17-limit
In 17-limit Just Intonation, all ratios in the system will contain no primes higher than 17. The 17-limit adds to the 13-limit a "minor ninth" of about 105¢ -- 17/16 -- and several other intervals between the 17th overtone and the lower ones.
17-limit Intervals
Here are all the 21-odd-limit intervals of 17:
| Ratio | Cents Value | Color Name | Name | |
|---|---|---|---|---|
| 18/17 | 98.955 | 17u1 | su 1sn | small septendecimal semitone |
| 17/16 | 104.955 | 17o2 | so 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 |
| 21/17 | 365.825 | 17uz3 | suzo 3rd | septendecimal submajor 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 | 1st septendecimal tritone |
| 17/12 | 603.000 | 17o5 | so 5th | 2nd septendecimal tritone |
| 26/17 | 735.572 | 17u3o5 | sutho 5th | septendecimal super-fifth |
| 17/11 | 753.637 | 17o1u6 | solu 6th | septendecimal subminor sixth |
| 34/21 | 834.175 | 17uz6 | suzo 6th | septendecimal superminor 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 | so 8ve | large septendecimal major seventh |
To avoid confusion with the solfege syllable So, the so 2nd, 5th and 8ve are sometimes called the iso 2nd, 5th and 8ve.