Kite's color notation: Difference between revisions

Line 1:

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:

Line 14:

Line 13:

'''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 = 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. These colors combine to make other colors: zo + gu = zogu = 7-over, 5-under. Zogu not guzo, higher primes always come first. Opposite colors cancel: yo + gu = wa.

== Interval Names ==

A color and a degree indicates a ratio, and vice versa. 2/1 = wa octave = w8. 7/5 = zogu 5th = zg5. Colors and degrees <u>always</u> add up predictably: 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~~.

The JI lattice consists of many '''lattice rows''', each one a chain of 5ths. Each lattice row has its own color, and each color has its own lattice row.

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

Line 25:

Line 27:

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

The lattice can be divided into planes. The wa plane contains the wa, yo and gu rows. The zo plane has zo and zogu, and the ru plane has ru and royo. The double zozogu microcomma 2401/2400 provides an automatic microtempering. For untempered JI only, the zozo plane and the ruru plane merge into one. This allows the rank-4 yaza lattice to be collapsed into 2 dimensions:

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

Line 34:

Line 38:

== 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.

Notes are named wC, zE♭, yyG#, etc. Notes are never large or small, only intervals are. Notes are never purple, Notes with no explicit color are assumed to be wa. Interval arithmetic: D + y3 = yF#. From yE to G = g3. The relative-notation lattices above can be superimposed on absolute-notation lattices like these to name every note:

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

[[File:Lattice51.png|frameless|810x810px]]

Triads are named after their 3rd: Cy, Gz, etc. The four main yaza triads:[[File:lattice62.png|alt=lattice62.png|640x138px|lattice62.png]]

Line 42:

Line 46:

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:

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

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

Line 48:

Line 52:

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 it has no 7th. There are h9 chords, s11 chords, etc.

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

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

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

Line 66:

Line 70:

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

'''Lova''' = 11-over, '''lu''' = 11-under, '''la''' = 11-all = 2.3.11. (Lova not lo, because "lo C" sounds like "low C".) Lova and lu are abbreviated to '''1o''' and '''1u''' on the score and in interval names and chord names, e.g. lova A = 1oA, lova 4th = 1o4 = 11/8 and C lova-7 = C1o7 = 1/1 - 11/9 - 3/2 - 11/6. The associated color is lavender (mnemonic: "e-leven-der"), which is a ~~'''~~pseudocolor~~'''~~ referring to both lova and lu, since they are only 7.1¢ apart (e.g. lo 3rd = 11/9 and lu 3rd = 27/22). More precisely, lova notes are lovender, and lu notes are luvender.

'''Lova''' = 11-over, '''lu''' = 11-under, '''la''' = 11-all = 2.3.11. (Lova not lo, because "lo C" sounds like "low C".) Lova and lu are abbreviated to '''1o''' and '''1u''' on the score and in interval names and chord names, e.g. lova A = 1oA, lova 4th = 1o4 = 11/8 and C lova-7 = C1o7 = 1/1 - 11/9 - 3/2 - 11/6. The associated color is lavender (mnemonic: "e-leven-der"), which is a pseudocolor referring to both lova and lu, since they are only 7.1¢ apart (e.g. lo 3rd = 11/9 and lu 3rd = 27/22). More precisely, lova notes are lovender, and lu notes are luvender.

~~While the note 11/8 from C can be written two ways, either as 1oF or as 1oF#, the interval 11/8 can only be written one way, as 1o4~~.

'''Tho''' = 13-over, '''thu''' = 13-under, '''tha''' = 13-all. Tho and thu are abbreviated as '''3o''' and '''3u''' on the score and in interval names, e.g. 13/8 = 3o6 = tho 6th.

Yala = 2.3.5.11, yazalatha = 2.3.5.7.11.13 = 13-limit, and yalatha nowa = 2.5.11.13.

While the note 11/8 from C can be written two ways, either as 1oF or as 1oF#, the interval 11/8 can only be written one way, as 1o4. This is the rationale for using large/small rather than major/minor. Intervals names and chord names become unambiguous for la and tha intervals.

'''So''' = 17-over, '''su''' = 17-under, '''sa''' = 17-all, abbreviated as '''17o''' and '''17u'''. '''Sova''' is an alternate form of so, to distinguish it from the solfege syllable Sol.

