31-odd-limit: Difference between revisions
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Proposed adding the smallest edo that comes closest to consistency |
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{{Odd-limit navigation}} | {{Odd-limit navigation|31}} | ||
{{ | {{Odd-limit intro|31}} | ||
*[[1/1]] | |||
*'''[[32/31]], [[31/16]]''' | * [[1/1]] | ||
*'''[[31/30]], [[60/31]]''' | * '''[[32/31]], [[31/16]]''' | ||
*[[30/29]], [[29/15]] | * '''[[31/30]], [[60/31]]''' | ||
*[[29/28]], [[56/29]] | * [[30/29]], [[29/15]] | ||
*[[28/27]], [[27/14]] | * [[29/28]], [[56/29]] | ||
*[[27/26]], [[52/27]] | * [[28/27]], [[27/14]] | ||
*[[26/25]], [[25/13]] | * [[27/26]], [[52/27]] | ||
*[[25/24]], [[48/25]] | * [[26/25]], [[25/13]] | ||
*[[24/23]], [[23/12]] | * [[25/24]], [[48/25]] | ||
*[[23/22]], [[44/23]] | * [[24/23]], [[23/12]] | ||
*[[22/21]], [[21/11]] | * [[23/22]], [[44/23]] | ||
*[[21/20]], [[40/21]] | * [[22/21]], [[21/11]] | ||
*[[20/19]], [[19/10]] | * [[21/20]], [[40/21]] | ||
*[[19/18]], [[36/19]] | * [[20/19]], [[19/10]] | ||
*[[18/17]], [[17/9]] | * [[19/18]], [[36/19]] | ||
*[[17/16]], [[32/17]] | * [[18/17]], [[17/9]] | ||
*[[16/15]], [[15/8]] | * [[17/16]], [[32/17]] | ||
*'''[[31/29]], [[58/31]]''' | * [[16/15]], [[15/8]] | ||
*[[15/14]], [[28/15]] | * '''[[31/29]], [[58/31]]''' | ||
*[[29/27]], [[54/29]] | * [[15/14]], [[28/15]] | ||
*[[14/13]], [[13/7]] | * [[29/27]], [[54/29]] | ||
*[[27/25]], [[50/27]] | * [[14/13]], [[13/7]] | ||
*[[13/12]], [[24/13]] | * [[27/25]], [[50/27]] | ||
*[[25/23]], [[46/25]] | * [[13/12]], [[24/13]] | ||
*[[12/11]], [[11/6]] | * [[25/23]], [[46/25]] | ||
*[[23/21]], [[42/23]] | * [[12/11]], [[11/6]] | ||
*'''[[34/31]], [[31/17]]''' | * [[23/21]], [[42/23]] | ||
*[[11/10]], [[20/11]] | * '''[[34/31]], [[31/17]]''' | ||
*[[32/29]], [[29/16]] | * [[11/10]], [[20/11]] | ||
*[[21/19]], [[38/21]] | * [[32/29]], [[29/16]] | ||
*'''[[31/28]], [[56/31]]''' | * [[21/19]], [[38/21]] | ||
*[[10/9]], [[9/5]] | * '''[[31/28]], [[56/31]]''' | ||
*[[29/26]], [[52/29]] | * [[10/9]], [[9/5]] | ||
*[[19/17]], [[34/19]] | * [[29/26]], [[52/29]] | ||
*[[28/25]], [[25/14]] | * [[19/17]], [[34/19]] | ||
*[[9/8]], [[16/9]] | * [[28/25]], [[25/14]] | ||
*[[26/23]], [[23/13]] | * [[9/8]], [[16/9]] | ||
*[[17/15]], [[30/17]] | * [[26/23]], [[23/13]] | ||
*[[25/22]], [[44/25]] | * [[17/15]], [[30/17]] | ||
*[[8/7]], [[7/4]] | * [[25/22]], [[44/25]] | ||
*'''[[31/27]], [[54/31]]''' | * [[8/7]], [[7/4]] | ||
*[[23/20]], [[40/23]] | * '''[[31/27]], [[54/31]]''' | ||
*[[15/13]], [[26/15]] | * [[23/20]], [[40/23]] | ||
*[[22/19]], [[19/11]] | * [[15/13]], [[26/15]] | ||
*[[29/25]], [[50/29]] | * [[22/19]], [[19/11]] | ||
