19-limit: Difference between revisions
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The 19-limit is a [[Rank and codimension|rank-8]] system, and can be modeled in a 7-dimensional [[lattice]], with the primes 3, 5, 7, 11, 13, 17, and 19 represented by each dimension. The prime 2 does not appear in the typical 19-limit lattice because octave equivalence is presumed. If octave equivalence is not presumed, an eighth dimension is need. | The 19-limit is a [[Rank and codimension|rank-8]] system, and can be modeled in a 7-dimensional [[lattice]], with the primes 3, 5, 7, 11, 13, 17, and 19 represented by each dimension. The prime 2 does not appear in the typical 19-limit lattice because octave equivalence is presumed. If octave equivalence is not presumed, an eighth dimension is need. | ||
These things are contained by the 19-limit, but not the 17-limit: | |||
* The [[19-odd-limit|19-]] and [[21-odd-limit]]; | |||
* Mode 10 and 11 of the harmonic or subharmonic series. | |||
== Terminology and notation == | == Terminology and notation == | ||
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; [[Joseph Monzo]] | ; [[Joseph Monzo]] | ||
* [https://www.youtube.com/watch?v=it5avwRE8PI ''Theme from Invisible Haircut''] (1990) | * [https://www.youtube.com/watch?v=it5avwRE8PI ''Theme from Invisible Haircut''] (1990) | ||
[[Category:19-limit| ]] <!-- main article --> | [[Category:19-limit| ]] <!-- main article --> |