Kite's color notation: Difference between revisions

Color notation has many features that other microtonal notations lack:

* No new symbols: all new accidentals are familiar characters; hence they are immediately speed-readable.

* Furthermore, they are all on the QWERTY keyboard, making the notation easily typeable.

* Most importantly, one can name not only notes but also intervals. As a result, color notation can name scales, chords, chord progressions and even prime subgroups and temperaments.

Every prime above 3 has two colors, an '''over''' color (prime in the numerator) and an '''under''' color (prime in the denominator). Over colors end with -o, and under colors end with -u. The color for 3-limit ends in -a for '''all''', which includes over (3/2, 9/8), under (4/3, 16/9) and neither (1/1, 2/1).   

The colors make a red-yellow-green-blue rainbow, with warm/cool colors indicating sharp/flat intervals. The rainbow of 3rds runs 9/7 - 5/4 - 6/5 - 7/6. Colors are abbreviated as '''w''', '''y''', '''g''', '''z''' and '''r'''. Use z (azure or Spanish/Portuguese azul), not b (blue), because b already means flat. Mnemonic: Z looks like 7 with an extra line on the bottom.

A color and a degree indicate a ratio, and vice versa. Every ratio has a spoken name and a written name. For 3/2, they are wa 5th and w5. Colors and degrees always add up predictably: z3 + g3 = zg5 = zogu 5th. Zogu, not guzo; higher primes always come first. Opposite colors cancel: y3 + g3 = w5.   

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!'''ratio'''

'''Compound''', abbreviated '''co-''' or '''c''', is a [[wikipedia:Interval_(music)#Compound_intervals|conventional music theory term]] that means widened by an octave. 15/4 is a compound yo 7th = coyo 7th = cy7. 5/1 is a double-compound yo 3rd = cocoyo 3rd = ccy3. 9/1 is a tricowa 2nd = c³w2. More examples in the [[Gallery of just intervals#Intervals larger than an octave|Gallery of just intervals]]. Mnemonic: co- as in co-pilot means auxiliary, thus a 9th is a co-2nd. See [[#Prime Subgroup Names]] below for another mnemonic.

Notes are named zEb, yyG#, etc. spoken as "zo E flat" and "yoyo G sharp". Notes are never large or small, only intervals are. Uncolored notes default to wa. The relative-notation lattice above can be mentally superimposed on this absolute-notation lattice to name every note and interval. For example, D + y3 = yF#, and from yE to ryF# = r2.  

[[File:Lattice51.png|frameless|962x962px]]

Just as wa means 3-all or 3-limit, '''ya''' means 5-all and includes wa, yo, gu, yoyo, gugu, etc. Ya = the 2.3.5 prime subgroup = 5-limit. '''Za''' = 7-all = 2.3.7 = no-fives 7-limit. Yaza = 2.3.5.7 = the full 7-limit. '''Nowa''' means without wa, and yaza nowa = 2.5.7.   

Prime 2 (even more colorless than wa) is '''clear''', abbreviated '''ca''', and yaza '''noca''' = 3.5.7 = [[Bohlen-Pierce]]. 2-limit intervals like 2/1 are called wa not clear, for simplicity. '''Nowaca''' means without 2 or 3, thus 5.7.11 is yazala nowaca. Clear/ca is only ever used in the terms noca and nowaca, and in certain theoretical discussions. However, an additional mnemonic for "co-" (compound, widened by an octave) is "clear-over", in the sense that the ratio's numerator is multiplied by 2.  

Colors for primes greater than 7 are named after the number itself, using the prefix '''i-''' for disambiguation as needed:   

|19/16

|23/16

|31/16

|37/32

|53/32

|59/32

|67/64

|-

|twetha

|twena

|thisa

|fowa

|97/64

|101/64

|107/64

|109/64

! word

|fitwewa

|fitwena

|fithitha

This makes the "pseudo-edomapping" <7 11 16 20 24 26 29 30 32 34 37...]. An alternative method would use the actual 7edo [[edomapping]], but that requires using every other 14edostep as boundaries, harder to remember and much less convenient than the 24edo boundaries used here. Since negative intervals will arise no matter what, convenience is prioritized. For the first 26 primes, the 24edo-based degrees correspond to [[Val#Shorthand_notation|7klmrs-edo]].

Exponent syllables aka multiplier syllables provide a way to shorten names that have repeated syllables. For example, 250/243 = 2¹ * 3^-5 * 5³ is a yoyoyo unison which shortens to triyo 1sn. Exponents can apply to magnitudes (Wa-22 = sasasawa 4th --> trisawa 4th) or octaves (13/1 = cococotho 6th --> tricotho 6th).   

