Kite's color notation: Difference between revisions

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This is a "crash course". For a full explanation, see [[KiteGiedraitis|Kite's]] book, "Alternative Tunings: Theory, Notation and Practice", available at [http://www.tallkite.com/AlternativeTunings.html www.TallKite.com].

== Interval Names ==

Every prime above 3 has two color names, one for '''over''' (prime in the numerator) and one for '''under''' (prime in the denominator). Over colors end with -o, and under colors with -u. Here's the colors for primes 3, 5 and 7:

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'''Ru''' = red (alarming, inflamed) = 7-under = supermajor

The colors come in a red-yellow-green-blue rainbow, with warm/cool colors indicating sharp/flat intervals. The rainbow of 3rds~~: r3 - y3 - g3 - z3~~ = 9/7 - 5/4 - 6/5 - 7/6. Azure is used instead of blue because b looks like a flat sign. Mnemonic: Z looks like 7 with an extra line on the bottom.

The colors come in a red-yellow-green-blue rainbow, with warm/cool colors indicating sharp/flat intervals. The rainbow of 3rds = 9/7 - 5/4 - 6/5 - 7/6. Azure is used instead of blue because b looks like a flat sign. Mnemonic: Z looks like 7 with an extra line on the bottom.

A color and a degree indicates a ratio, and vice versa. 3/2 = wa ~~5th~~ = w5. 7/5 = zogu 5th = zg5 (not guzo, higher primes always come first). Interval arithmetic always holds: 7/5 is a 5th because zg5 = z3 + g3, and two 3rds make a 5th.

A color and a degree indicates a ratio, and vice versa. 2/1 = wa 8ve = w8. 7/5 = zogu 5th = zg5 (not guzo, higher primes always come first). Interval arithmetic always holds: 7/5 is a 5th because zg5 = z3 + g3, and two 3rds make a 5th. Opposite colors cancel: y3 + g3 = w5.

[[File:Lattice32.png|694x694px]]

21/10 = zogu 9th = zg9. 25/16 = yoyo 5th = yy5. 128/125 = triple gu 2nd = g32. 50/49 = double ruyo negative 2nd = rryy-2. It's a negative 2nd because it goes up in pitch but down the scale: zg5 + rryy-2 = ry4.

21/10 = zogu 9th = zg9. 25/16 = yoyo 5th = yy5. 128/125 = triple gu 2nd = g32. 50/49 = double ruyo negative 2nd = rryy-2. It's a negative 2nd because it goes up in pitch but down the scale: zg5 + rryy-2 = ry4. Negative is different than descending, from ry4 to zg5 is a descending neg 2nd.

~~Notes~~ are ~~named wC~~, ~~zE♭~~, ~~yyG#~~, etc. ~~Notes are never large or small~~, ~~only intervals are~~.

More remote intervals are '''large''' (fifthward) and '''small''' (fourthward), abbreviated L and s. '''Central''' means neither large nor small. The '''magnitude''' is found by adding up all the monzo exponents but the first, dividing by 7, and rounding off. 0 = central, 1 = large, 2 = double large, etc. 81/64 = Lw3, 135/128 = Ly1. Magnitudes do not add up predictably like colors and degrees do: w2 + w2 = Lw3.

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 subgroup = 5-limit. '''Za''' = 7-all = 2.3.7. '''Yaza''' = 2.3.5.7 = 7-limit. Yaza nowa = 2.5.7. Prime 2 is clear, abbreviated '''ca''', and ~~non-8ve scales are~~ noca. 2-limit intervals like w8 are not ~~called~~ clear, for simplicity.

[[File:Lattice41a.png|731x731px]]

See [[Gallery of Just Intervals]] for more examples of interval names.

== Prime Subgroup Names ==

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 subgroup = 5-limit. '''Za''' = 7-all = 2.3.7. '''Yaza''' = 2.3.5.7 = 7-limit. Yaza nowa = 2.5.7.

Prime 2 is clear, abbreviated '''ca''', and yaza noca = 3.5.7. 2-limit intervals like w8 are called wa not clear, for simplicity.

== Note Names and Chord Names ==

Notes are named wC, zE♭, yyG#, etc. Notes are never large or small, only intervals are. Notes with no explicit color are assumed to be wa.

Interval arithmetic: wD + y3 = yF#. From yE to wG = g3.

Triads are named after their 3rd: Cy, Gz, etc. 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: yAg = yA + (w1 g3 w5) = yA + wC + yE.