@@ Line 1: / Line 1: @@
 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:
@@ Line 14: / Line 13: @@
 '''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 = 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. These colors combine to make other colors: zo + gu = zogu = 7-over, 5-under. Zogu not guzo, higher primes always come first. Opposite colors cancel: yo + gu = wa.
+== Interval Names ==
+A color and a degree indicates a ratio, and vice versa. 2/1 = wa octave = w8. 7/5 = zogu 5th = zg5. Colors and degrees <u>always</u> add up predictably: 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.
+The JI lattice consists of many '''lattice rows''', each one a chain of 5ths. Each lattice row has its own color, and each color has its own lattice row.
 [[File:Lattice32.png|694x694px]]
@@ Line 25: / Line 27: @@
 [[File:Lattice41a.png|731x731px]]
+The lattice can be divided into planes. The wa plane contains the wa, yo and gu rows. The zo plane has zo and zogu, and the ru plane has ru and royo. The double zozogu microcomma 2401/2400 provides an automatic microtempering. For untempered JI only, the zozo plane and the ruru plane merge into one. This allows the rank-4 yaza lattice to be collapsed into 2 dimensions:
 See [[Gallery of Just Intervals]] for more examples of interval names.
@@ Line 34: / Line 38: @@
 == 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.
+Notes are named wC, zE♭, yyG#, etc. Notes are never large or small, only intervals are. Notes are never purple, Notes with no explicit color are assumed to be wa. Interval arithmetic: D + y3 = yF#. From yE to G = g3. The relative-notation lattices above can be superimposed on absolute-notation lattices like these to name every note:
-Interval arithmetic: wD + y3 = yF#. From yE to wG = g3.
+[[File:Lattice51.png|frameless|810x810px]]
 Triads are named after their 3rd: Cy, Gz, etc. The four main yaza triads:[[File:lattice62.png|alt=lattice62.png|640x138px|lattice62.png]]
@@ Line 42: / Line 46: @@
 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:
+Tetrads are named Cy6, Dg7, etc. The 11 main yaza tetrads, with chord homonyms (same shape, different root) equated:
 [[File:Lattice63.png|639x639px]]
@@ Line 48: / Line 52: @@
 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 it has no 7th. There are h9 chords, s11 chords, etc.
-Alterations are in parentheses, additions never are. Omissions are indicated by "no". Examples: Ch7(zg5)zg9 = w1 y3 zg5 z7 zg9.
+Alterations are in parentheses, additions never are. Omissions are indicated by "no". Example: Ch7(zg5)zg9 = w1 y3 zg5 z7 zg9.
 The color of the 6th, 7th, and/or the 11th matches the color of the 3rd: Cy11 = C yE G yB D yF#.
@@ Line 66: / Line 70: @@
 Colors for primes > 7 are named after the number itself:
-'''Lova''' = 11-over, '''lu''' = 11-under, '''la''' = 11-all = 2.3.11. (Lova not lo, because "lo C" sounds like "low C".) Lova and lu are abbreviated to '''1o''' and '''1u''' on the score and in interval names and chord names, e.g. lova A = 1oA, lova 4th = 1o4 = 11/8 and C lova-7 = C1o7 = 1/1 - 11/9 - 3/2 - 11/6. The associated color is lavender (mnemonic: "e-leven-der"), which is a '''pseudocolor''' referring to both lova and lu, since they are only 7.1¢ apart (e.g. lo 3rd = 11/9 and lu 3rd = 27/22). More precisely, lova notes are lovender, and lu notes are luvender.
+'''Lova''' = 11-over, '''lu''' = 11-under, '''la''' = 11-all = 2.3.11. (Lova not lo, because "lo C" sounds like "low C".) Lova and lu are abbreviated to '''1o''' and '''1u''' on the score and in interval names and chord names, e.g. lova A = 1oA, lova 4th = 1o4 = 11/8 and C lova-7 = C1o7 = 1/1 - 11/9 - 3/2 - 11/6. The associated color is lavender (mnemonic: "e-leven-der"), which is a pseudocolor referring to both lova and lu, since they are only 7.1¢ apart (e.g. lo 3rd = 11/9 and lu 3rd = 27/22). More precisely, lova notes are lovender, and lu notes are luvender.
-While the note 11/8 from C can be written two ways, either as 1oF or as 1oF#, the interval 11/8 can only be written one way, as 1o4.
 '''Tho''' = 13-over, '''thu''' = 13-under, '''tha''' = 13-all. Tho and thu are abbreviated as '''3o''' and '''3u''' on the score and in interval names, e.g. 13/8 = 3o6 = tho 6th.
 Yala = 2.3.5.11, yazalatha = 2.3.5.7.11.13 = 13-limit, and yalatha nowa = 2.5.11.13.
+While the note 11/8 from C can be written two ways, either as 1oF or as 1oF#, the interval 11/8 can only be written one way, as 1o4. This is the rationale for using large/small rather than major/minor. Intervals names and chord names become unambiguous for la and tha intervals.
 '''So''' = 17-over, '''su''' = 17-under, '''sa''' = 17-all, abbreviated as '''17o''' and '''17u'''. '''Sova''' is an alternate form of so, to distinguish it from the solfege syllable Sol.