Kite's color notation: Difference between revisions

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Example: ratio = 63/40, monzo = [-3 2 -1 1>, color = zogu, stepspan = <7 11 16 20] dot [-3 2 -1 1> = -21 + 22 - 16 + 20 = 5 steps, degree = 5 + 1 = a 6th, magnitude = round [(2 + (-1) + 1) / 7] = round (2/7) = 0 = central, interval = zg6. 63/20 would be zg13 = czg6.

<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 X = the dot product of [0 0 c d e...> with the pseudo-edomapping. ~~Then b~~ = (2S - 2X + 3) ~~mod~~ 7 ~~+ 7M~~ - 3, and a = (S - X - ~~11b~~) / ~~7 + C~~. Convert the monzo to a ratio.

<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, S = 2 - 1 = 1 step, M = small = -1, C = 0. Monzo = [a b -2>~~, X~~ = <7 11 16] dot [0 0 -2> = -32~~, b~~ = ~~(2·1~~ - 2·(-32) + 3) ~~mod~~ 7 ~~+ 7·~~(-1) - 3 = ~~69 mod 7~~ - 7 - 3 = 6 - 10 = -~~4, a =~~ (1 - (-32) - 11·(-4)) / 7 + 0 = ~~77/7~~ = ~~11, monzo~~ = [11 -4 -2>, ratio = 2048/2025.

Example: interval = sgg2

* S = 2 - 1 = 1 step, M = small = -1, C = 0. Monzo = [a b -2>

* S' = <7 11 16] dot [0 0 -2> = -32. S - S' = 1 - (-32) = 33.

* M' = round ((2·33 + (-2)) / 7) = round (64 / 7) = 9. M - M' = -1 - 9 = -10.

* a = -3 (S - S') - 11 (M - M') + C = -3·33 - 11·(-10) + 0 = -99 + 110 = 11.

* b = 2 (S - S') + 7 (M - M') = 2·33 + 7·(-10) = 66 - 70 = -4

* Monzo = [11 -4 -2>, ratio = 2048/2025.

== Staff Notation ==

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 Example: ratio = 63/40, monzo = [-3 2 -1 1>, color = zogu, stepspan = <7 11 16 20] dot [-3 2 -1 1> = -21 + 22 - 16 + 20 = 5 steps, degree = 5 + 1 = a 6th, magnitude = round [(2 + (-1) + 1) / 7] = round (2/7) = 0 = central, interval = zg6. 63/20 would be zg13 = czg6.
-<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 X = the dot product of [0 0 c d e...> with the pseudo-edomapping. Then b = (2S - 2X + 3) mod 7 + 7M - 3, and a = (S - X - 11b) / 7 + C. Convert the monzo to a ratio.
+<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, S = 2 - 1 = 1 step, M = small = -1, C = 0. Monzo = [a b -2>, X = <7 11 16] dot [0 0 -2> = -32, b = (2·1 - 2·(-32) + 3) mod 7 + 7·(-1) - 3 = 69 mod 7 - 7 - 3 = 6 - 10 = -4, a = (1 - (-32) - 11·(-4)) / 7 + 0 = 77/7 = 11, monzo = [11 -4 -2>, ratio = 2048/2025.
+Example: interval = sgg2
+* S = 2 - 1 = 1 step, M = small = -1, C = 0. Monzo = [a b -2>
+* S' = <7 11 16] dot [0 0 -2> = -32. S - S' = 1 - (-32) = 33.
+* M' = round ((2·33 + (-2)) / 7) = round (64 / 7) = 9. M - M' = -1 - 9 = -10.
+* a = -3 (S - S') - 11 (M - M') + C = -3·33 - 11·(-10) + 0 = -99 + 110 = 11.
+* b = 2 (S - S') + 7 (M - M') = 2·33 + 7·(-10) = 66 - 70 = -4
+* Monzo = [11 -4 -2>, ratio = 2048/2025.
 == Staff Notation ==