17-limit
The 17-limit consists of just intonation intervals whose ratios contain no prime factors higher than 17. The 17-limit adds to the 13-limit a semitone of about 105¢ – 17/16 – and several other intervals between the 17th harmonic and the lower ones.
The 17-prime-limit is a rank-7 system, and can be modeled in a 6-dimensional lattice, with the primes 3, 5, 7, 11, 13, and 17 represented by each dimension. The prime 2 does not appear in the typical 17-limit lattice because octave equivalence is presumed. If octave equivalence is not presumed, a seventh dimension is needed.
Edo approximations
A list of edos with progressively better tunings for 17-limit intervals: 46, 58, 72, 103, 111, 121, 140, 171, 183, 217, 224, 270, 311, 354, 400, 422, 460, 494, 581, 742, 764, 814, 935, 954 and so on.
Another list of edos which provides relatively good tunings for 17-limit intervals (relative error < 5.4%): 46, 58, 72, 87, 94, 103, 111, 121, 130, 140, 171, 183, 190g, 212g, 217, 224, 243e, 270, 282, 301, 311, 320, 328, 342f, 354, 364, 373g, 383, 388, 400, 414, 422, 441, 460, 494, 525, 535, 540, 552g, 566g, 571, 581, 597, 624, 639, 643, 653, 684, 692, 711, 718, 742, 764, 814, 822, 836(f), 863efg, 867, 882, 908, 925, 935, 954 and so on.
- Note: wart notation is used to specify the val chosen for the edo. In the above list, "190g" means taking the second closest approximation of harmonic 17.
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 unison | 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 | lesser septendecimal tritone |
| 17/12 | 603.000 | 17o5 | so 5th | greater 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 octave | 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.