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
|
|  
|
|  
|
|  
|-
|-
|33/32
| 33/32
|53.273
| 53.273
|
|  
|
|  
|
|  
|-
|-
|33/31
| 33/31
|108.237
| 108.237
|
|  
|
|  
|
|  
|-
|-
|33/29
| 33/29
|223.696
| 223.696
|
|  
|
|  
|
|  
|-
|-
|38/33
| 38/33
|244.24
| 244.24
|
|  
|
|  
|
|  
|-
|-
|33/28
| 33/28
|284.447
| 284.447
|
|  
|
|  
|
|  
|-
|-
|40/33
| 40/33
|333.041
| 333.041
|
|  
|
|  
|
|  
|-
|-
|33/26
| 33/26
|412.745
| 412.745
|
|  
|
|  
|
|  
|-
|-
|33/25
| 33/25
|480.646
| 480.646
|
|  
|
|  
|
|  
|-
|-
|46/33
| 46/33
|575.001
| 575.001
|
|  
|
|  
|
|  
|-
|-
|33/23
| 33/23
|624.999
| 624.999
|
|  
|
|  
|
|  
|-
|-
|50/33
| 50/33
|719.354
| 719.354
|
|  
|
|  
|
|  
|-
|-
|52/33
| 52/33
|787.255
| 787.255
|
|  
|
|  
|
|  
|-
|-
|33/20
| 33/20
|866.959
| 866.959
|
|  
|
|  
|
|  
|-
|-
|56/33
| 56/33
|915.553
| 915.553
|
|  
|
|  
|
|  
|-
|-
|33/19
| 33/19
|955.76
| 955.76
|
|  
|
|  
|
|  
|-
|-
|58/33
| 58/33
|976.304
| 976.304
|
|  
|
|  
|
|  
|-
|-
|62/33
| 62/33
|1091.763
| 1091.763
|
|  
|
|  
|
|  
|-
|-
|64/33
| 64/33
|1146.727
| 1146.727
|
|  
|
|  
|
|  
|-
|-
|33/17
| 33/17
|1148.318
| 1148.318
|
|  
|
|  
|
|  
|}
|}
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).

Revision as of 15:29, 23 September 2025

← 31-odd-limit  33-odd-limit  35-odd-limit →

The 33-odd-limit is the set of all rational intervals which can be written as 2k(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.

Below is a list of all octave-reduced intervals in the 33-odd-limit.

Ratio Size (¢) Color name Name
34/33 51.682
33/32 53.273
33/31 108.237
33/29 223.696
38/33 244.24
33/28 284.447
40/33 333.041
33/26 412.745
33/25 480.646
46/33 575.001
33/23 624.999
50/33 719.354
52/33 787.255
33/20 866.959
56/33 915.553
33/19 955.76
58/33 976.304
62/33 1091.763
64/33 1146.727
33/17 1148.318

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).

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