Kite's thoughts on 41edo Lattices: Difference between revisions
changed "off zone" to "complex zone" |
m TallKite moved page 41edo Lattices to Kite's thoughts on 41edo Lattices: Editor VectorGraphics has repeatedly edited pages I've written about my own research and inserted misinformation. On discord he is openly hostile to me. This move is necessary to avoid a toxic work environment for me. |
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== Lattices == | == Lattices == | ||
=== The 5-limit (ya) Lattice === | === The 5-limit (ya) Lattice === | ||
This lattice uses [[Ups and | This lattice uses [[Ups and downs notation|ups and downs notation]] to name the [[41-edo|41-edo (aka 41-equal)]] notes: | ||
[[File:41equal lattice 5-limit.png|none|thumb|456x456px]] | [[File:41equal lattice 5-limit.png|none|thumb|456x456px]] | ||
The middle row is a chain of 5ths. Moving one step to the right (aka '''fifthwards''') adds a 5th, and one step to the left ('''fourthwards''') adds a 4th. Just like the 12-equal circle of 5ths, octave equivalence is assumed and each note represents an entire pitch class. Moving diagonally right-and-up (the 1:00 direction) adds a downmajor 3rd, 5/4. This '''yoward''' step adds prime 5. Moving '''guward''' left-and-down subtracts prime 5. (The terms yo and gu come from [[color notation]].) Since moving 5thwards/4thwards adds/subtracts prime 3, and the octave is prime 2, every octave-reduced 5-limit ratio appears exactly once in the lattice. Thus the lattice is a "map" of all possible 5-limit notes. | The middle row is a chain of 5ths. Moving one step to the right (aka '''fifthwards''') adds a 5th, and one step to the left ('''fourthwards''') adds a 4th. Just like the 12-equal circle of 5ths, octave equivalence is assumed and each note represents an entire pitch class. Moving diagonally right-and-up (the 1:00 direction) adds a downmajor 3rd, 5/4. This '''yoward''' step adds prime 5. Moving '''guward''' left-and-down subtracts prime 5. (The terms yo and gu come from [[color notation]].) Since moving 5thwards/4thwards adds/subtracts prime 3, and the octave is prime 2, every octave-reduced 5-limit ratio appears exactly once in the lattice. Thus the lattice is a "map" of all possible 5-limit notes. | ||