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) — vertical axis, on a chain of 12 tritaves — 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
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31-limit
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31-limit
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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

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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
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

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Limit Border

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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

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29-limit
31-limit

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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
3-6⋅292

841/729

d329,29

247.424383114
3-5⋅292

841/243

cd729,29

2149.379383979
3-4⋅292

841/81

3cd429,29

4051.334384845
3-3⋅292

841/27

4cd829,29

5953.289385710
3-2⋅292

841/9

6cd529,29

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3-4⋅29-1⋅31-1

1/72819

-17cd829,31

-19382.432770079
3-3⋅29-1⋅31-1

1/24273

-15cd529,31

-17480.477769213
3-2⋅29-1⋅31-1

1/8091

-13cm229,31

-15578.522768348
3-1⋅29-1⋅31-1

1/2697

-12cm629,31

-13676.567767483
29-1⋅31-1

1/899

-10cm329,31

-11774.612766617
31⋅29-1⋅31-1

3/899

-9cm729,31

-9872.657765752
32⋅29-1⋅31-1

9/899

-7cP429,31

-7970.702764887
33⋅29-1⋅31-1

27/899

-5cP129,31

-6068.747764021
34⋅29-1⋅31-1

81/899

-4cP529,31

-4166.792763156
35⋅29-1⋅31-1

243/899

-2cM229,31

-2264.837762290
36⋅29-1⋅31-1

729/899

-cM629,31

-362.882761425
3-6⋅291⋅31-1

29/22599

-10cdd52931

-11527.188383503
3-5⋅291⋅31-1

29/7533

-8cd22931

-9625.233382638
3-4⋅291⋅31-1

29/2511

-7cd62931

-7723.278381773
3-3⋅291⋅31-1

29/837

-5cd32931

-5821.323380907
3-2⋅291⋅31-1

29/279

-4cd72931

-3919.368380042
3-1⋅291⋅31-1

29/93

-2cd42931

-2017.413379177
291⋅31-1

29/31

-cd82931

-115.458378311
31⋅291⋅31-1

87/31

cd52931

1786.496622554
32⋅291⋅31-1

261/31

3cm22931

3688.451623420
33⋅291⋅31-1

783/31

4cm62931

5590.406624285
34⋅291⋅31-1

2349/31

6cm32931

7492.361625150
35⋅291⋅31-1

7047/31

7cm72931

9394.316626016
36⋅291⋅31-1

21141/31

9cP42931

11296.271626881
3-6⋅31-2

1/700569

-20cdd731,31

-23301.801150121
3-5⋅31-2

1/233523

-18cdd431,31

-21399.846149255
3-4⋅31-2

1/77841

-17cdd831,31

-19497.891148390
3-3⋅31-2

1/25947

-15cdd531,31

-17595.936147525
3-2⋅31-2

1/8649

-13cd231,31

-15693.981146659
3-1⋅31-2

1/2883

-12cd631,31

-13792.026145794
31-2

1/961

-10cd331,31

-11890.071144929
31⋅31-2

3/961

-9cd731,31

-9988.116144063
32⋅31-2

9/961

-7cd431,31

-8086.161143198
33⋅31-2

27/961

-6cd831,31

-6184.206142332
34⋅31-2

81/961

-4cd531,31

-4282.251141467
35⋅31-2

243/961

-2cm231,31

-2380.296140602
36⋅31-2

729/961

-cm631,31

-478.341139736
31-limit

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Limit Border
31-limit

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31-limit

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31-limit

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Limit Border
31-limit

~~

Limit Border
31-limit

~~

Limit Border
31-limit

~~

Limit Border
31-limit

~~

Limit Border
31-limit

~~

Limit Border
31-limit

~~

Limit Border
31-limit

~~

Limit Border
31-limit

~~

Limit Border
31-limit

~~

Limit Border

See also

Bohlen-Pierce scale

No-twos Z-function

Equal Division of the Tritave