
|
M6713
|
9
|
815.123572
|
-15.129674
|
-16.705082
|
CONSISTENT
|
9
|
815.123572
|
-15.129674
|
-16.705082
|
34⋅7-2
|
81/49
|
870.168191
|
A57,7
|
10
|
905.692858
|
35.524667
|
39.223746
|
CONSISTENT
|
10
|
905.692858
|
35.524667
|
39.223746
|
3-1⋅51
|
5/3
|
884.358713
|
M65
|
10
|
905.692858
|
21.334145
|
23.555606
|
CONSISTENT
|
10
|
905.692858
|
21.334145
|
23.555606
|
35⋅11-1⋅13-1
|
243/143
|
917.929400
|
A611,13
|
10
|
905.692858
|
-12.236543
|
-13.510698
|
CONSISTENT
|
10
|
905.692858
|
-12.236543
|
-13.510698
|
3-4⋅111⋅131
|
143/81
|
984.025601
|
d711,13
|
11
|
996.262143
|
12.236543
|
13.510698
|
CONSISTENT
|
11
|
996.262143
|
12.236543
|
13.510698
|
32⋅5-1
|
9/5
|
1017.596288
|
m75
|
11
|
996.262143
|
-21.334145
|
-23.555606
|
CONSISTENT
|
11
|
996.262143
|
-21.334145
|
-23.555606
|
3-3⋅72
|
49/27
|
1031.786810
|
d87,7
|
11
|
996.262143
|
-35.524667
|
-39.223746
|
CONSISTENT
|
11
|
996.262143
|
-35.524667
|
-39.223746
|
7-1⋅131
|
13/7
|
1071.701755
|
m7137
|
12
|
1086.831429
|
15.129674
|
16.705082
|
CONSISTENT
|
12
|
1086.831429
|
15.129674
|
16.705082
|
3-2⋅171
|
17/9
|
1101.045408
|
d817
|
12
|
1086.831429
|
-14.213979
|
-15.694039
|
CONSISTENT
|
12
|
1086.831429
|
-14.213979
|
-15.694039
|
31⋅71⋅11-1
|
21/11
|
1119.462965
|
P8711
|
12
|
1086.831429
|
-32.631536
|
-36.029362
|
CONSISTENT
|
12
|
1086.831429
|
-32.631536
|
-36.029362
|
35⋅5-3
|
243/125
|
1150.833863
|
d85,5,5
|
13
|
1177.400715
|
26.566852
|
29.333181
|
INCONSISTENT
|
12
|
1086.831429
|
-64.002434
|
-70.666819
|
35⋅11-2
|
243/121
|
1207.139120
|
cA111,11
|
13
|
1177.400715
|
-29.738405
|
-32.834978
|
CONSISTENT
|
13
|
1177.400715
|
-29.738405
|
-32.834978
|
3-3⋅51⋅111
|
55/27
|
1231.766654
|
P85,11
|
14
|
1267.970001
|
36.203347
|
39.973095
|
CONSISTENT
|
14
|
1267.970001
|
36.203347
|
39.973095
|
33⋅13-1
|
27/13
|
1265.337341
|
cA113
|
14
|
1267.970001
|
2.632660
|
2.906791
|
CONSISTENT
|
14
|
1267.970001
|
2.632660
|
2.906791
|
3-4⋅132
|
169/81
|
1273.235320
|
cd213,13
|
14
|
1267.970001
|
-5.265320
|
-5.813582
|
CONSISTENT
|
14
|
1267.970001
|
-5.265320
|
-5.813582
|
3-2⋅191
|
19/9
|
1293.603014
|
cm219
|
14
|
1267.970001
|
-25.633014
|
-28.302104
|
CONSISTENT
|
14
|
1267.970001
|
-25.633014
|
-28.302104
|
31⋅51⋅7-1
|
15/7
|
1319.442808
|
cA157
|
15
|
1358.539286
|
39.096478
|
43.167480
|
CONSISTENT
|
15
|
1358.539286
|
39.096478
|
43.167480
|
3-4⋅52⋅71
|
175/81
|
1333.633331
|
