Kite's color notation: Difference between revisions

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Colors for primes greater than 7 are named after the number itself, using the prefix '''i-''' for disambiguation as needed:

'''Lo''' = 11-over, '''lu''' = 11-under, and '''la''' = 11-all = 2.3.11 Because "lo C" sounds like "low C", lo when by itself becomes '''ilo''' ("ee-LOW"). But with other words it doesn't use i-, as in 11/7 = loru 5th. Lo and lu are abbreviated to '''1o''' and '''1u''' on the score and in interval names and chord names, e.g. ilo A = 1oA, ilo 4th = 1o4 = 11/8 and C ilo-7 = C1o7 = 1/1 - 11/9 - 3/2 - 11/6. Lolo is 1oo, triple-lu is 1u3, etc. The associated color is lavender (mnemonic: "e-leven-der"), which refers to both ilo and lu, since they are only 7.1¢ apart. Lavender is a '''pseudocolor''' that implies the [http://x31eq.com/cgi-bin/rt.cgi?ets=24_17&limit=2_3_11 Neuter] temperament. IIo notes could be called lovender, and lu notes could be called luvender. Both are "shades" of lavender.

'''Lo''' = 11-over, '''lu''' = 11-under, and '''la''' = 11-all = 2.3.11 Because "lo C" sounds like "low C", lo when by itself becomes '''ilo''' ("ee-LOW"). But with other words it doesn't use i-, as in 11/7 = loru 5th. Lo and lu are abbreviated to '''1o''' and '''1u''' on the score and in interval names and chord names, e.g. ilo A = 1oA, ilo 4th = 1o4 = 11/8, and C ilo seven = C1o7 = 1/1 - 11/9 - 3/2 - 11/6 on C. Lolo is 1oo, triple-lu is 1u3, etc. The associated color is lavender (mnemonic: "e-leven-der"), which refers to both ilo and lu, since they are only 7.1¢ apart. Lavender is a '''pseudocolor''' that implies the [http://x31eq.com/cgi-bin/rt.cgi?ets=24_17&limit=2_3_11 Neuter] temperament. IIo notes could be called lovender, and lu notes could be called luvender. Both are "shades" of lavender.

'''Tho''' = 13-over, '''thu''' = 13-under, and '''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. Languages without a "th" sound might use '''tro''', '''tru''' and '''tra'''. See the appendix in [http://www.tallkite.com/AlternativeTunings.html Kite's book] for more on translating colors into other languages.

Prime subgroups: yala = 2.3.5.11, zalatha nowa = 2.7.11.13. and yazalatha = 2.3.5.7.11.13 = the full 13-limit. '''Noya''' is a general term, not used in actual subgroup names, that indicates the absence of 5 and the presence of higher primes, e.g. zala, latha and zalatha are all noya. Likewise, there's '''noza''' and '''noyaza'''.

Prime subgroups: yala = 2.3.5.11, zalatha nowa = 2.7.11.13, and yazalatha = 2.3.5.7.11.13 = the full 13-limit. '''Noya''' is a general term, not used in actual subgroup names, that indicates the absence of 5 and the presence of higher primes, e.g. zala, latha and zalatha are all noya. Likewise, there's '''noza''' and '''noyaza'''.

On the score and in note names, the 1o accidental either raises by 33/32 or lowers by 729/704. The meaning will usually be clear from context, however it's safer to write at the top of the page either "1o4 = P4" or "1o4 = A4". Likewise, 3o6 should be noted as either m6 or M6. While the note 11/8 above C can be written two ways, either as 1oF or as 1oF#, the interval 11/8 can only be written one way, as 1o4. Likewise, 13/8 above C is either 3oA or 3oAb, but 13/8 is only 3o6. This is the rationale for using large/small/central rather than major/minor. 11/9 is ambiguously major or minor, but unambiguously central. Intervals names and chord names become unambiguous for la and tha intervals. Another rationale: commonly used intervals and chords are all central, and get concise names: gu 3rd not gu minor 3rd, A gu not A gu minor, etc. (see chord names below).

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== 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.

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.

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Omissions are indicated by "no", the Hendrix chord might be Ch7z10no5. Unless using po or qu, enharmonic substitutions aren't allowed. 7/3 is a 10th, never a 9th unless it's a qu 9th (e.g. Ch7zq9no5). 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.

