User:Contribution/No-twos 31-limit

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Intervals

Here is a table of all no-twos 31-limit intervals with at most two primes from 5 to 31 in the ratio (excepting 5-limit intervals, which have at most three) on the vertical axis, and on a chain of 12 tritaves on the horizontal axis.

It is obtained according to the same rules than this one: 31-limit.

For each interval, you'll find: its factorization, its just ratio, its Functional Just System notation, and its cents value.

Limit Border

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↓ 31-limit ↓
Limit Border

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↓ 31-limit ↓
Limit Border

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↓ 31-limit ↓
Limit Border

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↓ 31-limit ↓
Limit Border

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↓ 31-limit ↓
Limit Border

~~

↓ 31-limit ↓
Limit Border

~~

↓ 31-limit ↓
Limit Border

~~

↓ 31-limit ↓
Limit Border

~~

↓ 31-limit ↓
Limit Border

~~

↓ 31-limit ↓
Limit Border

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↓ 31-limit ↓
Limit Border

~~

↓ 31-limit ↓
Limit Border

~~

↓ 31-limit ↓
3−6⋅312

961/729

M331,31

478.341139736
3−5⋅312

961/243

cM731,31

2380.296140602
3−4⋅312

961/81

3cA431,31

4282.251141467
3−3⋅312

961/27

5cA131,31

6184.206142332
3−2⋅312

961/9

6cA531,31

8086.161143198
3−1⋅312

961/3

8cA231,31

9988.116144063
312

961/1

9cA631,31

11890.071144929
31⋅312

2883/1

11cA331,31

13792.026145794
32⋅312

8649/1

12cA731,31

15693.981146659
33⋅312

25947/1

14cAA431,31

17595.936147525
34⋅312

77841/1

16cAA131,31

19497.891148390
35⋅312

233523/1

17cAA531,31

21399.846149255
36⋅312

700569/1

19cAA231,31

23301.801150121
3−6⋅29−1⋅311

31/21141

−10cP53129

−11296.271626881
3−5⋅29−1⋅311

31/7047

−8cM23129

−9394.316626016
3−4⋅29−1⋅311

31/2349

−7cM63129

−7492.361625150
3−3⋅29−1⋅311

31/783

−5cM33129

−5590.406624285
3−2⋅29−1⋅311

31/261

−4cM73129

−3688.451623420
3−1⋅29−1⋅311

31/87

−2cA43129

−1786.496622554
29−1⋅311

31/29

A13129

115.458378311
31⋅29−1⋅311

93/29

cA53129

2017.413379177
32⋅29−1⋅311

279/29

3cA23129

3919.368380042
33⋅29−1⋅311

837/29

4cA63129

5821.323380907
34⋅29−1⋅311

2511/29

6cA33129

7723.278381773
35⋅29−1⋅311

7533/29

7cA73129

9625.233382638
36⋅29−1⋅311

22599/29

9cAA43129

11527.188383503
3−6⋅291⋅311

899/729

m329,31

362.882761425
3−5⋅291⋅311

899/243

cm729,31

2264.837762290
3−4⋅291⋅311

899/81

3cP429,31

4166.792763156
3−3⋅291⋅311

899/27

5cP129,31

6068.747764021
3−2⋅291⋅311

899/9

6cP529,31

7970.702764887
3−1⋅291⋅311

899/3

8cM229,31

9872.657765752
291⋅311

899/1

9cM629,31

11774.612766617
31⋅291⋅311

2697/1

11cM329,31

13676.567767483
32⋅291⋅311

8091/1

12cM729,31

15578.522768348
33⋅291⋅311

24273/1

14cA429,31

17480.477769213
34⋅291⋅311

72819/1

16cA129,31

19382.432770079
35⋅291⋅311

218457/1

17cA529,31

21284.387770944
36⋅291⋅311

655371/1

19cA229,31

23186.342771810
3−6⋅23−1⋅311

31/16767

−10cd83123

−10894.968779996
3−5⋅23−1⋅311

31/5589

−8cd53123

−8993.013779131
3−4⋅23−1⋅311

31/1863

−6cm23123

−7091.058778266
3−3⋅23−1⋅311

31/621

−5cm63123

−5189.103777400
3−2⋅23−1⋅311

31/207

−3cm33123

−3287.148776535
3−1⋅23−1⋅311

31/69

−2cm73123

−1385.193775670
23−1⋅311

31/23

P43123

516.761225196
31⋅23−1⋅311

93/23

2cP13123

2418.716226061
32⋅23−1⋅311

279/23

3cP53123

4320.671226927
33⋅23−1⋅311

837/23

5cM23123

6222.626227792
34⋅23−1⋅311

2511/23

6cM63123

8124.581228657
35⋅23−1⋅311

7533/23

