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33-odd-limit: Difference between revisions

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{{Odd-limit navigation}}The '''33-odd-limit''' is the set of all [[Rational interval|rational intervals]] which can be written as 2<sup>''k''</sup>(''a''/''b'') where ''a'', ''b'' ≤ 33 and ''k'' is an integer. To the [[31-odd-limit]], it adds 10 pairs of [[octave-reduced]] intervals involving 33.
{{Odd-limit navigation|33}}
 
{{Odd-limit intro|33}}
Below is a list of all octave-reduced intervals in the 31-odd-limit.


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{| class="wikitable"
{| class="wikitable"
!Ratio
! Ratio
!Size ([[Cents|¢]])
! Size ([[cents|¢]])
! colspan="2" |[[Color name]]
! colspan="2" | [[Color name]]
!Name
! Name
|-
|-
|34/33
| 34/33
|51.682
| 51.682
|
| solu 2nd
|
| 17o1u2
|
| greater septendecimal quartertone
|-
|-
|33/32
| 33/32
|53.273
| 53.273
|
| ilo unison
|
| 1o1
|
| undecimal quartertone
|-
|-
|33/31
| 33/31
|108.237
| 108.237
|
| thiwulo 2nd
|
| 31u1o2
|
| trigesimoprimal semitone
|-
|-
|33/29
| 33/29
|223.696
| 223.696
|
| twenulo 2nd
|
| 29u1o2
|
| vigesimononal whole tone
|-
|-
|38/33
| 38/33
|244.24
| 244.24
|
| nolu 3rd
|
| 19o1u3
|
| undevigesimal inframinor third
|-
|-
|33/28
| 33/28
|284.447
| 284.447
|
| loru 2nd
|
| 1or2
|
| undecimal ultramajor second
|-
|-
|40/33
| 40/33
|333.041
| 333.041
|
| luyo 3rd
|
| 1uy3
|
| undecimal supraminor third
|-
|-
|33/26
| 33/26
|412.745
| 412.745
|
| lothu 3rd
|
| 1o3u3
|
| tridecimal major third, major minthmic major third
|-
|-
|33/25
| 33/25
|480.646
| 480.646
|
| logugu 4th
|
| 1ogg4
|
| undecimal grave fourth
|-
|-
|46/33
| 46/33
|575.001
| 575.001
|
| twetholu 5th
|
| 23o1u5
|
| preziosismic vigesimotertial narrow tritone
|-
|-
|33/23
| 33/23
|624.999
| 624.999
|
| twethulo 4th
|
| 23u1o4
|
| preziosismic vigesimotertial wide tritone
|-
|-
|50/33
| 50/33
|719.354
| 719.354
|
| luyoyo 5th
|
| 1uyy5
|
| undecimal acute fifth
|-
|-
|52/33
| 52/33
|787.255
| 787.255
|
| lutho 6th
|
| 1u3o6
|
| tridecimal minor sixth, major minthmic minor sixth
|-
|-
|33/20
| 33/20
|866.959
| 866.959
|
| logu 6th
|
| 1og6
|
| undecimal submajor sixth
|-
|-
|56/33
| 56/33
|915.553
| 915.553
|
| luzo 7th
|
| 1uz7
|
| undecimal inframinor seventh
|-
|-
|33/19
| 33/19
|955.76
| 955.76
|
| nulo 6th
|
| 19u1o6
|
| undevigesimal ultramajor sixth
|-
|-
|58/33
| 58/33
|976.304
| 976.304
|
| twenolu 2nd
|
| 29o1u7
|
| vigesimononal minor seventh
|-
|-
|62/33
| 62/33
|1091.763
| 1091.763
|
| thiwolu 7th
|
| 31o1u7
|
| trigesimoprimal major seventh
|-
|-
|64/33
| 64/33
|1146.727
| 1146.727
|
| ilu octave
|
| 1u8
|
| undecimal infraoctave
|-
|-
|33/17
| 33/17
|1148.318
| 1148.318
|
| sulo 7th
|
| 17u1o7
|
| lesser septendecimal 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).
The smallest [[equal division of the octave]] which is consistent to the 33-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).
 
[[Category:33-odd-limit| ]] <!-- main article -->
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