Kite's color notation: Difference between revisions

== Chord Names ==

Triads are named after their 3rd, e.g. Cy. "Yo C" is a note, "C yo" is a chord. A chord is a list of intervals: a yo chord = (w1 y3 w5). The four main yaza triads:[[File:lattice62.png|alt=lattice62.png|640x138px|lattice62.png]]

If the root isn't wa, the root color is added to the interval color. The yo A gu chord = yAg = yA + (w1 g3 w5) = yA + wC + yE.

Tetrads are named Cy6 ("C yo six"), Dg7, etc. The 11 main yaza tetrads, with chord homonyms (same shape, different root) equated:

[[File:Lattice63.png|639x639px]]

The y,z7 chord is also called the h7 chord ("aitch-seven"), because it's part of the harmonic series. The s7 ("sub-seven") chord is part of the subharmonic series. It's the first 7 subharmonics, with the 3rd subharmonic becoming the root. Note that s7 has no 7th. There are h9 chords, s11 chords, etc. The number must be odd, Ch8 is invalid. Ch9,13 = w1 y3 w5 z7 w9 3o13 has an added 13th harmonic.

A 9th chord contains a 3rd, 5th and 7th. An 11th chord contains all these plus a 9th. A 13th chord contains all these plus an 11th. The 5th, 9th and/or 13th default to wa. The 6th, 7th, and/or 11th default to the color of the 3rd. Thus Cy13 = w1 y3 w5 y7 w9 y11 w13, and Cy9 and Cy11 are subsets of this chord. However, an add-11 chord defaults to a wa 11: Cz7,11 = w1 z3 w5 z7 w11. Added 9ths also default to wa: Cy,9 = w1 y3 w5 w9. 

<u>Alterations are always in parentheses</u>, additions never are, e.g. z7(zg5). An alteration's degree must match a note in the chord, e.g. z7(y6) is invalid. But an exception is made for sus chords, where degree 2 or 4 alter the 3rd: C(z4) = w1 z4 w5. The sus note defaults to wa: Cy9(4) = w1 w4 w5 y7 w9.

Omissions are indicated by "no", the Hendrix chord might be Ch7z10no5. <u>Enharmonic substitutions aren't allowed</u>, 7/3 is a m10, not an A9. A no3 chord can also be written as a 5 chord with an added note: C5z7 = w1 w5 z7, and C(zg5)z7 = w1 zg5 z7. Omissions in harmonic and subharmonic chords refer to degree not harmonic. Ch11no3 omits y3, not the 3rd harmonic w5. However, numbers ≥ 15 always refer to (sub)harmonics, as in Ch15 or Cs15. 

Notes on the staff default to wa. Non-wa notes have a color accidental like g, ry, etc. Like conventional sharp/flat accidentals, they apply to every such note in the measure and in the same octave. Unlike conventional accidentals which apply to a note (e.g. A), color accidentals only apply to one specific "version" of that note (e.g. A flat or A natural). For example, the yo accidental in the first chord applies to all the D naturals in that measure, but not to the D flats.

[[File:Notation example 1.png|frameless|781x781px]]

Staff notation can optionally include a color signature written above the staff. This makes color notation more similar to Johnston notation.

[[File:Notation example 2.png|786x786px]]

Color notation can optionally be made more similar to Sagittal notation by including two more accidentals, p and q (long forms po and qu = "ku"), to indicate raising/lowering by a pythagorean comma. For example, yF# = ypG♭, and zE♭= zqD#. This allows trills to always be written as a 2nd, less cluttered.[[File:Notation example 5a.png|992x992px]]

The tonic is always wa. The root of each chord has a color, which defaults to wa. C - Am - F - G7 might be Cy - yAg - Fy - Gy,w7.

In relative notation, the I, IV and V chords default to a wa root. II, III, VI and VII <u>must</u> have an explicit root-color. gCy - gGy - Ag becomes gIIIy - gVIIy - Ig.  

Keys are named after the colors used. The B♭h7 - E♭h7 - B♭h7 - Fh9 example above is in B♭ yo zo. Analogous to the relative and parallel major or minor, one can modulate to relative gu, parallel ru, etc. Modulating from a yo key to the relative gu means using gu chords on yo roots. Modulating from yo to the parallel gu = using gu chords on wa roots. Going from yo zo to the relative gu = using gu7 or gu ru-6 chords on yo roots. Going to the relative ru = same chords on zo roots.   

Temperaments are named after the color of the comma(s) they temper out. Meantone = the green temperament = gT. 5-limit Porcupine = triple yo = y³T. 7-limit Porcupine = triple yo and ru = y³&rT. Each porcupine has a different name, thus color names provide more information than standard temperament names. Both porcupines have the same [[pergen]], third-4th, thus pergens group together similar temperaments.         

The magnitude is part of the name: Schismic is LyT and shrutal is sggT. The degree is too, but only if the comma is not the smallest of the 7 ratios of that magnitude and color: Mavila is Ly1T and [[Father]] is g2T. The temperament name indicates the prime subgroup and the rank of the temperament. Thus ryyT ([[Marvel]]) is rank-3 because it has 2 explicit colors ru and yo and 2 implicit colors wa and clear, and 4 colors minus 1 comma = rank-3.         

If the comma is wa, an edo is implied. The temperament is named after the edo, not the comma. If the comma(s) don't include every prime in the subgroup, some primes are untempered. These are "plus" temperaments: Blackwood is 5edo+yT = 5-edo plus ya. 2.3.5.7 and 81/80 is g+zT = gu plus za.      

There are two ways to name multi-comma temperaments. The odd name minimizes the odd limit of the comma set, and the prime name minimizes the number and size of the primes used by each comma. The odd name for 7-limit [[Pajara]] is rryy&rT, and the prime name is sgg&rT. Often the two names are identical, e.g. y³&rT. The odd name is often shorter, and usually indicates commas more likely to be pumped. The prime name shows relationships between single-comma temperaments better. The question of which name to use is not yet fully resolved.         

Color notation merely renames ratios more conveniently, and strictly speaking, it only applies to just intonation. However, just as ratios can loosely describe edo notes, colors can be loosely applied to edos as well. A more precise application is to use ups and downs (^ and v) as "virtual colors", accidentals that always map to exactly one edostep. Notes are named up C sharp = ^C#. Ups and downs are used on the score just like color accidentals are. Intervals are named upmajor 3rd = ^M3, down 4th = v4, etc. Chords are named upminor 7th = ^m7, etc.                 

Rank-2 temperaments can be notated with ups and downs as well. Some require another accidental pair, lifts and drops (/ and \). See the [[Pergen|pergens]] page.