Table of 31edo intervals: Difference between revisions

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Below is a table of (important) [[31edo/Individual degrees|intervals]] consistently represented in [[31edo]]. Intervals are found significantly, though not exclusively, in the 2.3.5.7.11.23 and 2.5.7.13.17.19.29.31 subgroups.
<noinclude>Below is a table of (important) [[31edo/Individual degrees|intervals]] consistently represented in [[31edo]]. Intervals are found significantly, though not exclusively, in the 2.3.5.7.11.23 and 2.5.7.13.17.19.29.31 subgroups.
{| class="wikitable"
</noinclude>{| class="wikitable"
|+
! Step
!Step
! Cents
!Cents
! 3-limit
!3-limit
! 5-limit
!5-limit
! 7-limit
!7-limit
! 11-limit
!11-limit
! 13-limit
!13-limit
! 17-limit
!17-limit
! 19-limit
!19-limit
! 23-limit
!23-limit
! 29-limit
!29-limit
! 31-limit
!31-limit
|-
|-
|1
| 1
|38.71
| 38.71
|
|  
|128/125
| [[128/125]]
|36/35, 49/48, <br>50/49, 64/63
| [[36/35]], [[49/48]], <br />[[50/49]], [[64/63]]
|33/32, 45/44, <br>55/54, 56/55
| [[33/32]], [[45/44]], <br />[[55/54]], [[56/55]]
|40/39, 65/64
| [[40/39]], [[65/64]]
|35/34
| [[35/34]]
|39/38
| [[39/38]]
|46/45
| [[46/45]]
|
|  
|32/31
| [[32/31]]
|-
|-
|2
| 2
|77.42
| 77.42
|
|  
|25/24
| [[25/24]]
|21/20, 28/27
| [[21/20]], [[28/27]]
|22/21
| [[22/21]]
|
|  
|68/65
| [[68/65]]
|20/19
| [[20/19]]
|23/22
| [[23/22]]
|
|  
|
|  
|-
|-
|3
| 3
|116.13
| 116.13
|
|  
|16/15
| [[16/15]]
|15/14
| [[15/14]]
|77/72, 128/121
| [[77/72]], [[128/121]]
|14/13
| [[14/13]]
|17/16
| [[17/16]]
|
|  
|
|  
|
|  
|31/29
| [[31/29]]
|-
|-
|4
| 4
|154.84
| 154.84
|
|  
|
|  
|35/32
| [[35/32]]
|12/11, 11/10
| [[12/11]], [[11/10]]
|(13/12)
| ([[13/12]])
|
|  
|
|  
|23/21
| [[23/21]]
|32/29
| [[32/29]]
|
|  
|-
|-
|5
| 5
|193.55
| 193.55
|9/8
| [[9/8]]
|10/9
| [[10/9]]
|28/25
| [[28/25]]
|55/49
| [[55/49]]
|(39/35)
| ([[39/35]])
|
|  
|19/17
| [[19/17]]
|
|  
|29/26
| [[29/26]]
|
|  
|-
|-
|6
| 6
|232.26
| 232.26
|
|  
|144/125
| [[144/125]]
|8/7
| [[8/7]]
|25/22, 55/48
| [[25/22]], [[55/48]]
|15/13
| [[15/13]]
|17/15
| [[17/15]]
|
|  
|
|  
|
|  
|
|  
|-
|-
|7
| 7
|270.97
| 270.97
|
|  
|75/64
| [[75/64]]
|7/6
| [[7/6]]
|64/55
| [[64/55]]
|
|  
|20/17
| [[20/17]]
|
|  
|
|  
|
|  
|
|  
|-
|-
|8
| 8
|309.68
| 309.68
|32/27
| [[32/27]]
|6/5
| [[6/5]]
|25/21
| [[25/21]]
|77/64
| [[77/64]]
|
|  
|
|  
|19/16
| [[19/16]]
|
|  
|
|  
|
|  
|-
|-
|9
| 9
|348.39
| 348.39
|
|  
|
|  
|49/40
| [[49/40]]
|11/9, 27/22
| [[11/9]], [[27/22]]
|16/13, 39/32
| [[16/13]], [[39/32]]
|
|  
|
|  
|
|  
|
|  
|
|  
|-
|-
|10
| 10
|387.1
| 387.1
|
|  
|5/4
| [[5/4]]
|
|  
|96/77
| [[96/77]]
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|-
|-
|11
| 11
|425.81
| 425.81
|
|  
|32/25
