35-odd-limit: Difference between revisions
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{{Odd-limit navigation}} | {{Odd-limit navigation|35}} | ||
{{Odd-limit intro|35}} | |||
* [[1/1]] | * [[1/1]] | ||
| Line 134: | Line 133: | ||
{| class="wikitable" | {| class="wikitable" | ||
! Ratio | |||
! Size ([[cents|¢]]) | |||
! Color name | |||
! Name | |||
|- | |- | ||
|36/35 | | 36/35 | ||
|48.77 | | 48.77 | ||
| | | | ||
| | | | ||
|- | |- | ||
|35/34 | | 35/34 | ||
|50.184 | | 50.184 | ||
| | | | ||
| | | | ||
|- | |- | ||
|35/33 | | 35/33 | ||
|101.867 | | 101.867 | ||
| | | | ||
| | | | ||
|- | |- | ||
|38/35 | | 38/35 | ||
|142.353 | | 142.353 | ||
| | | | ||
| | | | ||
|- | |- | ||
|35/32 | | 35/32 | ||
|155.14 | | 155.14 | ||
| | | | ||
| | | | ||
|- | |- | ||
|35/31 | | 35/31 | ||
|210.104 | | 210.104 | ||
| | | | ||
| | | | ||
|- | |- | ||
|35/29 | | 35/29 | ||
|325.562 | | 325.562 | ||
| | | | ||
| | | | ||
|- | |- | ||
|44/35 | | 44/35 | ||
|396.178 | | 396.178 | ||
| | | | ||
| | | | ||
|- | |- | ||
|35/27 | | 35/27 | ||
|449.275 | | 449.275 | ||
| | | | ||
| | | | ||
|- | |- | ||
|46/35 | | 46/35 | ||
|473.135 | | 473.135 | ||
| | | | ||
| | | | ||
|- | |- | ||
|35/26 | | 35/26 | ||
|514.612 | | 514.612 | ||
| | | | ||
| | | | ||
|- | |- | ||
|48/35 | | 48/35 | ||
|546.815 | | 546.815 | ||
| | | | ||
| | | | ||
|- | |- | ||
|35/24 | | 35/24 | ||
|653.185 | | 653.185 | ||
| | | | ||
| | | | ||
|- | |- | ||
|52/35 | | 52/35 | ||
|685.388 | | 685.388 | ||
| | | | ||
| | | | ||
|- | |- | ||
|35/23 | | 35/23 | ||
|726.865 | | 726.865 | ||
| | | | ||
| | | | ||
|- | |- | ||
|54/35 | | 54/35 | ||
|750.725 | | 750.725 | ||
| | | | ||
| | | | ||
|- | |- | ||
|35/22 | | 35/22 | ||
|803.822 | | 803.822 | ||
| | | | ||
| | | | ||
|- | |- | ||
|58/35 | | 58/35 | ||
|874.438 | | 874.438 | ||
| | | | ||
| | | | ||
|- | |- | ||
|62/35 | | 62/35 | ||
|989.896 | | 989.896 | ||
| | | | ||
| | | | ||
|- | |- | ||
|64/35 | | 64/35 | ||
|1044.86 | | 1044.86 | ||
| | | | ||
| | | | ||
|- | |- | ||
|35/19 | | 35/19 | ||
|1057.627 | | 1057.627 | ||
| | | | ||
| | | | ||
|- | |- | ||
|66/35 | | 66/35 | ||
|1098.133 | | 1098.133 | ||
| | | | ||
| | | | ||
|- | |- | ||
|68/35 | | 68/35 | ||
|1149.816 | | 1149.816 | ||
| | | | ||
| | | | ||
|- | |- | ||
|35/18 | | 35/18 | ||
|1151.23 | | 1151.23 | ||
| | | | ||
| | | | ||
|} | |} | ||
The smallest [[equal division of the octave]] which is consistent to the 35-odd-limit is [[311edo]] (by virtue of it being consistent in the [[41-odd-limit]]); that which is distinctly consistent to the same is [[1600edo]] (by virtue of it being consistent in the [[37 | The smallest [[equal division of the octave]] which is consistent to the 35-odd-limit is [[311edo]] (by virtue of it being consistent in the [[41-odd-limit]]); that which is distinctly consistent to the same is [[1600edo]] (by virtue of it being consistent in the [[37-odd-limit]]). | ||
Revision as of 15:31, 23 September 2025
The 35-odd-limit is the set of all rational intervals which can be written as 2k(a/b) where a, b ≤ 35 and k is an integer. To the 33-odd-limit, it adds 12 pairs of octave-reduced intervals involving 35.