*'''[[36/31]], [[31/18]]''' | * [[29/25]], [[50/29]] | ||
*[[7/6]], [[12/7]] | * '''[[36/31]], [[31/18]]''' | ||
*[[34/29]], [[29/17]] | * [[7/6]], [[12/7]] | ||
*[[27/23]], [[46/27]] | * [[34/29]], [[29/17]] | ||
*[[20/17]], [[17/10]] | * [[27/23]], [[46/27]] | ||
*[[13/11]], [[22/13]] | * [[20/17]], [[17/10]] | ||
*[[32/27]], [[27/16]] | * [[13/11]], [[22/13]] | ||
*[[19/16]], [[32/19]] | * [[32/27]], [[27/16]] | ||
*[[25/21]], [[42/25]] | * [[19/16]], [[32/19]] | ||
*'''[[31/26]], [[52/31]]''' | * [[25/21]], [[42/25]] | ||
*[[6/5]], [[5/3]] | * '''[[31/26]], [[52/31]]''' | ||
*[[29/24]], [[48/29]] | * [[6/5]], [[5/3]] | ||
*[[23/19]], [[38/23]] | * [[29/24]], [[48/29]] | ||
*[[17/14]], [[28/17]] | * [[23/19]], [[38/23]] | ||
*[[28/23]], [[23/14]] | * [[17/14]], [[28/17]] | ||
*[[11/9]], [[18/11]] | * [[28/23]], [[23/14]] | ||
*'''[[38/31]], [[31/19]]''' | * [[11/9]], [[18/11]] | ||
*[[27/22]], [[44/27]] | * '''[[38/31]], [[31/19]]''' | ||
*[[16/13]], [[13/8]] | * [[27/22]], [[44/27]] | ||
*[[21/17]], [[34/21]] | * [[16/13]], [[13/8]] | ||
*[[26/21]], [[21/13]] | * [[21/17]], [[34/21]] | ||
*'''[[31/25]], [[50/31]]''' | * [[26/21]], [[21/13]] | ||
*[[36/29]], [[29/18]] | * '''[[31/25]], [[50/31]]''' | ||
*[[5/4]], [[8/5]] | * [[36/29]], [[29/18]] | ||
*[[34/27]], [[27/17]] | * [[5/4]], [[8/5]] | ||
*[[29/23]], [[46/29]] | * [[34/27]], [[27/17]] | ||
*[[24/19]], [[19/12]] | * [[29/23]], [[46/29]] | ||
*[[19/15]], [[30/19]] | * [[24/19]], [[19/12]] | ||
*[[14/11]], [[11/7]] | * [[19/15]], [[30/19]] | ||
*[[23/18]], [[36/23]] | * [[14/11]], [[11/7]] | ||
*[[32/25]], [[25/16]] | * [[23/18]], [[36/23]] | ||
*[[9/7]], [[14/9]] | * [[32/25]], [[25/16]] | ||
*'''[[40/31]], [[31/20]]''' | * [[9/7]], [[14/9]] | ||
*'''[[31/24]], [[48/31]]''' | * '''[[40/31]], [[31/20]]''' | ||
*[[22/17]], [[17/11]] | * '''[[31/24]], [[48/31]]''' | ||
*[[13/10]], [[20/13]] | * [[22/17]], [[17/11]] | ||
*[[30/23]], [[23/15]] | * [[13/10]], [[20/13]] | ||
*[[17/13]], [[26/17]] | * [[30/23]], [[23/15]] | ||
*[[38/29]], [[29/19]] | * [[17/13]], [[26/17]] | ||
*[[21/16]], [[32/21]] | * [[38/29]], [[29/19]] | ||
*[[25/19]], [[38/25]] | * [[21/16]], [[32/21]] | ||
*[[29/22]], [[44/29]] | * [[25/19]], [[38/25]] | ||
*[[4/3]], [[3/2]] | * [[29/22]], [[44/29]] | ||
*'''[[31/23]], [[46/31]]''' | * [[4/3]], [[3/2]] | ||
*[[27/20]], [[40/27]] | * '''[[31/23]], [[46/31]]''' | ||
*[[23/17]], [[34/23]] | * [[27/20]], [[40/27]] | ||
*'''[[42/31]], [[31/21]]''' | * [[23/17]], [[34/23]] | ||
*[[19/14]], [[28/19]] | * '''[[42/31]], [[31/21]]''' | ||
*[[34/25]], [[25/17]] | * [[19/14]], [[28/19]] | ||
*[[15/11]], [[22/15]] | * [[34/25]], [[25/17]] | ||
*[[26/19]], [[19/13]] | * [[15/11]], [[22/15]] | ||
*[[11/8]], [[16/11]] | * [[26/19]], [[19/13]] | ||