8cM33123

10026.536229523
36⋅23−1⋅311

22599/23

9cM73123

11928.491230388
3−6⋅231⋅311

713/729

-cM723,31

−38.420085460
3−5⋅231⋅311

713/243

cA423,31

1863.534915406
3−4⋅231⋅311

713/81

3cA123,31

3765.489916271
3−3⋅231⋅311

713/27

4cA523,31

5667.444917137
3−2⋅231⋅311

713/9

6cA223,31

7569.399918002
3−1⋅231⋅311

713/3

7cA623,31

9471.354918867
231⋅311

713/1

9cA323,31

11373.309919733
31⋅231⋅311

2139/1

10cA723,31

13275.264920598
32⋅231⋅311

6417/1

12cAA423,31

15177.219921463
33⋅231⋅311

19251/1

14cAA123,31

17079.174922329
34⋅231⋅311

57753/1

15cAA523,31

18981.129923194
35⋅231⋅311

173259/1

17cAA223,31

20883.084924060
36⋅231⋅311

519777/1

18cAA623,31

22785.039924925
3−6⋅19−1⋅311

31/13851

−9cM23119

−10564.207448860
3−5⋅19−1⋅311

31/4617

−8cM63119

−8662.252447995
3−4⋅19−1⋅311

31/1539

−6cM33119

−6760.297447130
3−3⋅19−1⋅311

31/513

−5cM73119

−4858.342446264
3−2⋅19−1⋅311

31/171

−3cA43119

−2956.387445399
3−1⋅19−1⋅311

31/57

-cA13119

−1054.432444533
19−1⋅311

31/19

A53119

847.522556332
31⋅19−1⋅311

93/19

2cA23119

2749.477557197
32⋅19−1⋅311

279/19

3cA63119

4651.432558063
33⋅19−1⋅311

837/19

5cA33119

6553.387558928
34⋅19−1⋅311

2511/19

6cA73119

8455.342559793
35⋅19−1⋅311

7533/19

8cAA43119

10357.297560659
36⋅19−1⋅311

22599/19

10cAA13119

12259.252561524
3−6⋅191⋅311

589/729

-cm619,31

−369.181416596
3−5⋅191⋅311

589/243

cm319,31

1532.773584270
3−4⋅191⋅311

589/81

2cm719,31

3434.728585135
3−3⋅191⋅311

589/27

4cP419,31

5336.683586000
3−2⋅191⋅311

589/9

6cP119,31

7238.638586866
3−1⋅191⋅311

589/3

7cP519,31

9140.593587731
191⋅311

589/1

9cM219,31

11042.548588597
31⋅191⋅311

1767/1

10cM619,31

12944.503589462
32⋅191⋅311

5301/1

12cM319,31

14846.458590327
33⋅191⋅311

15903/1

13cM719,31

16748.413591193
34⋅191⋅311

47709/1

15cA419,31

18650.368592058
35⋅191⋅311

143127/1

17cA119,31

20552.323592923
36⋅191⋅311

429381/1

18cA519,31

22454.278593789
3−6⋅17−1⋅311

31/12393

−9cM33117

−10371.649842228
3−5⋅17−1⋅311

31/4131

−8cM73117

−8469.694841363
3−4⋅17−1⋅311

31/1377

−6cA43117

−6567.739840498
3−3⋅17−1⋅311

31/459

−4cA13117

−4665.784839632
3−2⋅17−1⋅311

31/153

−3cA53117

−2763.829838767
3−1⋅17−1⋅311

31/51

-cA23117

−861.874837902
17−1⋅311

31/17

A63117

1040.080162964
31⋅17−1⋅311

93/17

2cA33117

2942.035163829
32⋅17−1⋅311

279/17

3cA73117

4843.990164695
33⋅17−1⋅311

837/17

5cAA43117

6745.945165560
34⋅17−1⋅311

2511/17

7cAA13117

8647.900166425
35⋅17−1⋅311

7533/17

8cAA53117

10549.855167291
36⋅17−1⋅311

22599/17

10cAA23117

12451.810168156
3−6⋅171⋅311

527/729

-cd517,31

−561.739023228
3−5⋅171⋅311

527/243

cm217,31

1340.215977638
3−4⋅171⋅311

527/81

2cm617,31

3242.170978503
3−3⋅171⋅311

527/27

4cm317,31

5144.125979368
3−2⋅171⋅311

527/9

5cm717,31

7046.080980234
3−1⋅171⋅311

527/3

7cP417,31

8948.035981099
171⋅311

527/1

9cP117,31

10849.990981965
31⋅171⋅311

1581/1

10cP517,31

12751.945982830
32⋅171⋅311

4743/1

12cM217,31

14653.900983695
33⋅171⋅311

14229/1

13cM617,31

16555.855984561
34⋅171⋅311

42687/1

15cM317,31

18457.810985426
35⋅171⋅311

128061/1

16cM717,31

20359.765986292
36⋅171⋅311

384183/1

18cA417,31

22261.720987157
3−6⋅13−1⋅311

31/9477

−9cM63113

−9907.222094497
3−5⋅13−1⋅311

31/3159

−7cM33113

−8005.267093632
3−4⋅13−1⋅311

31/1053

−6cM73113

−6103.312092767
3−3⋅13−1⋅311

31/351

−4cA43113

−4201.357091901
3−2⋅13−1⋅311

31/117

−2cA13113

−2299.402091036
3−1⋅13−1⋅311

31/39

-cA53113

−397.447090170
13−1⋅311

31/13

cA23113

1504.507910695
31⋅13−1⋅311

93/13

2cA63113

3406.462911560
32⋅13−1⋅311

279/13