| [[32/25]]
|9/7
| [[9/7]]
|14/11
| [[14/11]]
|
|  
|
|  
|
|  
|23/18
| [[23/18]]
|
|  
|
|  
|-
|-
|12
| 12
|464.52
| 464.52
|
|  
|125/96
| [[125/96]]
|21/16, 64/49
| [[21/16]], [[64/49]]
|33/25
| [[33/25]]
|13/10
| [[13/10]]
|17/13
| [[17/13]]
|
|  
|
|  
|
|  
|
|  
|-
|-
|13
| 13
|503.23
| 503.23
|4/3
| [[4/3]]
|27/20
| [[27/20]]
|
|  
|162/121
| [[162/121]]
|35/26
| [[35/26]]
|85/64
| [[85/64]]
|128/95
| [[128/95]]
|
|  
|
|  
|
|  
|-
|-
|14
| 14
|541.94
| 541.94
|
|  
|
|  
|48/35, 49/36
| [[48/35]], [[49/36]]
|11/8, 15/11
| [[11/8]], [[15/11]]
|
|  
|
|  
|26/19
| [[26/19]]
|
|  
|
|  
|
|  
|-
|-
|15
| 15
|580.65
| 580.65
|
|  
|45/32, 25/18
| [[45/32]], [[25/18]]
|7/5
| [[7/5]]
|108/77
| [[108/77]]
|
|  
|24/17
| [[24/17]]
|
|  
|32/23
| [[32/23]]
|
|  
|
|  
|-
|-
|16
| 16
|619.35
| 619.35
|
|  
|64/45, 36/25
| [[64/45]], [[36/25]]
|10/7
| [[10/7]]
|77/54
| [[77/54]]
|
|  
|17/12
| [[17/12]]
|
|  
|23/16
| [[23/16]]
|
|  
|
|  
|-
|-
|17
| 17
|658.06
| 658.06
|
|  
|
|  
|35/24, 72/49
| [[35/24]], [[72/49]]
|16/11, 22/15
| [[16/11]], [[22/15]]
|
|  
|
|  
|19/13
| [[19/13]]
|
|  
|
|  
|
|  
|-
|-
|18
| 18
|696.77
| 696.77
|3/2
| [[3/2]]
|40/27
| [[40/27]]
|
|  
|121/81
| [[121/81]]
|52/35
| [[52/35]]
|128/85
| [[128/85]]
|95/64
| [[95/64]]
|
|  
|
|  
|
|  
|-
|-
|19
| 19
|735.48
| 735.48
|
|  
|192/125
| [[192/125]]
|32/21, 49/32
| [[32/21]], [[49/32]]
|50/33
| [[50/33]]
|20/13
| [[20/13]]
|26/17
| [[26/17]]
|
|  
|
|  
|
|  
|
|  
|-
|-
|20
| 20
|774.19
| 774.19
|
|  
|25/16
| [[25/16]]
|14/9
| [[14/9]]
|11/7
| [[11/7]]
|
|  
|
|  
|
|  
|36/23
| [[36/23]]
|
|  
|
|  
|-
|-
|21
| 21
|812.9
| 812.9
|
|  
|8/5
| [[8/5]]
|
|  
|77/48
| [[77/48]]
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|-
|-
|22
| 22
|851.61
| 851.61
|
|  
|
|  
|49/30
| [[49/30]]
|18/11, 44/27
| [[18/11]], [[44/27]]
|13/8, 64/39
| [[13/8]], [[64/39]]
|
|  
|
|  
|
|  
|
|  
|
|  
|-
|-
|23
| 23
|890.32
| 890.32
|27/16
| [[27/16]]
|5/3
| [[5/3]]
|42/25
| [[42/25]]
|128/77
| [[128/77]]
|
|  
|
|  
|32/19
| [[32/19]]
|
|  
|
|  
|
|  
|-
|-
|24
| 24
|929.03
| 929.03
|
|  
|128/75
| [[128/75]]
|12/7
| [[12/7]]
|55/32
| [[55/32]]
|
|  
|17/10
| [[17/10]]
|
|  
|
|  
|
|  
|
|  
|-
|-
|25
| 25
|967.74
| 967.74
|
|  
|125/72
| [[125/72]]
|7/4
| [[7/4]]
|96/55
| [[96/55]]
|26/15
| [[26/15]]
|30/17
| [[30/17]]
|
|  
|
|  
|
|  
|
|  
|-
|-
|26
| 26
|1006.45
| 1006.45
|16/9
| [[16/9]]
|9/5
| [[9/5]]
|25/14
| [[25/14]]
|98/55
| [[98/55]]
|
|  
|
|  
|
|  
|
|  
|52/29
| [[52/29]]
|
|  
|-
|-
|27
| 27
|1045.16
| 1045.16
|
|  
|
|  
|64/35
| [[64/35]]
|11/6, 20/11
| [[11/6]], [[20/11]]
|24/13
| [[24/13]]
|
|  
|
|  
|42/23
| [[42/23]]
|29/16
| [[29/16]]
|
|  
|-
|-
|28
| 28
|1083.87
| 1083.87
|
|  