*[[40/29]], [[29/20]] | * [[11/8]], [[16/11]] | ||
*[[29/21]], [[42/29]] | * [[40/29]], [[29/20]] | ||
*[[18/13]], [[13/9]] | * [[29/21]], [[42/29]] | ||
*[[25/18]], [[36/25]] | * [[18/13]], [[13/9]] | ||
*[[32/23]], [[23/16]] | * [[25/18]], [[36/25]] | ||
*[[7/5]], [[10/7]] | * [[32/23]], [[23/16]] | ||
*[[38/27]], [[27/19]] | * [[7/5]], [[10/7]] | ||
*'''[[31/22]], [[44/31]]''' | * [[38/27]], [[27/19]] | ||
*[[24/17]], [[17/12]] | * '''[[31/22]], [[44/31]]''' | ||
* [[24/17]], [[17/12]] | |||
{| class="wikitable center-all right-2 left-5" | {| class="wikitable center-all right-2 left-5" | ||
!Ratio | ! Ratio | ||
!Size ([[cents|¢]]) | ! Size ([[cents|¢]]) | ||
! colspan="2" |[[Color name]] | ! colspan="2" |[[Color name]] | ||
!Name | ! Name | ||
|- | |- | ||
|[[32/31]] | | [[32/31]] | ||
|54.964 | | 54.964 | ||
|31u2 | | 31u2 | ||
|thiwu 2nd | | thiwu 2nd | ||
|lesser tricesimoprimal quartertone | | lesser tricesimoprimal quartertone | ||
|- | |- | ||
|[[31/30]] | | [[31/30]] | ||
|56.767 | | 56.767 | ||
|31og1 | | 31og1 | ||
|thiwogu unison | | thiwogu unison | ||
|greater tricesimoprimal quartertone | | greater tricesimoprimal quartertone | ||
|- | |- | ||
|[[31/29]] | | [[31/29]] | ||
|115.458 | | 115.458 | ||
|31o29u1 | | 31o29u1 | ||
|thiwotwenu unison | | thiwotwenu unison | ||
|tricesimoprimal augmented unison | | tricesimoprimal augmented unison | ||
|- | |- | ||
|[[34/31]] | | [[34/31]] | ||
|159.920 | | 159.920 | ||
|31u17o3 | | 31u17o3 | ||
|thiwuso 3rd | | thiwuso 3rd | ||
|tricesimoprimal diminished third | | tricesimoprimal diminished third | ||
|- | |- | ||
|[[31/28]] | | [[31/28]] | ||
|176.210 | | 176.210 | ||
|31or1 | | 31or1 | ||
|thiworu unison | | thiworu unison | ||
|tricesimoprimal superaugmented unison | | tricesimoprimal superaugmented unison | ||
|- | |- | ||
|[[31/27]] | | [[31/27]] | ||
|239.171 | | 239.171 | ||
|31o2 | | 31o2 | ||
|thiwo 2nd | | thiwo 2nd | ||
|tricesimoprimal supermajor second | | tricesimoprimal supermajor second | ||
|- | |- | ||
|[[36/31]] | | [[36/31]] | ||
|258.874 | | 258.874 | ||
|31u3 | | 31u3 | ||
|thiwu 3rd | | thiwu 3rd | ||
|tricesimoprimal inframinor third | | tricesimoprimal inframinor third | ||
|- | |- | ||
|[[31/26]] | | [[31/26]] | ||
|304.508 | | 304.508 | ||
|31o3u2 | | 31o3u2 | ||
|thiwothu 2nd | | thiwothu 2nd | ||
|tricesimoprimal augmented second | | tricesimoprimal augmented second | ||
|- | |- | ||
|[[38/31]] | | [[38/31]] | ||
|352.477 | | 352.477 | ||
|31u19o4 | | 31u19o4 | ||
|thiwuno 4th | | thiwuno 4th | ||
|tricesimoprimal diminished fourth | | tricesimoprimal diminished fourth | ||
|- | |- | ||
|[[31/25]] | | [[31/25]] | ||
|372.408 | | 372.408 | ||
|31ogg3 | | 31ogg3 | ||