cM25,5,7
|
15
|
1358.539286
|
24.905956
|
27.499340
|
CONSISTENT
|
15
|
1358.539286
|
24.905956
|
27.499340
|
5-1⋅111
|
11/5
|
1365.004228
|
cm2115
|
15
|
1358.539286
|
-6.464942
|
-7.138118
|
CONSISTENT
|
15
|
1358.539286
|
-6.464942
|
-7.138118
|
34⋅5-1⋅7-1
|
81/35
|
1452.680383
|
cM25,7
|
16
|
1449.108572
|
-3.571811
|
-3.943733
|
CONSISTENT
|
16
|
1449.108572
|
-3.571811
|
-3.943733
|
3-1⋅71
|
7/3
|
1466.870906
|
cm37
|
16
|
1449.108572
|
-17.762334
|
-19.611873
|
CONSISTENT
|
16
|
1449.108572
|
-17.762334
|
-19.611873
|
3-3⋅51⋅131
|
65/27
|
1520.976373
|
cm35,13
|
17
|
1539.677858
|
18.701485
|
20.648816
|
CONSISTENT
|
17
|
1539.677858
|
18.701485
|
20.648816
|
33⋅11-1
|
27/11
|
1554.547060
|
cM311
|
17
|
1539.677858
|
-14.869202
|
-16.417489
|
CONSISTENT
|
17
|
1539.677858
|
-14.869202
|
-16.417489
|
32⋅5-2⋅71
|
63/25
|
1600.108480
|
cd475,5
|
18
|
1630.247144
|
30.138663
|
33.276914
|
INCONSISTENT
|
17
|
1539.677858
|
-60.430623
|
-66.723086
|
31⋅111⋅13-1
|
33/13
|
1612.745281
|
cM31113
|
18
|
1630.247144
|
17.501862
|
19.324280
|
CONSISTENT
|
18
|
1630.247144
|
17.501862
|
19.324280
|
3-2⋅231
|
23/9
|
1624.364346
|
cM323
|
18
|
1630.247144
|
5.882798
|
6.495357
|
CONSISTENT
|
18
|
1630.247144
|
5.882798
|
6.495357
|
5-1⋅131
|
13/5
|
1654.213948
|
cd4135
|
18
|
1630.247144
|
-23.966804
|
-26.462397
|
CONSISTENT
|
18
|
1630.247144
|
-23.966804
|
-26.462397
|
34⋅31-1
|
81/31
|
1662.784431
|
cP431
|
18
|
1630.247144
|
-32.537287
|
-35.925300
|
CONSISTENT
|
18
|
1630.247144
|
-32.537287
|
-35.925300
|
35⋅7-1⋅13-1
|
243/91
|
1700.421436
|
cA37,13
|
19
|
1720.816429
|
20.394993
|
22.518664
|
CONSISTENT
|
19
|
1720.816429
|
20.394993
|
22.518664
|
33⋅51⋅7-2
|
135/49
|
1754.526904
|
cA357,7
|
19
|
1720.816429
|
-33.710474
|
-37.220647
|
INCONSISTENT
|
20
|
1811.385715
|
56.858812
|
62.779353
|
3-2⋅52
|
25/9
|
1768.717426
|
cA45,5
|
20
|
1811.385715
|
42.668289
|
47.111213
|
CONSISTENT
|
20
|
1811.385715
|
42.668289
|
47.111213
|
34⋅29-1
|
81/29
|
1778.242809
|
cA429
|
20
|
1811.385715
|
33.142906
|
36.593979
|
CONSISTENT
|
20
|
1811.385715
|
33.142906
|
36.593979
|
3-3⋅71⋅111
|
77/27
|
1814.278846
|
cd57,11
|
20
|
1811.385715
|
-2.893131
|
-3.194384
|
CONSISTENT
|
20
|
1811.385715
|
-2.893131
|
-3.194384
|
31
|
3/1
|
1901.955001
|
cP5
|
21
|
1901.955001
|
0
|
0
|
CONSISTENT
|
21
|
1901.955001
|
0
|
0
|
Main article: JI intervals approximated by various scales