Tetrads are named Cy6, Dg7, etc. The 11 main yaza tetrads, with homonyms equated:

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Alterations are in parentheses, additions never are. Omissions are indicated by "no". Examples: Ch7(zg5)zg9 = w1 y3 zg5 z7 zg9.

Chord ~~progressions:~~ The tonic is always wa. The root of each chord has a color, which defaults to wa. C - Am - F - G would be Cy - yAg - Fy - Gy.

The color of the 6th, 7th, and/or the 11th matches the color of the 3rd: Cy11 = C yE G yB D yF#.

== Chord Progressions and Keys ==

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

In relative notation, the I, IV and V chords are assumed to have wa roots unless otherwise specified, so this becomes Iy -- yVIg -- IVy -- Vy.

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[[File:Notation_example_1.png|alt=Notation example 1.png|619x81px|Notation example 1.png]]

~~More remote intervals~~ are ~~'''large''' (fifthward) and '''small''' (fourthward)~~, ~~abbreviated L and s. '''Central''' means neither large nor small~~. ~~The '''magnitude''' is found by adding up all the monzo exponents but~~ the ~~first, dividing by 7,~~ and ~~rounding off. 0 = central~~, ~~1 = large~~, ~~2 = double large~~, etc~~. 81/64 = Lw3.[[File:Lattice41a.png|731x731px]]~~

Keys are named as C gu, D zo yo, etc. Analogous to the relative and parallel major or minor, there is relative gu, parallel ru, etc.

Temperaments are named after the color of the comma(s) they temper out. 5-limit Porcupine = triple yo = y3T. 7-limit porcupine = triple yo and ru = y3&rT. The name indicates the prime subgroup and the rank of the temperament.

== Higher Primes ==

Colors for primes > 7 are named after the number itself:

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The alternate forms with -ova or -unda are only needed when the color word appears alone. Thus 11/7 = loru 5th, not lovaru 5th.

== Temperament Names ==

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. The magnitude is part of the name: Schismic is LyT. The degree is as well, 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.