|thiwogugu 3rd | | thiwogugu 3rd | ||
|tricesimoprimal submajor third | | tricesimoprimal submajor third | ||
|- | |- | ||
|[[40/31]] | | [[40/31]] | ||
|441.278 | | 441.278 | ||
|31uy4 | | 31uy4 | ||
|thiwuyo 4th | | thiwuyo 4th | ||
|tricesimoprimal semidiminished fourth | | tricesimoprimal semidiminished fourth | ||
|- | |- | ||
|[[31/24]] | | [[31/24]] | ||
|443.081 | | 443.081 | ||
|31o3 | | 31o3 | ||
|thiwo 3rd | | thiwo 3rd | ||
|tricesimoprimal supermajor third | | tricesimoprimal supermajor third | ||
|- | |- | ||
|[[31/23]] | | [[31/23]] | ||
|516.761 | | 516.761 | ||
|31o23u3 | | 31o23u3 | ||
|thiwotwethu 3rd | | thiwotwethu 3rd | ||
|tricesimoprimal augmented third | | tricesimoprimal augmented third | ||
|- | |- | ||
|[[42/31]] | | [[42/31]] | ||
|525.745 | | 525.745 | ||
|31uz5 | | 31uz5 | ||
|thiwuzo 5th | | thiwuzo 5th | ||
|tricesimoprimal diminished fifth | | tricesimoprimal diminished fifth | ||
|- | |- | ||
|[[31/22]] | | [[31/22]] | ||
|593.718 | | 593.718 | ||
|31o1u4 | | 31o1u4 | ||
|thiwolu 4th | | thiwolu 4th | ||
|lesser tricesimoprimal tritone | | lesser tricesimoprimal tritone | ||
|- | |- | ||
|[[44/31]] | | [[44/31]] | ||
|606.282 | | 606.282 | ||
|31u1o5 | | 31u1o5 | ||
|thiwulo 5th | | thiwulo 5th | ||
|greater tricesimoprimal tritone | | greater tricesimoprimal tritone | ||
|- | |- | ||
|[[31/21]] | | [[31/21]] | ||
|674.255 | | 674.255 | ||
|31or4 | | 31or4 | ||
|thiworu 4th | | thiworu 4th | ||
|tricesimoprimal augmented fourth | | tricesimoprimal augmented fourth | ||
|- | |- | ||
|[[46/31]] | | [[46/31]] | ||
|683.239 | | 683.239 | ||
|31u23o6 | | 31u23o6 | ||
|thiwotwetho 6th | | thiwotwetho 6th | ||
|tricesimoprimal subminor sixth | | tricesimoprimal subminor sixth | ||
|- | |- | ||
|[[48/31]] | | [[48/31]] | ||
|756.919 | | 756.919 | ||
|31u6 | | 31u6 | ||
|thiwu 6th | | thiwu 6th | ||
|tricesimoprimal supermajor sixth | | tricesimoprimal supermajor sixth | ||
|- | |- | ||
|[[31/20]] | | [[31/20]] | ||
|758.722 | | 758.722 | ||
|31og5 | | 31og5 | ||
|thiwogu 5th | | thiwogu 5th | ||
|tricesimoprimal semiaugmented fifth | | tricesimoprimal semiaugmented fifth | ||
|- | |- | ||
|[[50/31]] | | [[50/31]] | ||
|827.592 | | 827.592 | ||
|31uyy6 | | 31uyy6 | ||
|thiwuyoyo 6th | | thiwuyoyo 6th | ||
|tricesimoprimal supraminor sixth | | tricesimoprimal supraminor sixth | ||
|- | |- | ||
|[[31/19]] | | [[31/19]] | ||
|847.523 | | 847.523 | ||
|31o19u5 | | 31o19u5 | ||
|thiwonu 5th | | thiwonu 5th | ||
|tricesimoprimal augmented fifth | | tricesimoprimal augmented fifth | ||
|- | |- | ||
|[[52/31]] | | [[52/31]] | ||
|895.492 | | 895.492 | ||
|31u3o7 | | 31u3o7 | ||
|thiwutho 7th | | thiwutho 7th | ||
