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.
 * [[1/1]]
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 {| class="wikitable"
-!Ratio
+! Ratio
-!Size ([[Cents|¢]])
+! Size ([[Cents|¢]])
 ! 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).