37-odd-limit: Difference between revisions
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{{Odd-limit navigation}} | {{Odd-limit navigation|37}} | ||
{{Odd-limit intro|37}} | |||
* [[1/1]] | * [[1/1]] | ||
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{| class="wikitable" | {| class="wikitable" | ||
! Ratio | |||
! Size ([[cents|¢]]) | |||
! Color name | |||
! Name | |||
|- | |- | ||
|38/37 | | 38/37 | ||
|46.169 | | 46.169 | ||
| | | | ||
| | | | ||
|- | |- | ||
|37/36 | | 37/36 | ||
|47.434 | | 47.434 | ||
| | | | ||
| | | | ||
|- | |- | ||
|37/35 | | 37/35 | ||
|96.204 | | 96.204 | ||
| | | | ||
| | | | ||
|- | |- | ||
|40/37 | | 40/37 | ||
|134.97 | | 134.97 | ||
| | | | ||
| | | | ||
|- | |- | ||
|37/34 | | 37/34 | ||
|146.389 | | 146.389 | ||
| | | | ||
| | | | ||
|- | |- | ||
|37/33 | | 37/33 | ||
|198.071 | | 198.071 | ||
| | | | ||
| | | | ||
|- | |- | ||
|42/37 | | 42/37 | ||
|219.437 | | 219.437 | ||
| | | | ||
| | | | ||
|- | |- | ||
|37/32 | | 37/32 | ||
|251.344 | | 251.344 | ||
| | | | ||
| | | | ||
|- | |- | ||
|44/37 | | 44/37 | ||
|299.974 | | 299.974 | ||
| | | | ||
| | | | ||
|- | |- | ||
|37/31 | | 37/31 | ||
|306.308 | | 306.308 | ||
| | | | ||
| | | | ||
|- | |- | ||
|37/30 | | 37/30 | ||
|363.075 | | 363.075 | ||
| | | | ||
| | | | ||
|- | |- | ||
|46/37 | | 46/37 | ||
|376.93 | | 376.93 | ||
| | | | ||
| | | | ||
|- | |- | ||
|37/29 | | 37/29 | ||
|421.767 | | 421.767 | ||
| | | | ||
| | | | ||
|- | |- | ||
|48/37 | | 48/37 | ||
|450.611 | | 450.611 | ||
| | | | ||
| | | | ||
|- | |- | ||
|37/28 | | 37/28 | ||
|482.518 | | 482.518 | ||
| | | | ||
| | | | ||
|- | |- | ||
|50/37 | | 50/37 | ||
|521.283 | | 521.283 | ||
| | | | ||
| | | | ||
|- | |- | ||
|37/27 | | 37/27 | ||
|545.479 | | 545.479 | ||
| | | | ||
| | | | ||
|- | |- | ||
|52/37 | | 52/37 | ||
|589.184 | | 589.184 | ||
| | | | ||
| | | | ||
|- | |- | ||
|37/26 | | 37/26 | ||
|610.816 | | 610.816 | ||
| | | | ||
| | | | ||
|- | |- | ||
|54/37 | | 54/37 | ||
|654.521 | | 654.521 | ||
| | | | ||
| | | | ||
|- | |- | ||
|37/25 | | 37/25 | ||
|678.717 | | 678.717 | ||
| | | | ||
| | | | ||
|- | |- | ||
|56/37 | | 56/37 | ||
|717.482 | | 717.482 | ||
| | | | ||
| | | | ||
|} | |} | ||
The smallest [[equal division of the octave]] which is consistent to the 37-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]]. | The smallest [[equal division of the octave]] which is consistent to the 37-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]]. | ||
Revision as of 15:35, 23 September 2025
The 37-odd-limit is the set of all rational intervals which can be written as 2k(a/b) where a, b ≤ 37 and k is an integer. To the 35-odd-limit, it adds 18 pairs of octave-reduced intervals involving 37.
Below is a list of all octave-reduced intervals in the 37-odd-limit.
- 1/1
- 38/37, 37/19
- 37/36, 72/37
- 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
- 37/35, 70/37
- 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
- 40/37, 37/20
- 13/12, 24/13
- 38/35, 35/19
- 25/23, 46/25
- 37/34, 68/37
- 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
- 37/33, 66/37
- 9/8, 16/9
- 35/31, 62/35
- 26/23, 23/13
- 17/15, 30/17
- 42/37, 37/21
- 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
- 37/32, 64/37
- 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
- 44/37, 37/22
- 25/21, 42/25
- 31/26, 52/31
- 37/31, 62/37
- 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
- 37/30, 60/37
- 21/17, 34/21
- 26/21, 21/13
- 31/25, 50/31
- 36/29, 29/18
- 46/37, 37/23
- 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
- 37/29, 58/37
- 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
- 48/37, 37/24
- 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
- 37/28, 56/37
- 4/3, 3/2
- 35/26, 52/35
- 31/23, 46/31
- 27/20, 40/27
- 50/37, 37/25
- 23/17, 34/23
- 42/31, 31/21
- 19/14, 28/19
- 34/25, 25/17
- 15/11, 22/15
- 26/19, 19/13
- 37/27, 54/37
- 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
- 52/37, 37/26
- 38/27, 27/19
- 31/22, 44/31
- 24/17, 17/12
| Ratio | Size (¢) | Color name | Name |
|---|---|---|---|
| 38/37 | 46.169 | ||
| 37/36 | 47.434 | ||
| 37/35 | 96.204 | ||
| 40/37 | 134.97 | ||
| 37/34 | 146.389 | ||
| 37/33 | 198.071 | ||
| 42/37 | 219.437 | ||
| 37/32 | 251.344 | ||
| 44/37 | 299.974 | ||
| 37/31 | 306.308 | ||
| 37/30 | 363.075 | ||
| 46/37 | 376.93 | ||
| 37/29 | 421.767 | ||
| 48/37 | 450.611 | ||
| 37/28 | 482.518 | ||
| 50/37 | 521.283 | ||
| 37/27 | 545.479 | ||
| 52/37 | 589.184 | ||
| 37/26 | 610.816 | ||
| 54/37 | 654.521 | ||
| 37/25 | 678.717 | ||
| 56/37 | 717.482 |
The smallest equal division of the octave which is consistent to the 37-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.