4cA33113

5308.417912426
33⋅13−1⋅311

837/13

5cA73113

7210.372913291
34⋅13−1⋅311

2511/13

7cAA43113

9112.327914156
35⋅13−1⋅311

7533/13

9cAA13113

11014.282915022
36⋅13−1⋅311

22599/13

10cAA53113

12916.237915887
3−6⋅131⋅311

403/729

-cm213,31

−1026.166770959
3−5⋅131⋅311

403/243

m613,31

875.788229907
3−4⋅131⋅311

403/81

2cm313,31

2777.743230772
3−3⋅131⋅311

403/27

3cm713,31

4679.698231637
3−2⋅131⋅311

403/9

5cP413,31

6581.653232503
3−1⋅131⋅311

403/3

7cP113,31

8483.608233368
131⋅311

403/1

8cP513,31

10385.563234234
31⋅131⋅311

1209/1

10cM213,31

12287.518235099
32⋅131⋅311

3627/1

11cM613,31

14189.473235964
33⋅131⋅311

10881/1

13cM313,31

16091.428236830
34⋅131⋅311

32643/1

14cM713,31

17993.383237695
35⋅131⋅311

97929/1

16cA413,31

19895.338238560
36⋅131⋅311

293787/1

18cA113,31

21797.293239426
3−6⋅11−1⋅311

31/8019

−8cP13111

−9618.012375093
3−5⋅11−1⋅311

31/2673

−7cP53111

−7716.057374227
3−4⋅11−1⋅311

31/891

−5cM23111

−5814.102373362
3−3⋅11−1⋅311

31/297

−4cM63111

−3912.147372497
3−2⋅11−1⋅311

31/99

−2cM33111

−2010.192371631
3−1⋅11−1⋅311

31/33

-cM73111

−108.237370766
11−1⋅311

31/11

cA43111

1793.717630099
31⋅11−1⋅311

93/11

3cA13111

3695.672630965
32⋅11−1⋅311

279/11

4cA53111

5597.627631830
33⋅11−1⋅311

837/11

6cA23111

7499.582632696
34⋅11−1⋅311

2511/11

7cA63111

9401.537633561
35⋅11−1⋅311

7533/11

9cA33111

11303.492634426
36⋅11−1⋅311

22599/11

10cA73111

13205.447635292
3−6⋅111⋅311

341/729

−2cm711,31

−1315.376490363
3−5⋅111⋅311

341/243

P411,31

586.578510502
3−4⋅111⋅311

341/81

2cP111,31

2488.533511367
3−3⋅111⋅311

341/27

3cP511,31

4390.488512233
3−2⋅111⋅311

341/9

5cM211,31

6292.443513098
3−1⋅111⋅311

341/3

6cM611,31

8194.398513964
111⋅311

341/1

8cM311,31

10096.353514829
31⋅111⋅311

1023/1

9cM711,31

11998.308515694
32⋅111⋅311

3069/1

11cA411,31

13900.263516560
33⋅111⋅311

9207/1

13cA111,31

15802.218517425
34⋅111⋅311

27621/1

14cA511,31

17704.173518291
35⋅111⋅311

82863/1

16cA211,31

19606.128519156
36⋅111⋅311

248589/1

17cA611,31

21508.083520021
3−6⋅7−1⋅311

31/5103

−8cP5317

−8835.520339197
3−5⋅7−1⋅311

31/1701

−6cM2317

−6933.565338332
3−4⋅7−1⋅311

31/567

−5cM6317

−5031.610337466
3−3⋅7−1⋅311

31/189

−3cM3317

−3129.655336601
3−2⋅7−1⋅311

31/63

−2cM7317

−1227.700335736
3−1⋅7−1⋅311

31/21

A4317

674.254665130
7−1⋅311

31/7

2cA1317

2576.209665995
31⋅7−1⋅311

93/7

3cA5317

4478.164666861
32⋅7−1⋅311

279/7

5cA2317

6380.119667726
33⋅7−1⋅311

837/7

6cA6317

8282.074668591
34⋅7−1⋅311

2511/7

8cA3317

10184.029669457
35⋅7−1⋅311

7533/7

9cA7317

12085.984670322
36⋅7−1⋅311

22599/7

11cAA4317

13987.939671187
3−6⋅71⋅311

217/729

−2cm37,31

−2097.868526259
3−5⋅71⋅311

217/243

-cm77,31

−195.913525394
3−4⋅71⋅311

217/81

cP47,31

1706.041475472
3−3⋅71⋅311

217/27

3cP17,31

3607.996476337
3−2⋅71⋅311

217/9

4cP57,31

5509.951477203
3−1⋅71⋅311

217/3

6cM27,31

7411.906478068
71⋅311

217/1

7cM67,31

9313.861478933
31⋅71⋅311

651/1

9cM37,31

11215.816479799
32⋅71⋅311

1953/1

10cM77,31

13117.771480664
33⋅71⋅311

5859/1

12cA47,31

15019.726481530
34⋅71⋅311

17577/1

14cA17,31

16921.681482395
35⋅71⋅311

52731/1

15cA57,31

18823.636483260
36⋅71⋅311

158193/1

17cA27,31

20725.591484126
3−6⋅5−1⋅311

31/3645

−7cm2315

−8253.008146593
3−5⋅5−1⋅311

31/1215

−6cm6315

−6351.053145728
3−4⋅5−1⋅311

31/405

−4cm3315

−4449.098144862
3−3⋅5−1⋅311

31/135

−3cm7315

−2547.143143997
3−2⋅5−1⋅311

31/45

-cP4315

−645.188143131
3−1⋅5−1⋅311

31/15

P8315

1256.766857734
5−1⋅311

31/5

2cP5315

3158.721858599
31⋅5−1⋅311

93/5