|tricesimoprimal diminished seventh | | tricesimoprimal diminished seventh | ||
|- | |- | ||
|[[31/18]] | | [[31/18]] | ||
|941.126 | | 941.126 | ||
|31o6 | | 31o6 | ||
|thiwo 6th | | thiwo 6th | ||
|tricesimoprimal ultramajor sixth | | tricesimoprimal ultramajor sixth | ||
|- | |- | ||
|[[54/31]] | | [[54/31]] | ||
|960.829 | | 960.829 | ||
|31u7 | | 31u7 | ||
|thiwu 7th | | thiwu 7th | ||
|tricesimoprimal subminor seventh | | tricesimoprimal subminor seventh | ||
|- | |- | ||
|[[56/31]] | | [[56/31]] | ||
|1023.790 | | 1023.790 | ||
|31uz8 | | 31uz8 | ||
|thiwuzo octave | | thiwuzo octave | ||
|tricesimoprimal supradiminished octave | | tricesimoprimal supradiminished octave | ||
|- | |- | ||
|[[31/17]] | | [[31/17]] | ||
|1040.080 | | 1040.080 | ||
|31o17u6 | | 31o17u6 | ||
|thiwosu 6th | | thiwosu 6th | ||
|tricesimoprimal augmented sixth | | tricesimoprimal augmented sixth | ||
|- | |- | ||
|[[58/31]] | | [[58/31]] | ||
|1084.542 | | 1084.542 | ||
|31u29o8 | | 31u29o8 | ||
|thiwutweno octave | | thiwutweno octave | ||
|tricesimoprimal diminished octave | | tricesimoprimal diminished octave | ||
|- | |- | ||
|[[60/31]] | | [[60/31]] | ||
|1143.233 | | 1143.233 | ||
|31uy8 | | 31uy8 | ||
|thiwuyo octave | | thiwuyo octave | ||
|lesser tricesimoprimal infraoctave | | lesser tricesimoprimal infraoctave | ||
|- | |- | ||
|[[31/16]] | | [[31/16]] | ||
|1145.036 | | 1145.036 | ||
|31o7 | | 31o7 | ||
|thiwo 7th | | thiwo 7th | ||
|greater tricesimoprimal infraoctave | | greater tricesimoprimal infraoctave | ||
|} | |} | ||
The smallest [[equal division of the octave]] that comes closest to being consistent in the 31-odd-limit is [[217edo]] (misses 23/14, 23/21, 29/23, and their octave complements), the one which is truly consistent is [[311edo]] (by virtue of it being consistent through the 41-odd-limit); that which is distinctly consistent to the same is [[1600edo]] (by virtue of it being distinctly consistent through the 37-odd-limit). | The smallest [[equal division of the octave]] that comes closest to being consistent in the 31-odd-limit is [[217edo]] (misses 23/14, 23/21, 29/23, and their octave complements), the one which is truly consistent is [[311edo]] (by virtue of it being consistent through the 41-odd-limit); that which is distinctly consistent to the same is [[1600edo]] (by virtue of it being distinctly consistent through the 37-odd-limit). | ||
[[Category:31-odd-limit| ]] <!-- main article --> | [[Category:31-odd-limit| ]] <!-- main article --> | ||
Revision as of 15:26, 23 September 2025
The 31-odd-limit is the set of all rational intervals which can be written as 2k(a/b) where a, b ≤ 31 and k is an integer. To the 29-odd-limit, it adds 15 pairs of octave-reduced intervals involving 31.
