Kite's color notation: Difference between revisions

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This is ~~the "crash course"~~. For a full explanation, see [[KiteGiedraitis|Kite's]] book, [http://www.tallkite.com/AlternativeTunings.html "Alternative Tunings: Theory, Notation and Practice"].

This is a very brief summary. For a full explanation, see [[KiteGiedraitis|Kite's]] book, [http://www.tallkite.com/AlternativeTunings.html "Alternative Tunings: Theory, Notation and Practice"].

== Color Names for Primes 3, 5 and 7 ==

Every prime above 3 has two colors, an '''over''' color (prime in the numerator) and an '''under''' color (prime in the denominator). Over colors end with -o, and under colors end with -u. The color for 3-limit ends in -a for '''all''', which includes over (3/2, 9/8), under (4/3, 16/9) and neither (1/1, 2/1).

'''Wa''' = white (strong but colorless) = 3-limit

'''Wa''' = white (strong but colorless) = 3-limit

'''Yo''' = yellow (warm and sunny) = 5-over = major

'''Yo''' = yellow (warm and sunny) = 5-over = major

'''Gu''' ("goo") = green (not as bright as yellow) = 5-under = minor

'''Zo''' = blue/azure (dark and bluesy) = 7-over = subminor

'''Gu''' ("goo") = green (not as bright as yellow) = 5-under = minor

'''Ru''' = red (alarming, inflamed) = 7-under = supermajor

'''Zo''' = blue/azure (dark and bluesy) = 7-over = subminor

'''Ru''' = red (alarming, inflamed) = 7-under = supermajor

The colors come in a red-yellow-green-blue rainbow, with warm/cool colors indicating sharp/flat intervals. The rainbow of 3rds runs 9/7 - 5/4 - 6/5 - 7/6. Colors are abbreviated as w, y, z, etc. Use z (azure) not b (blue), because b looks like a flat sign. Mnemonic: Z looks like 7 with an extra line on the bottom.

~~:''For more color names see [[Gallery of Just Intervals #Gallery of Just Intervals|Gallery of Just Intervals]].''~~

== Interval Names ==

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21/10 = zogu 9th = zg9. 25/16 = yoyo 5th = yy5. 128/125 = triple gu 2nd = g32. 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.

~~Remote~~ intervals are '''large''' (fifthward) and '''small''' (fourthward), abbreviated L and s. '''Central''' means neither large nor small. The '''magnitude''' is found by adding up all the monzo exponents except the first one, dividing by 7, and rounding off. 0 = central, 1 = large, 2 = double large, etc. 81/64 = Lw3, 135/128 = Ly1. Magnitudes do not add up predictably like colors and degrees do: w2 + w2 = Lw3.

The next table lists various 7-limit intervals, see the [[Gallery of Just Intervals]] for many more examples.

{| class="wikitable"

!'''ratio'''

!'''cents'''

!'''color & degree'''

!'''shorthand'''

