17-limit: Difference between revisions
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{{Prime limit navigation|17}} | {{Prime limit navigation|17}} | ||
The '''17-limit''' consists of [[just intonation]] [[interval]]s whose [[ratio]]s contain no [[prime factor]]s 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 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. | The 17-prime-limit is a [[Rank and codimension|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 == | == Edo approximations == | ||
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{| class="wikitable" | {| class="wikitable" | ||
|- | |- | ||
! | ! Ratio | ||
! | ! Cents Value | ||
! colspan="2" |[[Kite's color notation|Color Name]] | ! colspan="2" |[[Kite's color notation|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 | |||
|} | |} | ||