4cM2315

5060.676859465
32⋅5−1⋅311

279/5

5cM6315

6962.631860330
33⋅5−1⋅311

837/5

7cM3315

8864.586861196
34⋅5−1⋅311

2511/5

8cM7315

10766.541862061
35⋅5−1⋅311

7533/5

10cA4315

12668.496862926
36⋅5−1⋅311

22599/5

12cA1315

14570.451863792
3−6⋅51⋅311

155/729

−3cM65,31

−2680.380718863
3−5⋅51⋅311

155/243

-cM35,31

−778.425717998
3−4⋅51⋅311

155/81

M75,31

1123.529282868
3−3⋅51⋅311

155/27

2cA45,31

3025.484283733
3−2⋅51⋅311

155/9

4cA15,31

4927.439284598
3−1⋅51⋅311

155/3

5cA55,31

6829.394285464
51⋅311

155/1

7cA25,31

8731.349286329
31⋅51⋅311

465/1

8cA65,31

10633.304287194
32⋅51⋅311

1395/1

10cA35,31

12535.259288060
33⋅51⋅311

4185/1

11cA75,31

14437.214288925
34⋅51⋅311

12555/1

13cAA45,31

16339.169289791
35⋅51⋅311

37665/1

15cAA15,31

18241.124290656
36⋅51⋅311

112995/1

16cAA55,31

20143.079291521
3−6⋅311

31/729

−5cP431

−5466.694432728
3−5⋅311

31/243

−3cP131

−3564.739431863
3−4⋅311

31/81

−2cP531

−1662.784430997
3−3⋅311

31/27

M231

239.170569868
3−2⋅311

31/9

cM631

2141.125570733
3−1⋅311

31/3

3cM331

4043.080571599
311

31/1

4cM731

5945.035572464
31⋅311

93/1

6cA431

7846.990573330
32⋅311

279/1

8cA131

9748.945574195
33⋅311

837/1

9cA531

11650.900575060
34⋅311

2511/1

11cA231

13552.855575926
35⋅311

7533/1

12cA631

15454.810576791
36⋅311

22599/1

14cA331

17356.765577657
↑ 31-limit ↑

~~

Limit Border

~~

↓ 29-limit ↓
↑ 31-limit ↑

~~

Limit Border

~~

↓ 29-limit ↓
↑ 31-limit ↑

~~

Limit Border

~~

↓ 29-limit ↓
↑ 31-limit ↑

~~

Limit Border

~~

↓ 29-limit ↓
↑ 31-limit ↑

~~

Limit Border

~~

↓ 29-limit ↓
↑ 31-limit ↑

~~

Limit Border

~~

↓ 29-limit ↓
↑ 31-limit ↑

~~

Limit Border

~~

↓ 29-limit ↓
↑ 31-limit ↑

~~

Limit Border

~~

↓ 29-limit ↓
↑ 31-limit ↑

~~

Limit Border

~~

↓ 29-limit ↓
↑ 31-limit ↑

~~

Limit Border

~~

↓ 29-limit ↓
↑ 31-limit ↑

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Limit Border

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↓ 29-limit ↓
↑ 31-limit ↑

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Limit Border

~~

↓ 29-limit ↓
↑ 31-limit ↑

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Limit Border

~~

↓ 29-limit ↓
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↑ 29-limit ↑

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↑ 7-limit ↑

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↓ 5-limit ↓
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↑ 5-limit ↑

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Limit Border

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↑ 5-limit ↑

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↑ 5-limit ↑

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Limit Border

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Limit Border

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Limit Border

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Limit Border

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↑ 5-limit ↑

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Limit Border

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↓ 3-limit ↓
↑ 5-limit ↑

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Limit Border

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↓ 3-limit ↓
↑ 5-limit ↑

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Limit Border

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↑ 3-limit ↑

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↑ 5-limit ↑

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↑ 5-limit ↑

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↓ 7-limit ↓