Below is a list of all octave-reduced intervals in the 31-odd-limit.
- 1/1
- 32/31, 31/16
- 31/30, 60/31
- 30/29, 29/15
- 29/28, 56/29
- 28/27, 27/14
- 27/26, 52/27
- 26/25, 25/13
- 25/24, 48/25
- 24/23, 23/12
- 23/22, 44/23
- 22/21, 21/11
- 21/20, 40/21
- 20/19, 19/10
- 19/18, 36/19
- 18/17, 17/9
- 17/16, 32/17
- 16/15, 15/8
- 31/29, 58/31
- 15/14, 28/15
- 29/27, 54/29
- 14/13, 13/7
- 27/25, 50/27
- 13/12, 24/13
- 25/23, 46/25
- 12/11, 11/6
- 23/21, 42/23
- 34/31, 31/17
- 11/10, 20/11
- 32/29, 29/16
- 21/19, 38/21
- 31/28, 56/31
- 10/9, 9/5
- 29/26, 52/29
- 19/17, 34/19
- 28/25, 25/14
- 9/8, 16/9
- 26/23, 23/13
- 17/15, 30/17
- 25/22, 44/25
- 8/7, 7/4
- 31/27, 54/31
- 23/20, 40/23
- 15/13, 26/15
- 22/19, 19/11
- 29/25, 50/29
- 36/31, 31/18
- 7/6, 12/7
- 34/29, 29/17
- 27/23, 46/27
- 20/17, 17/10
- 13/11, 22/13
- 32/27, 27/16
- 19/16, 32/19
- 25/21, 42/25
- 31/26, 52/31
- 6/5, 5/3
- 29/24, 48/29
- 23/19, 38/23
- 17/14, 28/17
- 28/23, 23/14
- 11/9, 18/11
- 38/31, 31/19
- 27/22, 44/27
- 16/13, 13/8
- 21/17, 34/21
- 26/21, 21/13
- 31/25, 50/31
- 36/29, 29/18
- 5/4, 8/5
- 34/27, 27/17
- 29/23, 46/29
- 24/19, 19/12
- 19/15, 30/19
- 14/11, 11/7
- 23/18, 36/23
- 32/25, 25/16
- 9/7, 14/9
- 40/31, 31/20
- 31/24, 48/31
- 22/17, 17/11
- 13/10, 20/13
- 30/23, 23/15
- 17/13, 26/17
- 38/29, 29/19
- 21/16, 32/21
- 25/19, 38/25
- 29/22, 44/29
- 4/3, 3/2
- 31/23, 46/31
- 27/20, 40/27
- 23/17, 34/23
- 42/31, 31/21
- 19/14, 28/19
- 34/25, 25/17
- 15/11, 22/15
- 26/19, 19/13
- 11/8, 16/11
- 40/29, 29/20
- 29/21, 42/29
- 18/13, 13/9
- 25/18, 36/25
- 32/23, 23/16
- 7/5, 10/7
- 38/27, 27/19
- 31/22, 44/31
- 24/17, 17/12
| Ratio | Size (¢) | Color name | Name | |
|---|---|---|---|---|
| 32/31 | 54.964 | 31u2 | thiwu 2nd | lesser tricesimoprimal quartertone |
| 31/30 | 56.767 | 31og1 | thiwogu unison | greater tricesimoprimal quartertone |
| 31/29 | 115.458 | 31o29u1 | thiwotwenu unison | tricesimoprimal augmented unison |
| 34/31 | 159.920 | 31u17o3 | thiwuso 3rd | tricesimoprimal diminished third |
| 31/28 | 176.210 | 31or1 | thiworu unison | tricesimoprimal superaugmented unison |
| 31/27 | 239.171 | 31o2 | thiwo 2nd | tricesimoprimal supermajor second |
| 36/31 | 258.874 | 31u3 | thiwu 3rd | tricesimoprimal inframinor third |
