17-odd-limit: Difference between revisions
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{{ | {{Odd-limit navigation|17}} | ||
{{Odd-limit intro|17}} | |||
* [[1/1]] | * [[1/1]] | ||
* '''[[18/17]] | * '''[[18/17]], [[17/9]]''' | ||
* '''[[17/16]] | * '''[[17/16]], [[32/17]]''' | ||
* [[16/15]], [[15/8]] | * [[16/15]], [[15/8]] | ||
* [[15/14]], [[28/15]] | * [[15/14]], [[28/15]] | ||
| Line 13: | Line 13: | ||
* [[10/9]], [[9/5]] | * [[10/9]], [[9/5]] | ||
* [[9/8]], [[16/9]] | * [[9/8]], [[16/9]] | ||
* '''[[17/15]] | * '''[[17/15]], [[30/17]]''' | ||
* [[8/7]], [[7/4]] | * [[8/7]], [[7/4]] | ||
* [[15/13]], [[26/15]] | * [[15/13]], [[26/15]] | ||
* [[7/6]], [[12/7]] | * [[7/6]], [[12/7]] | ||
* '''[[20/17]] | * '''[[20/17]], [[17/10]]''' | ||
* [[13/11]], [[22/13]] | * [[13/11]], [[22/13]] | ||
* [[6/5]], [[5/3]] | * [[6/5]], [[5/3]] | ||
* '''[[17/14]] | * '''[[17/14]], [[28/17]]''' | ||
* [[11/9]], [[18/11]] | * [[11/9]], [[18/11]] | ||
* [[16/13]], [[13/8]] | * [[16/13]], [[13/8]] | ||
| Line 26: | Line 26: | ||
* [[14/11]], [[11/7]] | * [[14/11]], [[11/7]] | ||
* [[9/7]], [[14/9]] | * [[9/7]], [[14/9]] | ||
* '''[[22/17]] | * '''[[22/17]], [[17/11]]''' | ||
* [[13/10]], [[20/13]] | * [[13/10]], [[20/13]] | ||
* '''[[17/13]] | * '''[[17/13]], [[26/17]]''' | ||
* [[4/3]], [[3/2]] | * [[4/3]], [[3/2]] | ||
* [[15/11]], [[22/15]] | * [[15/11]], [[22/15]] | ||
| Line 34: | Line 34: | ||
* [[18/13]], [[13/9]] | * [[18/13]], [[13/9]] | ||
* [[7/5]], [[10/7]] | * [[7/5]], [[10/7]] | ||
* '''[[24/17]] | * '''[[24/17]], [[17/12]]''' | ||
{| class="wikitable center-all right-2 left-5" | {| class="wikitable center-all right-2 left-5" | ||
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| large septendecimal major seventh | | large septendecimal major seventh | ||
|} | |} | ||
The smallest [[equal division of the octave]] which is consistent in the 17-odd-limit is [[58edo]]. | |||
[[ | The one which is distinctly consistent in the same is [[149edo]]. | ||
[[Category: | |||
== See also == | |||
* [[17-limit]] ([[prime limit]]) | |||
[[Category:17-odd-limit| ]] <!-- main article --> | |||
Latest revision as of 13:46, 8 October 2025
The 17-odd-limit is the set of all rational intervals which can be written as 2k(a/b) where a, b ≤ 17 and k is an integer. To the 15-odd-limit, it adds 8 pairs of octave-reduced intervals involving 17.
Below is a list of all octave-reduced intervals in the 17-odd-limit.
- 1/1
- 18/17, 17/9
- 17/16, 32/17
- 16/15, 15/8
- 15/14, 28/15
- 14/13, 13/7
- 13/12, 24/13
- 12/11, 11/6
- 11/10, 20/11
- 10/9, 9/5
- 9/8, 16/9
- 17/15, 30/17
- 8/7, 7/4
- 15/13, 26/15
- 7/6, 12/7
- 20/17, 17/10
- 13/11, 22/13
- 6/5, 5/3
- 17/14, 28/17
- 11/9, 18/11
- 16/13, 13/8
- 5/4, 8/5
- 14/11, 11/7
- 9/7, 14/9
- 22/17, 17/11
- 13/10, 20/13
- 17/13, 26/17
- 4/3, 3/2
- 15/11, 22/15
- 11/8, 16/11
- 18/13, 13/9
- 7/5, 10/7
- 24/17, 17/12
| Ratio | Size (¢) | Color name | Name | |
|---|---|---|---|---|
| 18/17 | 98.955 | 17u1 | su unison | small septendecimal semitone |
| 17/16 | 104.955 | 17o2 | iso 2nd | large septendecimal semitone |
| 17/15 | 216.687 | 17og3 | sogu 3rd | septendecimal whole tone |
| 20/17 | 281.358 | 17uy2 | suyo 2nd | septendecimal minor third |
| 17/14 | 336.130 | 17or3 | soru 3rd | septendecimal supraminor third |
| 22/17 | 446.363 | 17u1o3 | sulo 3rd | septendecimal supermajor third |
| 17/13 | 464.428 | 17o3u4 | sothu 4th | septendecimal sub-fourth |
| 24/17 | 597.000 | 17u4 | su 4th | lesser septendecimal tritone |
| 17/12 | 603.000 | 17o5 | iso 5th | greater septendecimal tritone |
| 26/17 | 735.572 | 17u3o5 | sutho 5th | septendecimal super-fifth |
| 17/11 | 753.637 | 17o1u6 | solu 6th | septendecimal subminor sixth |
| 28/17 | 863.870 | 17uz6 | suzo 6th | septendecimal submajor sixth |
| 17/10 | 918.642 | 17og7 | sogu 7th | septendecimal major sixth |
| 30/17 | 983.313 | 17uy6 | suyo 6th | septendecimal minor seventh |
| 32/17 | 1095.045 | 17u7 | su 7th | small septendecimal major seventh |
| 17/9 | 1101.045 | 17o8 | iso octave | large septendecimal major seventh |
The smallest equal division of the octave which is consistent in the 17-odd-limit is 58edo.
The one which is distinctly consistent in the same is 149edo.