↑ 5-limit ↑

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Limit Border

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↓ 7-limit ↓
↑ 5-limit ↑

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Limit Border

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↓ 7-limit ↓
↑ 5-limit ↑

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Limit Border

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↓ 7-limit ↓
↑ 5-limit ↑

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Limit Border

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↓ 7-limit ↓
↑ 5-limit ↑

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Limit Border

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↓ 7-limit ↓
↑ 5-limit ↑

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Limit Border

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↓ 7-limit ↓
↑ 5-limit ↑

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Limit Border

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↓ 7-limit ↓
↑ 5-limit ↑

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Limit Border

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↓ 7-limit ↓
↑ 5-limit ↑

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Limit Border

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↓ 7-limit ↓
↑ 5-limit ↑

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Limit Border

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↑ 7-limit ↑

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↑ 7-limit ↑

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↓ 11-limit ↓
↑ 7-limit ↑

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↓ 11-limit ↓
↑ 7-limit ↑

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~~

↓ 11-limit ↓
↑ 7-limit ↑

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~~

↓ 11-limit ↓
↑ 7-limit ↑

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~~

↓ 11-limit ↓
↑ 7-limit ↑

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~~

↓ 11-limit ↓
↑ 7-limit ↑

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Limit Border

~~

↓ 11-limit ↓
↑ 7-limit ↑

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~~

↓ 11-limit ↓
↑ 7-limit ↑

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~~

↓ 11-limit ↓
↑ 7-limit ↑

~~

Limit Border

~~

↓ 11-limit ↓
↑ 7-limit ↑

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~~

↓ 11-limit ↓
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↑ 11-limit ↑

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Limit Border

~~

↓ 13-limit ↓
↑ 11-limit ↑

~~

Limit Border

~~

↓ 13-limit ↓
↑ 11-limit ↑

~~

Limit Border

~~

↓ 13-limit ↓
↑ 11-limit ↑

~~

Limit Border

~~

↓ 13-limit ↓
↑ 11-limit ↑

~~

Limit Border

~~

↓ 13-limit ↓
↑ 11-limit ↑

~~

Limit Border

~~

↓ 13-limit ↓
↑ 11-limit ↑

~~

Limit Border

~~

↓ 13-limit ↓
↑ 11-limit ↑

~~

Limit Border

~~

↓ 13-limit ↓
↑ 11-limit ↑

~~

Limit Border

~~

↓ 13-limit ↓
↑ 11-limit ↑

~~

Limit Border

~~

↓ 13-limit ↓
↑ 11-limit ↑

~~

Limit Border

~~

↓ 13-limit ↓
↑ 11-limit ↑

~~

Limit Border

~~

↓ 13-limit ↓
↑ 11-limit ↑

~~

Limit Border

~~

↓ 13-limit ↓
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↑ 17-limit ↑

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Limit Border

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↓ 19-limit ↓
↑ 17-limit ↑

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Limit Border

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↓ 19-limit ↓
↑ 17-limit ↑

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See also