31-odd-limit: Difference between revisions

{{Odd-limit navigation}}

{{odd-limit intro|31}}

*[[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 ([[cents|¢]])

!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).