Kite's color notation: Difference between revisions

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The prefix i- is only needed when confusion is possible. Thus 19/15 = nogu 4th, not inogu 4th, and 29o = twenty-no, not twenty-ino.

For any prime P, the degree of the ratio P/1 is determined by its 8ve-reduced cents, and how it relates to 12edo: 0-50¢ = 1sn, 50-250¢ = 2nd, 250-450¢ = 3rd, 450-600¢ = 4th, 600-750¢ = 5th, 750-950¢ = 6th, 950-1150¢ = 7th, and 1150-1200¢ = 8ve. Thus 23/16 = 628¢ is a 5th, 31/16 = 1145¢ is a 7th, and 37/32 = 251¢ is a 3rd. This makes the "pseudo-edomapping" <7 11 16 20 24 26 29 30 32 34 34 37...|. (An alternate method is to use the 7edo [[edomapping]], but that requires using every other 14edostep as boundaries, less convenient than the 24edo boundaries used here.)

== Converting a ratio to/from a color name ==

Often the conversion can be done by breaking down the ratio into simple, familiar ratios. For example, 45/32 is 5/4 times 9/8, which is y3 plus w2. The colors and degrees are summed, making y4. The magnitude must be found either visually from the lattices above, or from the monzo directly. 45/32 = |-5 2 1>, and 2 + 1 is less than 4, so y4 is central, and 45/32 = y4.

Often the conversion can be done by breaking down the ratio into simple, familiar ratios. For example, 45/32 is 5/4 times 9/8, which is y3 plus w2. The colors and degrees are summed, making y4. The magnitude is <u>not</u> summed, and must be found either visually from the lattices above, or from the monzo directly. 45/32 = |-5 2 1>, and 2 + 1 is less than 4, so y4 is central, and 45/32 = y4.

For more complex ratios, a more direct method is needed:

Converting a ratio: Find the [[Monzos|monzo]] by prime factorization. To find the color, combine all the appropriate colors for each prime > 3, higher primes first. To find the degree, first find the stepspan, which is the dot product of the monzo with the ~~7edo [[Patent val|~~edomapping]] <7 11 16 20 24 26 29 30...|. Then add 1, or subtract 1 if the stepspan is negative. To find the magnitude, add up all the monzo exponents except the first one, divide by 7, and round off. Combine the magnitude, color and degree to make the color name.

Converting a ratio: Find the [[Monzos|monzo]] by prime factorization. To find the color, combine all the appropriate colors for each prime > 3, higher primes first. To find the degree, first find the stepspan, which is the dot product of the monzo with the "pseudo-edomapping" discussed above <7 11 16 20 24 26 29 30...|. Then add 1, or subtract 1 if the stepspan is negative. To find the magnitude, add up all the monzo exponents except the first one, divide by 7, and round off. Combine the magnitude, color and degree to make the color name.

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.

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 The prefix i- is only needed when confusion is possible. Thus 19/15 = nogu 4th, not inogu 4th, and 29o = twenty-no, not twenty-ino.
+For any prime P, the degree of the ratio P/1 is determined by its 8ve-reduced cents, and how it relates to 12edo: 0-50¢ = 1sn, 50-250¢ = 2nd, 250-450¢ = 3rd, 450-600¢ = 4th, 600-750¢ = 5th, 750-950¢ = 6th, 950-1150¢ = 7th, and 1150-1200¢ = 8ve. Thus 23/16 = 628¢ is a 5th, 31/16 = 1145¢ is a 7th, and 37/32 = 251¢ is a 3rd. This makes the "pseudo-edomapping" <7 11 16 20 24 26 29 30 32 34 34 37...|. (An alternate method is to use the 7edo [[edomapping]], but that requires using every other 14edostep as boundaries, less convenient than the 24edo boundaries used here.)
 == Converting a ratio to/from a color name ==
-Often the conversion can be done by breaking down the ratio into simple, familiar ratios. For example, 45/32 is 5/4 times 9/8, which is y3 plus w2. The colors and degrees are summed, making y4. The magnitude must be found either visually from the lattices above, or from the monzo directly. 45/32 = |-5 2 1>, and 2 + 1 is less than 4, so y4 is central, and 45/32 = y4.
+Often the conversion can be done by breaking down the ratio into simple, familiar ratios. For example, 45/32 is 5/4 times 9/8, which is y3 plus w2. The colors and degrees are summed, making y4. The magnitude is <u>not</u> summed, and must be found either visually from the lattices above, or from the monzo directly. 45/32 = |-5 2 1>, and 2 + 1 is less than 4, so y4 is central, and 45/32 = y4.
 For more complex ratios, a more direct method is needed:
-Converting a ratio: Find the [[Monzos|monzo]] by prime factorization. To find the color, combine all the appropriate colors for each prime > 3, higher primes first. To find the degree, first find the stepspan, which is the dot product of the monzo with the 7edo [[Patent val|edomapping]] <7 11 16 20 24 26 29 30...|. Then add 1, or subtract 1 if the stepspan is negative. To find the magnitude, add up all the monzo exponents except the first one, divide by 7, and round off. Combine the magnitude, color and degree to make the color name.
+Converting a ratio: Find the [[Monzos|monzo]] by prime factorization. To find the color, combine all the appropriate colors for each prime > 3, higher primes first. To find the degree, first find the stepspan, which is the dot product of the monzo with the "pseudo-edomapping" discussed above <7 11 16 20 24 26 29 30...|. Then add 1, or subtract 1 if the stepspan is negative. To find the magnitude, add up all the monzo exponents except the first one, divide by 7, and round off. Combine the magnitude, color and degree to make the color name.
 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.