|-

|1/1

|0¢

|wa unison

|w1

|-

|21/20

|84¢

|zogu 2nd

|zg2

|-

|16/15

|112¢

|gu 2nd

|g2

|-

|10/9

|182¢

|yo 2nd

|y2

|-

|9/8

|204¢

|wa 2nd

|w2

|-

|8/7

|231¢

|ru 2nd

|r2

|-

|7/6

|267¢

|zo 3rd

|z3

|-

|32/27

|294¢

|wa 3rd

|w3

|-

|6/5

|316¢

|gu 3rd

|g3

|-

|5/4

|386¢

|yo 3rd

|y3

|-

|9/7

|435¢

|ru 3rd

|r3

|-

|21/16

|471¢

|zo 4th

|z4

|-

|4/3

|498¢

|wa 4th

|w4

|-

|27/20

|520¢

|gu 4th

|g4

|-

|7/5

|583¢

|zogu 5th

|zg5

|-

|45/32

|590¢

|yo 4th

|y4

|-

|64/45

|610¢

|gu 5th

|g5

|-

|10/7

|617¢

|ruyo 4th

|ry4

|-

|40/27

|680¢

|yo 5th

|y5

|-

|3/2

|702¢

|wa 5th

|w5

|-

|32/21

|729¢

|ru 5th

|r5

|-

|14/9

|765¢

|zo 6th

|z6

|-

|8/5

|814¢

|gu 6th

|g6

|-

|5/3

|884¢

|yo 6th

|y6

|-

|27/16

|906¢

|wa 6th

|w6

|-

|12/7

|933¢

|ru 6th

|r6

|-

|7/4

|969¢

|zo 7th

|z7

|-

|16/9

|996¢

|wa 7th

|w7

|-

|9/5

|1018¢

|gu 7th

|g7

|-

|15/8

|1088¢

|yo 7th

|y7

|-

|40/21

|1116¢

|ruyo 7th

|ry7

|-

|2/1

|1200¢

|wa octave

|w8

|}

Yo and ru intervals tend to be major, and gu and zo ones tend to be minor. But interval quality is redundant (if a third is yo, it must be major) and not unique (there are other major thirds available). See the "Higher Primes" section below for why quality isn't used with color names. Instead of augmented and diminished, remote intervals are '''large''' (fifthward) and '''small''' (fourthward), abbreviated L and s. '''Central''' means neither large nor small. The '''magnitude''' is found by adding up all the monzo exponents except the first one, dividing by 7, and rounding off. 0 = central, 1 = large, 2 = double large, etc. 81/64 = Lw3, 135/128 = Ly1. Magnitudes do not add up predictably like colors and degrees do: w2 + w2 = Lw3.

[[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 (the pyth comma) is simply the wa comma. 81/80 = g1 is the gu comma. LLg-2 = g1 + 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.

~~See the [[Gallery of Just Intervals]] for more examples of interval names.~~

== Note Names ==

Notes are named ~~zE♭~~, 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. Thus D + y3 = yF#, and from yE to ryF# = r2.

[[File:Lattice51.png|frameless|962x962px]]

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Prime 2 (even more colorless than wa) is clear, abbreviated '''ca''', and yaza noca = 3.5.7. 2-limit intervals like 2/1 are called wa not clear, for simplicity.

Subgroups which omit 5 or 7 are '''noya''' or '''noza''', and those which omit both are '''noyaza'''. Unlike nowa, these terms aren't used in actual subgroup names. They are general descriptive terms, e.g. zala, latha and zalatha are all noya.

== Color Names for Higher Primes ==

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

'''ilo''' = 11-over, '''lu''' = 11-under, and '''la''' = 11-all = 2.3.11 (ilo not lo, because "lo C" sounds like "low C"). ilo 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. 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. ilo notes could be called lovender, and lu notes could be called luvender. Both are "shades" of lavender.

'''ilo''' ("ee-LOW") = 11-over, '''lu''' = 11-under, and '''la''' = 11-all = 2.3.11 (ilo not lo, because "lo C" sounds like "low C"). ilo 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. 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. ilo 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.

'''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.

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The disambiguation prefix i- is only needed when the color word appears alone, and confusion is possible. Thus 11/7 = loru 5th, not iloru 5th, and 29o = twenty-no, not twenty-ino.

== Converting a ~~monzo~~ to/from a color name ==

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

Converting a [[Monzos|monzo]]~~: to~~ find the degree, first find the dot product of the monzo with the 7edo [[~~patent~~ val]] ~~or edomapping~~ <7 11 16 20 24 26 29 30|. Then add 1, or subtract 1 if the ~~answer~~ is negative~~. To find the color, combine all the appropriate colors for each prime, highest prime first~~. To find the magnitude, add up all the monzo exponents except the first one, divide by 7, and round off.

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.