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 s7 has no 7th. Ch9 = y,z7,w9 and Ch11 = y,z7,w9,1o11. Cs9 = g,r6,w11 and Cs11 = g,r6,w11,1u9. All harmonic numbers must be odd, Ch8 is invalid. For any odd number N > 7, ChN would be 1:3:5:7...N and CsN would be 3/(1:3:5:7...N). Additions refer to harmonics or subharmonics, not degrees: Cs7,11 adds 1u9, not w11. To add w11, use colors: Cs7,w11. Alterations and omissions refer to degrees, not (sub)harmonics: Cs7(zg5) alters the w5, not the 5th subharmonic g3. Ch9no5 omits w5, not y3. However, Ch19no15 ~~refers to the 15th harmonic~~, since degrees above 13 aren't conventionally used.

The y,z7 chord is also called the h7 chord ("aitch-seven"), because it's part of the harmonic series. The s7 ("sub-seven" or "ess-seven") chord is part of the subharmonic series. It's the first 7 subharmonics, with the 3rd subharmonic becoming the root. Note that s7 has no 7th. Ch9 = y,z7,w9 and Ch11 = y,z7,w9,1o11. Cs9 = g,r6,w11 and Cs11 = g,r6,w11,1u9. All harmonic numbers must be odd, Ch8 is invalid. For any odd number N > 7, ChN would be 1:3:5:7...N and CsN would be 3/(1:3:5:7...N). Additions refer to harmonics or subharmonics, not degrees: Cs7,11 adds 1u9, not w11. To add w11, use colors: Cs7,w11. Alterations and omissions refer to degrees, not (sub)harmonics: Cs7(zg5) alters the w5, not the 5th subharmonic g3. Ch9no5 omits w5, not y3. However, all numbers ≥ 15 refer to (sub)harmonics (e.g. Ch19no15), since degrees above 13 aren't conventionally used.

Chords can be classified as '''bicolored''' (e.g. g7 or r6), '''tricolored''' (e.g. z7(zg5) or z,y6), '''quadricolored''', etc.

Chords can be classified as '''bicolored''' (e.g. g7 or r6), '''tricolored''' (e.g. z7(zg5) or z,y6), '''quadricolored''' (e.g. s7(zg5) or h7,zg9), etc.