|15/8
| [[15/8]]
|28/15
| [[28/15]]
|144/77, 121/64
| [[144/77]], [[121/64]]
|13/7
| [[13/7]]
|32/17
| [[32/17]]
|
|  
|
|  
|
|  
|58/31
| [[58/31]]
|-
|-
|29
| 29
|1122.58
| 1122.58
|
|  
|48/25
| [[48/25]]
|27/14, 40/21
| [[27/14]], [[40/21]]
|21/11
| [[21/11]]
|
|  
|65/34
| [[65/34]]
|19/10
| [[19/10]]
|44/23
| [[44/23]]
|
|  
|
|  
|-
|-
|30
| 30
|1161.29
| 1161.29
|
|  
|125/64
| [[125/64]]
|49/25, 35/18
| [[49/25]], [[35/18]]
|88/45, 64/33
| [[88/45]], [[64/33]]
|39/20
| [[39/20]]
|
|  
|
|  
|45/23
| [[45/23]]
|
|  
|31/16
| [[31/16]]
|-
|-
|31
| 31
|1200
| 1200
|2/1
| [[2/1]]
|2/1
| [[2/1]]
|2/1
| [[2/1]]
|2/1
| [[2/1]]
|2/1
| [[2/1]]
|2/1
| [[2/1]]
|2/1
| [[2/1]]
|2/1
| [[2/1]]
|2/1
| [[2/1]]
|2/1
| [[2/1]]
|}
<includeonly>
{{Navbar table|cols=12|Table of 31edo intervals}}
</includeonly>
|}<noinclude>
[[Category:31edo]]
[[Category:31edo]]
[[Category:Tables of edo intervals]]
[[Category:Tables of edo intervals]]
</noinclude>

Latest revision as of 09:58, 30 December 2025

Below is a table of (important) intervals consistently represented in 31edo. Intervals are found significantly, though not exclusively, in the 2.3.5.7.11.23 and 2.5.7.13.17.19.29.31 subgroups.

Step Cents 3-limit 5-limit 7-limit 11-limit 13-limit 17-limit 19-limit 23-limit 29-limit 31-limit
1 38.71 128/125 36/35, 49/48,
50/49, 64/63 		33/32, 45/44,
55/54, 56/55 		40/39, 65/64 35/34 39/38 46/45 32/31
2 77.42 25/24 21/20, 28/27 22/21 68/65 20/19 23/22
3 116.13 16/15 15/14 77/72, 128/121 14/13 17/16 31/29
4 154.84 35/32 12/11, 11/10 (13/12) 23/21 32/29
5 193.55 9/8 10/9 28/25 55/49 (39/35) 19/17 29/26
6 232.26 144/125 8/7 25/22, 55/48 15/13 17/15
7 270.97 75/64 7/6 64/55 20/17
8 309.68 32/27 6/5 25/21 77/64 19/16
9 348.39 49/40 11/9, 27/22 16/13, 39/32
10 387.1 5/4 96/77
11 425.81 32/25 9/7 14/11 23/18
12 464.52 125/96 21/16, 64/49 33/25 13/10 17/13
13 503.23 4/3 27/20 162/121 35/26 85/64 128/95
14 541.94 48/35, 49/36 11/8, 15/11 26/19
15 580.65 45/32, 25/18 7/5 108/77 24/17 32/23
16 619.35 64/45, 36/25 10/7 77/54 17/12 23/16
17 658.06 35/24, 72/49 16/11, 22/15 19/13
18 696.77 3/2 40/27 121/81 52/35 128/85 95/64
19 735.48 192/125 32/21, 49/32 50/33 20/13 26/17
20 774.19 25/16 14/9 11/7 36/23
21 812.9 8/5 77/48
22 851.61 49/30 18/11, 44/27 13/8, 64/39
23 890.32 27/16 5/3 42/25 128/77 32/19
24 929.03 128/75 12/7 55/32 17/10
25 967.74 125/72 7/4 96/55 26/15 30/17
26 1006.45 16/9 9/5 25/14 98/55 52/29
27 1045.16 64/35 11/6, 20/11 24/13 42/23 29/16
28 1083.87 15/8 28/15 144/77, 121/64 13/7 32/17 58/31
29 1122.58 48/25 27/14, 40/21 21/11 65/34 19/10 44/23
30 1161.29 125/64 49/25, 35/18 88/45, 64/33 39/20 45/23 31/16
31 1200 2/1 2/1 2/1 2/1 2/1 2/1 2/1 2/1 2/1 2/1
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