Below is a list of all octave-reduced intervals in the 35-odd-limit.
- 1/1
- 36/35, 35/18
- 35/34, 68/35
- 34/33, 33/17
- 33/32, 64/33
- 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
- 35/33, 66/35
- 17/16, 32/17
- 33/31, 62/33
- 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
- 38/35, 35/19
- 25/23, 46/25
- 12/11, 11/6
- 35/32, 64/35
- 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
- 35/31, 62/35
- 26/23, 23/13
- 17/15, 30/17
- 25/22, 44/25
- 33/29, 58/33
- 8/7, 7/4
- 31/27, 54/31
- 23/20, 40/23
- 38/33, 33/19
- 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
- 33/28, 56/33
- 13/11, 22/13
- 32/27, 27/16
- 19/16, 32/19
- 25/21, 42/25
- 31/26, 52/31
- 6/5, 5/3
- 35/29, 58/35
- 29/24, 48/29
- 23/19, 38/23
- 40/33, 33/20
- 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
- 44/35, 35/22
- 34/27, 27/17
- 29/23, 46/29
- 24/19, 19/12
- 19/15, 30/19
- 33/26, 52/33
- 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
- 35/27, 54/35
- 13/10, 20/13
- 30/23, 23/15
- 17/13, 26/17
- 38/29, 29/19
- 21/16, 32/21
- 46/35, 35/23
- 25/19, 38/25
- 29/22, 44/29
- 33/25, 50/33
- 4/3, 3/2
- 35/26, 52/35
- 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
- 48/35, 35/24
- 11/8, 16/11
- 40/29, 29/20
- 29/21, 42/29
- 18/13, 13/9
- 25/18, 36/25
- 32/23, 23/16
- 46/33, 33/23
- 7/5, 10/7
- 38/27, 27/19
- 31/22, 44/31
- 24/17, 17/12
| Ratio | Size (¢) | Color name | Name |
|---|---|---|---|
| 36/35 | 48.77 | ||
| 35/34 | 50.184 | ||
| 35/33 | 101.867 | ||
| 38/35 | 142.353 | ||
| 35/32 | 155.14 | ||
| 35/31 | 210.104 | ||
| 35/29 | 325.562 | ||
| 44/35 | 396.178 | ||
| 35/27 | 449.275 | ||
| 46/35 | 473.135 | ||
| 35/26 | 514.612 | ||
| 48/35 | 546.815 | ||
| 35/24 | 653.185 | ||
| 52/35 | 685.388 | ||
| 35/23 | 726.865 | ||
| 54/35 | 750.725 | ||
| 35/22 | 803.822 | ||
| 58/35 | 874.438 | ||
| 62/35 | 989.896 | ||
| 64/35 | 1044.86 | ||
| 35/19 | 1057.627 | ||
| 66/35 | 1098.133 | ||
| 68/35 | 1149.816 | ||
| 35/18 | 1151.23 |
The smallest equal division of the octave which is consistent to the 35-odd-limit is 311edo (by virtue of it being consistent in the 41-odd-limit); that which is distinctly consistent to the same is 1600edo (by virtue of it being consistent in the 37-odd-limit).