User:Squib/Unnamed music theory: Difference between revisions
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==Theory== | ==Theory== | ||
This theory organizes pitches as points on a 2D lattice defined by primes 2 and 3, then divides that lattice into a fixed number of pitch classes ("colors") which can be used to approximate other primes. The result of this is a clearly specified tuning | This theory organizes pitches as points on a 2D lattice defined by primes 2 and 3, then divides that lattice into a fixed number of pitch classes ("colors") which can be used to approximate other primes. The result of this is a clearly specified tuning and layout that uses colors to intuitively show harmonic relationships and progression. | ||
==Derivation== | ==Derivation== | ||
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[[File:First 33 tunings.jpg|thumb|Sketch of the 33 tunings from n=1 to n=6 in no particular order, and example intervals in the top right]] | [[File:First 33 tunings.jpg|thumb|Sketch of the 33 tunings from n=1 to n=6 in no particular order, and example intervals in the top right]] | ||
==Random== | |||
In two dimensions, the number of tunings with N colors is the sum of the unique factors of N. So there are 6+3+2+1=12 6-color tunings in two dimensions. The amount of *three*-dimensional tunings with N colors is the sum of the factors of N times the sum of *their* factors. So the number of 3D 6-color tunings is 6(6+3+2+1)+3(3+1)+2(2+1)+1(1) = 91. | |||