Kite's color notation: Difference between revisions

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

Colors can be doubled or tripled: 25/16 = yoyo 5th = yy5 and 128/125 = triple gu 2nd = g32. Quadruple and quintuple are abbreviated '''quad''' and '''quint''', as in the quadgu comma 648/625. Degrees can be negative: 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 negative 2nd.

Colors can be doubled or tripled: 25/16 = yoyo 5th = yy5 and 128/125 = triple gu 2nd = g32. Quadruple and quintuple are abbreviated '''quad''' and '''quint''', as in the quadgu comma 648/625.

The next table lists all the intervals in the lattice above. See the [[Gallery of Just Intervals]] for many more examples.

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[[File:Lattice41a.png|833x833px]]

A '''comma''' is 10-50¢, a '''minicomma''' is 1-10¢, and a '''microcomma''' is 0-1¢. These categories allow us to omit the magnitude in the spoken name. Thus sgg2 is not the small gugu 2nd, but simply the gugu comma. The double-large wa negative 2nd (LLw-2, the pyth comma) is simply the wa comma. 81/80 = g1 is the gu comma. LLg-2 (the sum of g1 and LLw-2) is also gu and also a comma, but LLg-2 is not the gu comma, because its odd limit is higher. Thus its name can't be shortened.

Degrees can be negative: 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 negative 2nd. There are also diminished unisons, which raise the pitch but diminish the quality. For example, if 11/8 is a P4, two of them are a m7 of 121/64 = 1102¢. Going from a yo M7 = 1088¢ up to this m7 raises the pitch, and 121/120 is a d1.

A '''comma''' is 10-50¢, a '''minicomma''' is 1-10¢, and a '''microcomma''' is 0-1¢. These categories allow us to omit the magnitude in the spoken name. Thus sgg2 is not the small gugu 2nd, but simply the gugu comma. The double-large wa negative 2nd (LLw-2, the pyth comma) is simply the wa comma. 81/80 = g1 is the gu comma. LLg-2 (the sum of g1 and LLw-2) is also gu and also a comma, but LLg-2 is not the gu comma, because its odd limit is higher. Thus its name can't be shortened. 3-limit commas such as L3w-2 = (-30, 19) can be abbreviated as wa-19.

== Note Names ==

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== Chord names ==

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". Qualities such as major and minor aren't used, because a chord with an 11/9 3rd is hard to classify. The four main yaza triads:

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:

[[File:lattice62.png|alt=lattice62.png|640x138px|lattice62.png]]

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

Tetrads are named e.g. "C yo six" = Cy6 = C yE G yA. The 11 main yaza tetrads, with chord homonyms (same shape, different root) equated:

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

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~~.

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, see z7,11:

[[File:Lattice64.png|660x660px]]

Alterations are always in parentheses, additions never are, e.g. z7(zg5) and z,y6. An alteration's degree must match a note in the chord, e.g. Cz7(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~~. Thirdless dyads are written C5 or C(zg5)~~.

Alterations are always in parentheses, additions never are, e.g. z7(zg5) and z,y6. An alteration's degree must match a note in the chord, e.g. Cz7(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. Enharmonic substitutions aren't allowed, 7/3 is a m10, not an A9. A no3 tetrad can also be written as a 5 chord with an added 6th or 7th: Cy6no3 = C5y6, and Cz7(zg5)no3 = C(zg5)z7.

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

~~'''(OBSOLETE LINKS, IGNORE THEM):'''~~

~~[[Paradoxical_intervals|Paradoxical intervals]]~~

[[Category:color_notation]]

@@ Line 19: / Line 19: @@
 [[File:Lattice32.png|694x694px]]
-Colors can be doubled or tripled: 25/16 = yoyo 5th = yy5 and 128/125 = triple gu 2nd = g<sup>3</sup>2. Quadruple and quintuple are abbreviated '''quad''' and '''quint''', as in the quadgu comma 648/625. Degrees can be negative: 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 negative 2nd.
+Colors can be doubled or tripled: 25/16 = yoyo 5th = yy5 and 128/125 = triple gu 2nd = g<sup>3</sup>2. Quadruple and quintuple are abbreviated '''quad''' and '''quint''', as in the quadgu comma 648/625.
 The next table lists all the intervals in the lattice above. See the [[Gallery of Just Intervals]] for many more examples.
@@ Line 161: / Line 161: @@
 [[File:Lattice41a.png|833x833px]]
-A '''comma''' is 10-50¢, a '''minicomma''' is 1-10¢, and a '''microcomma''' is 0-1¢. These categories allow us to omit the magnitude in the spoken name. Thus sgg2 is not the small gugu 2nd, but simply the gugu comma. The double-large wa negative 2nd (LLw-2, the pyth comma) is simply the wa comma. 81/80 = g1 is the gu comma. LLg-2 (the sum of g1 and LLw-2) is also gu and also a comma, but LLg-2 is not <u>the</u> gu comma, because its odd limit is higher. Thus its name can't be shortened.
+Degrees can be negative: 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 negative 2nd. There are also diminished unisons, which raise the pitch but diminish the quality. For example, if 11/8 is a P4, two of them are a m7 of 121/64 = 1102¢. Going from a yo M7 = 1088¢ up to this m7 raises the pitch, and 121/120 is a d1.
+A '''comma''' is 10-50¢, a '''minicomma''' is 1-10¢, and a '''microcomma''' is 0-1¢. These categories allow us to omit the magnitude in the spoken name. Thus sgg2 is not the small gugu 2nd, but simply the gugu comma. The double-large wa negative 2nd (LLw-2, the pyth comma) is simply the wa comma. 81/80 = g1 is the gu comma. LLg-2 (the sum of g1 and LLw-2) is also gu and also a comma, but LLg-2 is not <u>the</u> gu comma, because its odd limit is higher. Thus its name can't be shortened. 3-limit commas such as L<sup>3</sup>w-2 = (-30, 19) can be abbreviated as wa-19.
 == Note Names ==
@@ Line 215: / Line 217: @@
 == Chord names ==
-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". Qualities such as major and minor aren't used, because a chord with an 11/9 3rd is hard to classify. The four main yaza triads:
+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:
 [[File:lattice62.png|alt=lattice62.png|640x138px|lattice62.png]]
-Tetrads are named Cy6, "C yo six", etc. The 11 main yaza tetrads, with chord homonyms (same shape, different root) equated:
+Tetrads are named e.g. "C yo six" = Cy6 = C yE G yA. The 11 main yaza tetrads, with chord homonyms (same shape, different root) equated:
 [[File:Lattice63.png|639x639px]]
-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.
+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, see z7,11:
+[[File:Lattice64.png|660x660px]]
-<u>Alterations are always in parentheses</u>, additions never are, e.g. z7(zg5) and z,y6. An alteration's degree must match a note in the chord, e.g. Cz7(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. Thirdless dyads are written C5 or C(zg5).
+<u>Alterations are always in parentheses</u>, additions never are, e.g. z7(zg5) and z,y6. An alteration's degree must match a note in the chord, e.g. Cz7(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 tetrad can also be written as a 5 chord with an added 6th or 7th: Cy6no3 = C5y6, and Cz7(zg5)no3 = C(zg5)z7.
@@ Line 259: / Line 263: @@
 Rank-2 temperaments can be notated with ups and downs as well. Some require an additional accidental pair, lifts and drops (/ and \). See [[Pergen|pergens]].
-'''(OBSOLETE LINKS, IGNORE THEM):'''
-[[Paradoxical_intervals|Paradoxical intervals]]
 [[Category:color_notation]]