Kite's thoughts on 41edo Lattices: Difference between revisions

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== Lattices ==

=== The 5-limit (ya) Lattice ===

This lattice uses [[Ups and ~~Downs Notation~~|ups and downs notation]] to name the [[41-edo|41-edo (aka 41-equal)]] notes:

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]]

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.

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== Commas Part II ==

The Kite guitar fretboard is made up of alternating rainbow zones and ~~off~~ zones. Playing a Gu or Ru pump on the Kite guitar forces one to either shift a pitch or walk into the ~~off~~ zone. Going into the ~~off~~ zone makes the tonic drift sharp or flat by half a fret. But playing a Saruyo pump forces one to walk up the neck clear through the ~~off~~ zone into the next rainbow zone. The tonic drifts flat and then sharp! Depending on the melody, this can result in the scale temporarily containing offperfect tonics, 4ths and 5ths, which can be disconcerting.

The Kite guitar fretboard is made up of alternating rainbow zones and complex zones. Playing a Gu or Ru pump on the Kite guitar forces one to either shift a pitch or walk into the complex zone. Going into the complex zone makes the tonic drift sharp or flat by half a fret. But playing a Saruyo pump forces one to walk up the neck clear through the complex zone into the next rainbow zone. The tonic drifts flat and then sharp! Depending on the melody, this can result in the scale temporarily containing offperfect tonics, 4ths and 5ths, which can be disconcerting.

We can call Saruyo a walk-once comma, and Ru and Gu walk-halfway commas. All no-fret commas are no-walk, walk-once, walk-twice, etc. All half-fret commas are walk-halfway, walk-one-and-a-half, etc.

@@ Line 4: / Line 4: @@
 == Lattices ==
 === The 5-limit (ya) Lattice ===
-This lattice uses [[Ups and Downs Notation|ups and downs notation]] to name the [[41-edo|41-edo (aka 41-equal)]] notes:
+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]]
 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.
@@ Line 131: / Line 131: @@
 == Commas Part II ==
-The Kite guitar fretboard is made up of alternating rainbow zones and off zones. Playing a Gu or Ru pump on the Kite guitar forces one to either shift a pitch or walk into the off zone. Going into the off zone makes the tonic drift sharp or flat by half a fret. But playing a Saruyo pump forces one to walk up the neck clear through the off zone into the next rainbow zone. The tonic drifts flat and then sharp! Depending on the melody, this can result in the scale temporarily containing offperfect tonics, 4ths and 5ths, which can be disconcerting.
+The Kite guitar fretboard is made up of alternating rainbow zones and complex zones. Playing a Gu or Ru pump on the Kite guitar forces one to either shift a pitch or walk into the complex zone. Going into the complex zone makes the tonic drift sharp or flat by half a fret. But playing a Saruyo pump forces one to walk up the neck clear through the complex zone into the next rainbow zone. The tonic drifts flat and then sharp! Depending on the melody, this can result in the scale temporarily containing offperfect tonics, 4ths and 5ths, which can be disconcerting.
 We can call Saruyo a walk-once comma, and Ru and Gu walk-halfway commas. All no-fret commas are no-walk, walk-once, walk-twice, etc. All half-fret commas are walk-halfway, walk-one-and-a-half, etc.