Kite's color notation: Difference between revisions

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.  

'''Twetho''' = 23-over, '''twethu''' = 23-under, and '''twetha''' = 23-all, abbreviated as '''23o''', '''23u''' and '''23a'''. 2.3.5.7.23 = yaza23a = yazatwetha. 23/16 = 23o5 = twetho 5th, and 23/22 = 23o1u2 = twetholu 2nd. 529/512 = 23oo2 = bitwetho 2nd (not twethotho, because that means 23-over 13-over).  

{| class="wikitable"

!prime

|19o

|23o

|31o

|37o

|53o

|59o

|67o

|-

!word

|twetho

|tweno

|thiso

|fowo

|siwo

|siso

|}

For any prime P, the degree of the ratio P/1 is chosen to minimize negative intervals. It is determined by its 8ve-reduced cents, and how it relates to 12edo:     

!4th

!5th

!7th

!8ve

|-

|250-450¢

|450-600¢

|950-1150¢

|1150-1200¢

|}

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).   

Long color names use hyphens to make the name easier to parse. There are strict rules for hyphenation, to ensure uniformity.  

*Put a hyphen before and after "seventy", "eighty", etc.

The hyphen after the magnitude is omitted if it would create a subunit of 1 syllable. Thus layo, lalagu and sagugu are all unhyphenated. However, the last rule always holds, e.g. 284/243 =  2² * 3^-5 * 71 is a sa-seventy-wo 3rd.

Often a ratio can be converted by breaking it down into simpler ratios with familiar color names, then adding. For example, 45/32 is 5/4 times 9/8, which is y3 plus w2. The colors and degrees are summed, making y4. The magnitude is <u>not</u> summed, and must be found either visually from the lattices above, or from the monzo directly. 45/32 = [-5 2 1>, and (2+1)/7 rounds to 0, so it's central, and 45/32 = y4.     

Example: ratio = 63/40     

<u>'''Converting a color name'''</u>: Let S be the stepspan of the interval, S = degree - sign (degree). Let M be the magnitude of the color name, with L = 1, LL = 2, etc. Small is negative and central is zero. Let C be the number of "co-" prefixes. Let the monzo be [a b c d e...>. The colors directly give you all the monzo entries except a and b. Let S' = the dot product of [0 0 c d e...> with the pseudo-edomapping. Let M' = round ((2 (S - S') + c + d + e + ...) / 7). Then a = -3 (S - S') - 11 (M - M') + C and b = 2 (S - S') + 7 (M - M'). (Derivation [https://gist.github.com/m-yac/2236a03dd9fe89a992477fbcbc63746c here]) Convert the monzo to a ratio.     

Example: interval = sgg2 = sagugu 2nd     

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.

L and s never appear on the staff. Tripled colors are written as y3 not y³ or yyy. In MuseScore, color accidentals are made by adding fingerings to the notes, then editing the fingering text. A fingering can be copied from one note and pasted to another note. The font used here is Arial Black.

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 be 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.   

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]].           

Temperament names are further explained at [[Color notation/Temperament Names]].           

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.                 

Chords are named similarly to color notation, with the various qualities downmajor, upminor, mid, etc. replacing colors. Major is the default quality, thus C = C major and Cv = C downmajor. The 6th, 7th and 11th inherit their quality from the 3rd, thus C upminor 9th = C ^Eb G ^Bb D. Chord roots can have ups and downs, as in Cv - Gv - vA^m - Fv or Iv - Vv - vVI^m - IVv. In roman numeral notation, chord roots can be downflat, mid, etc., as in Iv7 - vbIII^m6 - IVv7 or I~7 - ~III - V7. Lower-case roman numerals are never used for minor chords, because vii could mean either seven-minor or down-two-minor. Instead vii is written either VIIm or vIIm. See the [http://tallkite.com/misc_files/notation%20guide%20for%20edos%205-72.pdf notation guide for edos 5-72]                 

'''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.   

{| class="wikitable" style="text-align:center"

|-

|2

|(clear)

|bi ("bee")

|squared

|-

|3

|wa (white)

|tri ("tree")

|cubed

|-

|yo (yellow)

|y

|ya

| —

|-

|7

|ru (red)

|r

| —

|sep

|1o

|lu

|ila

|1a

|23u

|twetha

|twethe

|^23

|}

Higher primes: 29o = tweno, 31o = thiwo, 37o = thiso, 41o = fowo, 43o = fotho, 47o = foso, 53o = fitho, 59o = fino, 61o = siwo, 67o = sino.  

{| class="wikitable"

|+

|Diminished temperament = 648/625 = Quadgu = g⁴T

|-

|w-

|alternate interval format, only used for 3-limit commas

|32/27 = wa 3rd = w3, 81/64 = lawa 3rd = Lw3

|-

| style="text-align:center" |s

|small, diminished by 2187/2048 from the central ratio

| colspan="2" |noca

|remove 2 (clear) from the prime subgroup, i.e. non-8ve

|-

| colspan="2" |nowaca

|-

| colspan="2" |i-

|no 3rd = omit the 3rd, ino 3rd = 19/16

|-

| colspan="2" | -a-

|Trizogu = z³g³ = 1029/1000, Trizo-agu = z³g = 343/320

|-

| style="text-align:center" | -wd

|refers to the direction of chord root movement

|-

|har

| style="text-align:center" |h

|refers to a harmonic series (otonal) chord

|-

|sub

| style="text-align:center" |s

|7/(7:6:5:4) = C sub seven = Cs7

|-

|-

|up

|-

|down