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The 31-odd-limit is the set of all rational intervals for which neither the numerator nor the denominator of the frequency ratio exceeds 31, once all powers of 2 are removed. To the 29-odd-limit, it adds 15 interval pairs involving 31.

Below is a list of all octave-reduced intervals in the 31-odd-limit.

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 subminor 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 supramajor 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 which is consistent to the 31-odd-limit 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).