=='''FULL EXPLANATION:'''==

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 This is a "crash course". For a full explanation, see [[KiteGiedraitis|Kite's]] book, "Alternative Tunings: Theory, Notation and Practice", available at [http://www.tallkite.com/AlternativeTunings.html www.TallKite.com].
+== Interval Names ==
 Every prime above 3 has two color names, one for '''over''' (prime in the numerator) and one for '''under''' (prime in the denominator). Over colors end with -o, and under colors with -u. Here's the colors for primes 3, 5 and 7:
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 '''Ru''' = red (alarming, inflamed) = 7-under = supermajor
-The colors come in a red-yellow-green-blue rainbow, with warm/cool colors indicating sharp/flat intervals. The rainbow of 3rds: r3 - y3 - g3 - z3 = 9/7 - 5/4 - 6/5 - 7/6. Azure is used instead of blue because b looks like a flat sign. Mnemonic: Z looks like 7 with an extra line on the bottom.
+The colors come in a red-yellow-green-blue rainbow, with warm/cool colors indicating sharp/flat intervals. The rainbow of 3rds = 9/7 - 5/4 - 6/5 - 7/6. Azure is used instead of blue because b looks like a flat sign. Mnemonic: Z looks like 7 with an extra line on the bottom.
-A color and a degree indicates a ratio, and vice versa. 3/2 = wa 5th = w5. 7/5 = zogu 5th = zg5 (not guzo, higher primes always come first). Interval arithmetic <u>always</u> holds: 7/5 is a 5th because zg5 = z3 + g3, and two 3rds make a 5th.
+A color and a degree indicates a ratio, and vice versa. 2/1 = wa 8ve = w8. 7/5 = zogu 5th = zg5 (not guzo, higher primes always come first). Interval arithmetic <u>always</u> holds: 7/5 is a 5th because zg5 = z3 + g3, and two 3rds make a 5th. Opposite colors cancel: y3 + g3 = w5.
 [[File:Lattice32.png|694x694px]]
-/10 = zogu 9th = zg9. 25/16 = yoyo 5th = yy5. 128/125 = triple gu 2nd = g<sup>3</sup>2. 50/49 = double ruyo negative 2nd = rryy-2. It's a negative 2nd because it goes up in pitch but down the scale: zg5 + rryy-2 = ry4.
+/10 = zogu 9th = zg9. 25/16 = yoyo 5th = yy5. 128/125 = triple gu 2nd = g<sup>3</sup>2. 50/49 = double ruyo negative 2nd = rryy-2. It's a negative 2nd because it goes up in pitch but down the scale: zg5 + rryy-2 = ry4. Negative is different than descending, from ry4 to zg5 is a descending neg 2nd.
-Notes are named wC, zE♭, yyG#, etc. Notes are never large or small, only intervals are.
+More remote intervals are '''large''' (fifthward) and '''small''' (fourthward), abbreviated L and s. '''Central''' means neither large nor small. The '''magnitude''' is found by adding up all the monzo exponents but the first, dividing by 7, and rounding off. 0 = central, 1 = large, 2 = double large, etc. 81/64 = Lw3, 135/128 = Ly1. Magnitudes do not add up predictably like colors and degrees do: w2 + w2 = Lw3.
-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 subgroup = 5-limit. '''Za''' = 7-all = 2.3.7. '''Yaza''' = 2.3.5.7 = 7-limit. Yaza nowa = 2.5.7. Prime 2 is clear, abbreviated '''ca''', and non-8ve scales are noca. 2-limit intervals like w8 are not called clear, for simplicity.
+[[File:Lattice41a.png|731x731px]]
+See [[Gallery of Just Intervals]] for more examples of interval names.
+== Prime Subgroup Names ==
+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 subgroup = 5-limit. '''Za''' = 7-all = 2.3.7. '''Yaza''' = 2.3.5.7 = 7-limit. Yaza nowa = 2.5.7.
+Prime 2 is clear, abbreviated '''ca''', and yaza noca = 3.5.7. 2-limit intervals like w8 are called wa not clear, for simplicity.
+== Note Names and Chord Names ==
+Notes are named wC, zE♭, yyG#, etc. Notes are never large or small, only intervals are. Notes with no explicit color are assumed to be wa.
+Interval arithmetic: wD + y3 = yF#. From yE to wG = g3.
 Triads are named after their 3rd: Cy, Gz, etc. 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: yAg = yA + (w1 g3 w5) = yA + wC + yE.
 Tetrads are named Cy6, Dg7, etc. The 11 main yaza tetrads, with homonyms equated:
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 Alterations are in parentheses, additions never are. Omissions are indicated by "no". Examples: Ch7(zg5)zg9 = w1 y3 zg5 z7 zg9.
-Chord progressions: The tonic is always wa. The root of each chord has a color, which defaults to wa. C - Am - F - G would be Cy - yAg - Fy - Gy.
+The color of the 6th, 7th, and/or the 11th matches the color of the 3rd: Cy11 = C yE G yB D yF#.
+== Chord Progressions and Keys ==
+The tonic is always wa. The root of each chord has a color, which defaults to wa. C - Am - F - G would be Cy - yAg - Fy - Gy.
 In relative notation, the I, IV and V chords are assumed to have wa roots unless otherwise specified, so this becomes Iy -- yVIg -- IVy -- Vy.
@@ Line 43: / Line 61: @@
 [[File:Notation_example_1.png|alt=Notation example 1.png|619x81px|Notation example 1.png]]
-More remote intervals are '''large''' (fifthward) and '''small''' (fourthward), abbreviated L and s. '''Central''' means neither large nor small. The '''magnitude''' is found by adding up all the monzo exponents but the first, dividing by 7, and rounding off. 0 = central, 1 = large, 2 = double large, etc. 81/64 = Lw3.[[File:Lattice41a.png|731x731px]]
+Keys are named as C gu, D zo yo, etc. Analogous to the relative and parallel major or minor, there is relative gu, parallel ru, etc.
-Temperaments are named after the color of the comma(s) they temper out. 5-limit Porcupine = triple yo = y<sup>3</sup>T. 7-limit porcupine = triple yo and ru = y<sup>3</sup>&rT.  The name indicates the prime subgroup and the rank of the temperament.
+== Higher Primes ==
 Colors for primes > 7 are named after the number itself:
@@ Line 66: / Line 83: @@
 The alternate forms with -ova or -unda are only needed when the color word appears alone. Thus 11/7 = loru 5th, not lovaru 5th.
+== Temperament Names ==
+Temperaments are named after the color of the comma(s) they temper out. Meantone = the green temperament = gT. 5-limit Porcupine = triple yo = y<sup>3</sup>T. 7-limit porcupine = triple yo and ru = y<sup>3</sup>&rT. The magnitude is part of the name: Schismic is LyT. The degree is as well, 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.
 =='''<u>FULL EXPLANATION</u>:'''==