Kite's color notation: Difference between revisions

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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.

Any ratio under 50¢ can be called a '''comma''', allowing us to omit the magnitude and degree 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|double odd limit]] is higher. Thus its name can't be shortened. 3-limit commas such as L3w-2 = (-30, 19) can be abbreviated as w-19, the wa-19 comma.

Any ratio under 50¢ can be called a '''comma''', allowing us to omit the magnitude and degree 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|double odd limit]] is higher. Thus its name can't be shortened. The comma of a certain color is the ratio < 50¢ with the least double odd limit that isn't a multiple of another comma. 3-limit commas such as L3w-2 = (-30, 19) can be abbreviated as w-19, the wa-19 comma.

'''Wide''', abbreviated '''W''', means widened by an octave. 15/4 = Wy7 = wide yo 7th. 5/1 = WWy3 = double-wide yo 3rd.

== Note Names ==

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

Notes are named zEb, yyG#, etc. spoken as "zo E flat", "yoyo G sharp". Notes are never large or small, only intervals are. Uncolored notes default to wa. The relative-notation lattice above can be 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]]

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 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.
-Any ratio under 50¢ can be called a '''comma''', allowing us to omit the magnitude and degree 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|double 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 w-19, the wa-19 comma.
+Any ratio under 50¢ can be called a '''comma''', allowing us to omit the magnitude and degree 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|double odd limit]] is higher. Thus its name can't be shortened. <u>The</u> comma of a certain color is the ratio < 50¢ with the least double odd limit that isn't a multiple of another comma. 3-limit commas such as L<sup>3</sup>w-2 = (-30, 19) can be abbreviated as w-19, the wa-19 comma.
 '''Wide''', abbreviated '''W''', means widened by an octave. 15/4 = Wy7 = wide yo 7th. 5/1 = WWy3 = double-wide yo 3rd.
 == Note Names ==
-Notes are named zEb, yyG#, etc. spoken as "zo E flat", "yoyo G sharp". Notes are never large or small, only intervals are. Uncolored notes default to wa. The relative-notation lattice above can be superimposed on this absolute-notation lattice to name every note. Thus D + y3 = yF#, and from yE to ryF# = r2.
+Notes are named zEb, yyG#, etc. spoken as "zo E flat", "yoyo G sharp". Notes are never large or small, only intervals are. Uncolored notes default to wa. The relative-notation lattice above can be 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]]