*Monzo = [11 -4 -2>, ratio = 2048/2025.

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.

This 10-page score uses the free open-source font Petaluma Script. The letters are 9pt, except that a "z" between two staff lines is 8pt. [[File:Evening Rondo colors.pdf]]

Triads are named after their 3rd, e.g. a yo chord has a yo 3rd. A yo chord rooted on C is a Cy chord = "C yo" = C yE G. Qualities such as major and minor aren't used, because a chord with an 11/9 3rd is hard to classify. Thirdless dyads are written C5 = w1 w5 or C(zg5) = w1 zg5. The four main yaza triads:

Chords can be classified as '''bicolored''' (e.g. g7 or r6), '''tricolored''' (e.g. z7(zg5) or z,y6), '''quadricolored''' (e.g. s6(zg5) or h7,zg9), etc.   

The tonic is always wa. The root of each chord has a color, which defaults to wa. C - Am - F - G7 might become Cy - yAg - Fy - Gy,w7, spoken as "C yo, yo A gu, F yo, G yo wa-seven". If the root isn't wa, the root color is added to each interval's color. Thus yAg = yA + (w1 g3 w5) = yA + wC + yE.   

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 means using gu chords on <u>wa</u> roots. Going from yo zo to the relative gu means using chords with gu and/or ru in them on yo roots. Going to the relative ru means using the same chords on zo roots. Going from yo zo to the parallel gu ru means using the same chords on wa roots. One can also modulate '''fourthward''' or '''fifthward''', abbreviated '''4thwd''' or '''5thwd'''. Modulating in either direction is modulating '''waward'''. Modulating from a yo key to the relative gu, then from there to the parallel yo is modulating '''yoward'''. A root movement by a yo interval (e.g. Iy - yVIg) is a yoward move. Likewise, there's '''guward''', and '''y<u>a</u>ward''' includes both. Likewise, there's '''zoward''', '''ruward''', '''zaward''', '''iloward''', etc.   

Temperaments are named after the comma(s) they temper out. Commas are named using an alternate format that omits the degree. [[Meantone]] is the Gu temperament. [[Srutal]] is Sagugu. [[Porcupine]] is Triyo or y³T, where "T" stands for temperament. Certain commas over 90¢ use the -bi suffix, e.g. [[Mavila]] is Layobi or Ly#2T, because Layo is [[Schismic]]. Certain wa commas use yet another alternate format, e.g. Mercator's comma is Wa-53 or w-53.           

MOS and MODMOS scales can be named as e.g. Triyo[8]. Individual modes can be named as 2nd Triyo[8], 3rd Triyo[7] b7, etc. See [[Naming Rank-2 Scales using Mode Numbers]].           

Color notation merely renames ratios more conveniently, and strictly speaking, it only applies to just intonation. However, ratios are often used to loosely describe intervals in [[EDO|edos]], and colors can be used as well. A more precise notation uses [[Ups and Downs Notation|'''ups''' '''and''' '''downs''']] (^ and v) as "virtual colors", accidentals that always map to exactly one edostep. Ups and downs are used on the score just like color accidentals are. Notes are named e.g. up C sharp = ^C#. Some edos (5, 7, 9, 12, 16, 19, 23, etc.) don't require ups and downs.                 

[[Tour of Regular Temperaments|Rank-2 temperaments]] can be notated with ups and downs as well. Plain and mid are also used in this context. Certain temperaments require an additional pair of virtual colors, '''lifts''' and '''drops''' (/ and \). Notes are named lift C = /C, downdrop F sharp = v\F#, etc. Intervals are named drop 4th = \4, uplift major 3rd = ^/M3, etc. Plain means neither up nor down nor lifted nor dropped. There may be upmid or liftmid intervals. Chords are named C-up add lift-seven = C^,/7 = C ^E G /Bb, C uplift-seven = C^/7 = C ^/E G ^/Bb, etc. See [[Pergen|pergens]].  

'''Over''' = prime in the numerator. '''Under''' = prime in the denominator. '''All''' = over, under or neither: wa = 3-limit, ya = 2.3.5, yaza = 2.3.5.7. '''Exponent''' = repeated syllable: triyo = yoyoyo = 125-over.   

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[[Category:Color notation| ]] <!-- main article -->

[[Category:Just intonation]]

[[Category:Notation]]