17-limit: Difference between revisions

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In 17-limit [[~~Just_intonation|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.

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.

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 need.

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[[EDO]]s which provides an excellent tuning for 17-limit intervals are: 46, 58, 72, 80, 94, 111, 121, 149, 159, 183, 217, 253, 270, 282, 301, 311, 320, 354, 364, 383, 388, 400, 414, 422, 436, 441, 460, 494, 525, 535, 581, 597, 615, 624, 639, 643, 653, 684, 692, 718, 742, 764, 771, 776, 814, 860, 867, 882, 894, 908, 925, 935, 954, 981, 995, and 997 among others.

==17-limit ~~Intervals~~==

== 17-limit intervals ==

Here are all the [[21-odd-limit]] intervals of 17:

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* [[Harmonic limit]]

* [[17-odd-limit]]

* [[~~seventeen~~ limit tetrads]]

* [[Seventeen limit tetrads]]

[[Category:17-limit| ]]

~~[[Category:Limit]]~~

[[Category:Prime limit]]

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-In 17-limit [[Just_intonation|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.
+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.
 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 need.
@@ Line 5: / Line 5: @@
 [[EDO]]s which provides an excellent tuning for 17-limit intervals are: 46, 58, 72, 80, 94, 111, 121, 149, 159, 183, 217, 253, 270, 282, 301, 311, 320, 354, 364, 383, 388, 400, 414, 422, 436, 441, 460, 494, 525, 535, 581, 597, 615, 624, 639, 643, 653, 684, 692, 718, 742, 764, 771, 776, 814, 860, 867, 882, 894, 908, 925, 935, 954, 981, 995, and 997 among others.
-==17-limit Intervals==
+== 17-limit intervals ==
 Here are all the [[21-odd-limit]] intervals of 17:
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 * [[Harmonic limit]]
 * [[17-odd-limit]]
-* [[seventeen limit tetrads]]
+* [[Seventeen limit tetrads]]
 [[Category:17-limit| ]] <!-- main article -->
-[[Category:Limit]]
 [[Category:Prime limit]]