== Chord Progressions, Keys and Modulations ==

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 Colors for primes greater than 7 are named after the number itself, using the prefix '''i-''' for disambiguation as needed:
-'''Lo''' = 11-over, '''lu''' = 11-under, and '''la''' = 11-all = 2.3.11 Because "lo C" sounds like "low C", lo when by itself becomes '''ilo''' ("ee-LOW"). But with other words it doesn't use i-, as in 11/7 = loru 5th. Lo and lu are abbreviated to '''1o''' and '''1u''' on the score and in interval names and chord names, e.g. ilo A = 1oA, ilo 4th = 1o4 = 11/8 and C ilo-7 = C1o7 = 1/1 - 11/9 - 3/2 - 11/6. Lolo is 1oo, triple-lu is 1u<sup>3</sup>, etc. The associated color is lavender (mnemonic: "e-leven-der"), which refers to both ilo and lu, since they are only 7.1¢ apart. Lavender is a '''pseudocolor''' that implies the [http://x31eq.com/cgi-bin/rt.cgi?ets=24_17&limit=2_3_11 Neuter] temperament. IIo notes could be called lovender, and lu notes could be called luvender. Both are "shades" of lavender.
+'''Lo''' = 11-over, '''lu''' = 11-under, and '''la''' = 11-all = 2.3.11 Because "lo C" sounds like "low C", lo when by itself becomes '''ilo''' ("ee-LOW"). But with other words it doesn't use i-, as in 11/7 = loru 5th. Lo and lu are abbreviated to '''1o''' and '''1u''' on the score and in interval names and chord names, e.g. ilo A = 1oA, ilo 4th = 1o4 = 11/8, and C ilo seven = C1o7 = 1/1 - 11/9 - 3/2 - 11/6 on C. Lolo is 1oo, triple-lu is 1u<sup>3</sup>, etc. The associated color is lavender (mnemonic: "e-leven-der"), which refers to both ilo and lu, since they are only 7.1¢ apart. Lavender is a '''pseudocolor''' that implies the [http://x31eq.com/cgi-bin/rt.cgi?ets=24_17&limit=2_3_11 Neuter] temperament. IIo notes could be called lovender, and lu notes could be called luvender. Both are "shades" of lavender.
 '''Tho''' = 13-over, '''thu''' = 13-under, and '''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. Languages without a "th" sound might use '''tro''', '''tru''' and '''tra'''. See the appendix in [http://www.tallkite.com/AlternativeTunings.html Kite's book] for more on translating colors into other languages.
-Prime subgroups: yala = 2.3.5.11, zalatha nowa = 2.7.11.13. and yazalatha = 2.3.5.7.11.13 = the full 13-limit. '''Noya''' is a general term, not used in actual subgroup names, that indicates the absence of 5 and the presence of higher primes, e.g. zala, latha and zalatha are all noya. Likewise, there's '''noza''' and '''noyaza'''.
+Prime subgroups: yala = 2.3.5.11, zalatha nowa = 2.7.11.13, and yazalatha = 2.3.5.7.11.13 = the full 13-limit. '''Noya''' is a general term, not used in actual subgroup names, that indicates the absence of 5 and the presence of higher primes, e.g. zala, latha and zalatha are all noya. Likewise, there's '''noza''' and '''noyaza'''.
 On the score and in note names, the 1o accidental either raises by 33/32 or lowers by 729/704. The meaning will usually be clear from context, however it's safer to write at the top of the page either "1o4 = P4" or "1o4 = A4". Likewise, 3o6 should be noted as either m6 or M6. While the note 11/8 above C can be written two ways, either as 1oF or as 1oF#, the interval 11/8 can only be written one way, as 1o4. Likewise, 13/8 above C is either 3oA or 3oAb, but 13/8 is only 3o6. <u>This is the rationale for using large/small/central rather than major/minor</u>. 11/9 is ambiguously major or minor, but unambiguously central. Intervals names and chord names become unambiguous for la and tha intervals. Another rationale: commonly used intervals and chords are all central, and get concise names: gu 3rd not gu minor 3rd, A gu not A gu minor, etc. (see chord names below).
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 == 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.
+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.
@@ Line 236: / Line 240: @@
 Omissions are indicated by "no", the Hendrix chord might be Ch7z10no5. Unless using po or qu, <u>enharmonic substitutions aren't allowed</u>. 7/3 is a 10th, never a 9th unless it's a qu 9th (e.g. Ch7zq9no5). 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.
-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 s7 has no 7th. Ch9 = y,z7,w9 and Ch11 = y,z7,w9,1o11. Cs9 = g,r6,w11 and Cs11 = g,r6,w11,1u9. All harmonic numbers must be odd, Ch8 is invalid. For any odd number N > 7, ChN would be 1:3:5:7...N and CsN would be 3/(1:3:5:7...N).  <u>Additions refer to harmonics or subharmonics</u>, not degrees: Cs7,11 adds 1u9, not w11. To add w11, use colors: Cs7,w11.  <u>Alterations and omissions refer to degrees</u>, not (sub)harmonics: Cs7(zg5) alters the w5, not the 5th subharmonic g3. Ch9no5 omits w5, not y3. However, Ch19no15 refers to the 15th harmonic, since degrees above 13 aren't conventionally used.
+The y,z7 chord is also called the h7 chord ("aitch-seven"), because it's part of the harmonic series. The s7 ("sub-seven" or "ess-seven") chord is part of the subharmonic series. It's the first 7 subharmonics, with the 3rd subharmonic becoming the root. Note that s7 has no 7th. Ch9 = y,z7,w9 and Ch11 = y,z7,w9,1o11. Cs9 = g,r6,w11 and Cs11 = g,r6,w11,1u9. All harmonic numbers must be odd, Ch8 is invalid. For any odd number N > 7, ChN would be 1:3:5:7...N and CsN would be 3/(1:3:5:7...N).  <u>Additions refer to harmonics or subharmonics</u>, not degrees: Cs7,11 adds 1u9, not w11. To add w11, use colors: Cs7,w11.  <u>Alterations and omissions refer to degrees</u>, not (sub)harmonics: Cs7(zg5) alters the w5, not the 5th subharmonic g3. Ch9no5 omits w5, not y3. However, <u>all numbers ≥ 15 refer to (sub)harmonics</u> (e.g. Ch19no15), since degrees above 13 aren't conventionally used.
-Chords can be classified as '''bicolored''' (e.g. g7 or r6), '''tricolored''' (e.g. z7(zg5) or z,y6), '''quadricolored''', etc.
+Chords can be classified as '''bicolored''' (e.g. g7 or r6), '''tricolored''' (e.g. z7(zg5) or z,y6), '''quadricolored''' (e.g. s7(zg5) or h7,zg9), etc.
 == Chord Progressions, Keys and Modulations ==