37-odd-limit: Difference between revisions
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{{Odd-limit navigation}}The 37'''-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'' ≤ 37 and ''k'' is an integer. To the [[ | {{Odd-limit navigation}}The 37'''-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'' ≤ 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. | Below is a list of all octave-reduced intervals in the 37-odd-limit. | ||
* [[1/1]] | * [[1/1]] | ||
* [[38/37]], [[37/19]] | * '''[[38/37]], [[37/19]]''' | ||
* [[37/36]], [[72/37]] | * '''[[37/36]], [[72/37]]''' | ||
* [[36/35]], [[35/18]] | * [[36/35]], [[35/18]] | ||
* [[35/34]], [[68/35]] | * [[35/34]], [[68/35]] | ||
| Line 24: | Line 24: | ||
* [[20/19]], [[19/10]] | * [[20/19]], [[19/10]] | ||
* [[19/18]], [[36/19]] | * [[19/18]], [[36/19]] | ||
* [[37/35]], [[70/37]] | * '''[[37/35]], [[70/37]]''' | ||
* [[18/17]], [[17/9]] | * [[18/17]], [[17/9]] | ||
* [[35/33]], [[66/35]] | * [[35/33]], [[66/35]] | ||
| Line 35: | Line 35: | ||
* [[14/13]], [[13/7]] | * [[14/13]], [[13/7]] | ||
* [[27/25]], [[50/27]] | * [[27/25]], [[50/27]] | ||
* [[40/37]], [[37/20]] | * '''[[40/37]], [[37/20]]''' | ||
* [[13/12]], [[24/13]] | * [[13/12]], [[24/13]] | ||
* [[38/35]], [[35/19]] | * [[38/35]], [[35/19]] | ||
* [[25/23]], [[46/25]] | * [[25/23]], [[46/25]] | ||
* [[37/34]], [[68/37]] | * '''[[37/34]], [[68/37]]''' | ||
* [[12/11]], [[11/6]] | * [[12/11]], [[11/6]] | ||
* [[35/32]], [[64/35]] | * [[35/32]], [[64/35]] | ||
| Line 52: | Line 52: | ||
* [[19/17]], [[34/19]] | * [[19/17]], [[34/19]] | ||
* [[28/25]], [[25/14]] | * [[28/25]], [[25/14]] | ||
* [[37/33]], [[66/37]] | * '''[[37/33]], [[66/37]]''' | ||
* [[9/8]], [[16/9]] | * [[9/8]], [[16/9]] | ||
* [[35/31]], [[62/35]] | * [[35/31]], [[62/35]] | ||
* [[26/23]], [[23/13]] | * [[26/23]], [[23/13]] | ||
* [[17/15]], [[30/17]] | * [[17/15]], [[30/17]] | ||
* [[42/37]], [[37/21]] | * '''[[42/37]], [[37/21]]''' | ||
* [[25/22]], [[44/25]] | * [[25/22]], [[44/25]] | ||
* [[33/29]], [[58/33]] | * [[33/29]], [[58/33]] | ||
| Line 65: | Line 65: | ||
* [[38/33]], [[33/19]] | * [[38/33]], [[33/19]] | ||
* [[15/13]], [[26/15]] | * [[15/13]], [[26/15]] | ||
* [[37/32]], [[64/37]] | * '''[[37/32]], [[64/37]]''' | ||
* [[22/19]], [[19/11]] | * [[22/19]], [[19/11]] | ||
* [[29/25]], [[50/29]] | * [[29/25]], [[50/29]] | ||
| Line 77: | Line 77: | ||
* [[32/27]], [[27/16]] | * [[32/27]], [[27/16]] | ||
* [[19/16]], [[32/19]] | * [[19/16]], [[32/19]] | ||
* [[44/37]], [[37/22]] | * '''[[44/37]], [[37/22]]''' | ||
* [[25/21]], [[42/25]] | * [[25/21]], [[42/25]] | ||