| 31/26 | 304.508 | 31o3u2 | thiwothu 2nd | tricesimoprimal augmented second |
| 38/31 | 352.477 | 31u19o4 | thiwuno 4th | tricesimoprimal diminished fourth |
| 31/25 | 372.408 | 31ogg3 | thiwogugu 3rd | tricesimoprimal submajor third |
| 40/31 | 441.278 | 31uy4 | thiwuyo 4th | tricesimoprimal semidiminished fourth |
| 31/24 | 443.081 | 31o3 | thiwo 3rd | tricesimoprimal supermajor third |
| 31/23 | 516.761 | 31o23u3 | thiwotwethu 3rd | tricesimoprimal augmented third |
| 42/31 | 525.745 | 31uz5 | thiwuzo 5th | tricesimoprimal diminished fifth |
| 31/22 | 593.718 | 31o1u4 | thiwolu 4th | lesser tricesimoprimal tritone |
| 44/31 | 606.282 | 31u1o5 | thiwulo 5th | greater tricesimoprimal tritone |
| 31/21 | 674.255 | 31or4 | thiworu 4th | tricesimoprimal augmented fourth |
| 46/31 | 683.239 | 31u23o6 | thiwotwetho 6th | tricesimoprimal subminor sixth |
| 48/31 | 756.919 | 31u6 | thiwu 6th | tricesimoprimal supermajor sixth |
| 31/20 | 758.722 | 31og5 | thiwogu 5th | tricesimoprimal semiaugmented fifth |
| 50/31 | 827.592 | 31uyy6 | thiwuyoyo 6th | tricesimoprimal supraminor sixth |
| 31/19 | 847.523 | 31o19u5 | thiwonu 5th | tricesimoprimal augmented fifth |
| 52/31 | 895.492 | 31u3o7 | thiwutho 7th | tricesimoprimal diminished seventh |
| 31/18 | 941.126 | 31o6 | thiwo 6th | tricesimoprimal ultramajor sixth |
| 54/31 | 960.829 | 31u7 | thiwu 7th | tricesimoprimal subminor seventh |
| 56/31 | 1023.790 | 31uz8 | thiwuzo octave | tricesimoprimal supradiminished octave |
| 31/17 | 1040.080 | 31o17u6 | thiwosu 6th | tricesimoprimal augmented sixth |
| 58/31 | 1084.542 | 31u29o8 | thiwutweno octave | tricesimoprimal diminished octave |
| 60/31 | 1143.233 | 31uy8 | thiwuyo octave | lesser tricesimoprimal infraoctave |
| 31/16 | 1145.036 | 31o7 | thiwo 7th | greater tricesimoprimal infraoctave |
The smallest equal division of the octave that comes closest to being consistent in the 31-odd-limit is 217edo (misses 23/14, 23/21, 29/23, and their octave complements), the one which is truly consistent is 311edo (by virtue of it being consistent through the 41-odd-limit); that which is distinctly consistent to the same is 1600edo (by virtue of it being distinctly consistent through the 37-odd-limit).