19-limit: Difference between revisions
Move from "Music in just intonation" page |
+a note on the categorization of 19-limit intervals |
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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. | ||
== Terminology and notation == | |||
19/16 is most commonly considered a minor third, as 1-19/16-3/2 is an important {{w|tertian}} chord. The [[Functional Just System]] and [[Helmholtz-Ellis notation]] agree. However, 19/16 may act as an augmented second in certain cases. This is more complex on its own but may simplify certain combinations with other intervals, especially if [[17/16]] is considered augmented unison and/or if [[23/16]] is considered an augmented fourth. Perhaps most interestingly, [[Sagittal notation]] provides an accidental to enharmonically spell intervals of [[harmonic class|HC19]] this way. | |||
== Edo approximations == | == Edo approximations == | ||