* [[31/26]], [[52/31]] | * [[31/26]], [[52/31]] | ||
* [[37/31]], [[62/37]] | * '''[[37/31]], [[62/37]]''' | ||
* [[6/5]], [[5/3]] | * [[6/5]], [[5/3]] | ||
* [[35/29]], [[58/35]] | * [[35/29]], [[58/35]] | ||
| Line 92: | Line 92: | ||
* [[27/22]], [[44/27]] | * [[27/22]], [[44/27]] | ||
* [[16/13]], [[13/8]] | * [[16/13]], [[13/8]] | ||
* [[37/30]], [[60/37]] | * '''[[37/30]], [[60/37]]''' | ||
* [[21/17]], [[34/21]] | * [[21/17]], [[34/21]] | ||
* [[26/21]], [[21/13]] | * [[26/21]], [[21/13]] | ||
* [[31/25]], [[50/31]] | * [[31/25]], [[50/31]] | ||
* [[36/29]], [[29/18]] | * [[36/29]], [[29/18]] | ||
* [[46/37]], [[37/23]] | * '''[[46/37]], [[37/23]]''' | ||
* [[5/4]], [[8/5]] | * [[5/4]], [[8/5]] | ||
* [[44/35]], [[35/22]] | * [[44/35]], [[35/22]] | ||
| Line 106: | Line 106: | ||
* [[33/26]], [[52/33]] | * [[33/26]], [[52/33]] | ||
* [[14/11]], [[11/7]] | * [[14/11]], [[11/7]] | ||
* [[37/29]], [[58/37]] | * '''[[37/29]], [[58/37]]''' | ||
* [[23/18]], [[36/23]] | * [[23/18]], [[36/23]] | ||
* [[32/25]], [[25/16]] | * [[32/25]], [[25/16]] | ||
| Line 114: | Line 114: | ||
* [[22/17]], [[17/11]] | * [[22/17]], [[17/11]] | ||
* [[35/27]], [[54/35]] | * [[35/27]], [[54/35]] | ||
* [[48/37]], [[37/24]] | * '''[[48/37]], [[37/24]]''' | ||
* [[13/10]], [[20/13]] | * [[13/10]], [[20/13]] | ||
* [[30/23]], [[23/15]] | * [[30/23]], [[23/15]] | ||
| Line 124: | Line 124: | ||
* [[29/22]], [[44/29]] | * [[29/22]], [[44/29]] | ||
* [[33/25]], [[50/33]] | * [[33/25]], [[50/33]] | ||
* [[37/28]], [[56/37]] | * '''[[37/28]], [[56/37]]''' | ||
* [[4/3]], [[3/2]] | * [[4/3]], [[3/2]] | ||
* [[35/26]], [[52/35]] | * [[35/26]], [[52/35]] | ||
* [[31/23]], [[46/31]] | * [[31/23]], [[46/31]] | ||
* [[27/20]], [[40/27]] | * [[27/20]], [[40/27]] | ||
* [[50/37]], [[37/25]] | * '''[[50/37]], [[37/25]]''' | ||
* [[23/17]], [[34/23]] | * [[23/17]], [[34/23]] | ||
* [[42/31]], [[31/21]] | * [[42/31]], [[31/21]] | ||
| Line 136: | Line 136: | ||
* [[15/11]], [[22/15]] | * [[15/11]], [[22/15]] | ||
* [[26/19]], [[19/13]] | * [[26/19]], [[19/13]] | ||
* [[37/27]], [[54/37]] | * '''[[37/27]], [[54/37]]''' | ||
* [[48/35]], [[35/24]] | * [[48/35]], [[35/24]] | ||
* [[11/8]], [[16/11]] | * [[11/8]], [[16/11]] | ||
| Line 146: | Line 146: | ||
* [[46/33]], [[33/23]] | * [[46/33]], [[33/23]] | ||
* [[7/5]], [[10/7]] | * [[7/5]], [[10/7]] | ||
* [[52/37]], [[37/26]] | * '''[[52/37]], [[37/26]]''' | ||
* [[38/27]], [[27/19]] | * [[38/27]], [[27/19]] | ||
* [[31/22]], [[44/31]] | * [[31/22]], [[44/31]] | ||
Revision as of 21:27, 18 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.