Example: ratio = 63/40, monzo = |-3 2 -1 1>, color = zg, stepspan = -21+22-16+20 = 5, degree = 5+1 = 6, magnitude = round [(2-1+1)/7] = round (2/7) = 0, interval = zg6.

Converting a color name: 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 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 7edo edomapping. Then b = (2S - 2X + 3) mod 7 + 7M - 3, and a = (S - X - 11b) / 7. Convert the monzo to a ratio.

~~Converting a color name~~: ~~The colors directly give you all the~~ monzo ~~entries except the first two.~~ (~~more to come..~~.)

Example: interval = sgg2, S = 2-1 = 1, M = -1, monzo = |a b -2>, X = <7 11 16| dot |0 0 -2> = -32, b = (2-(-64)+3) mod 7 + 7(-1) - 3 = 6-7-3 = -4, a = (1-(-32)-(-44))/7 = 77/7 = 11, monzo = |11 -4 -1>, ratio = 2048/2025.

== Chord Names ==

@@ Line 1: / Line 1: @@
-This is the "crash course". For a full explanation, see [[KiteGiedraitis|Kite's]] book, [http://www.tallkite.com/AlternativeTunings.html "Alternative Tunings: Theory, Notation and Practice"].
+This is a <u>very</u> brief summary. For a full explanation, see [[KiteGiedraitis|Kite's]] book, [http://www.tallkite.com/AlternativeTunings.html "Alternative Tunings: Theory, Notation and Practice"].
 == Color Names for Primes 3, 5 and 7 ==
 Every prime above 3 has two colors, an '''over''' color (prime in the numerator) and an '''under''' color (prime in the denominator). Over colors end with -o, and under colors end with -u. The color for 3-limit ends in -a for '''all''', which includes over (3/2, 9/8), under (4/3, 16/9) and neither (1/1, 2/1).
-'''Wa''' = white (strong but colorless) = 3-limit
+'''Wa''' = white (strong but colorless) = 3-limit <br/>
+'''Yo''' = yellow (warm and sunny) = 5-over = major <br/>
-'''Yo''' = yellow (warm and sunny) = 5-over = major
+'''Gu''' ("goo") = green (not as bright as yellow) = 5-under = minor <br/>
+'''Zo''' = blue/azure (dark and bluesy) = 7-over = subminor <br/>
-'''Gu''' ("goo") = green (not as bright as yellow) = 5-under = minor
+'''Ru''' = red (alarming, inflamed) = 7-under = supermajor
-'''Zo''' = blue/azure (dark and bluesy) = 7-over = subminor
-'''Ru''' = red (alarming, inflamed) = 7-under = supermajor
 The colors come in a red-yellow-green-blue rainbow, with warm/cool colors indicating sharp/flat intervals. The rainbow of 3rds runs 9/7 - 5/4 - 6/5 - 7/6. Colors are abbreviated as w, y, z, etc. Use z (azure) not b (blue), because b looks like a flat sign. Mnemonic: Z looks like 7 with an extra line on the bottom.
-:''For more color names see [[Gallery of Just Intervals #Gallery of Just Intervals|Gallery of Just Intervals]].''
 == Interval Names ==
@@ Line 27: / Line 21: @@
 /10 = zogu 9th = zg9. 25/16 = yoyo 5th = yy5. 128/125 = triple gu 2nd = g<sup>3</sup>2. 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.
-Remote intervals are '''large''' (fifthward) and '''small''' (fourthward), abbreviated L and s. '''Central''' means neither large nor small. The '''magnitude''' is found by adding up all the monzo exponents except the first one, dividing by 7, and rounding off. 0 = central, 1 = large, 2 = double large, etc. 81/64 = Lw3, 135/128 = Ly1. Magnitudes do not add up predictably like colors and degrees do: w2 + w2 = Lw3.
+The next table lists various 7-limit intervals, see the [[Gallery of Just Intervals]] for many more examples.
+{| class="wikitable"
+!'''ratio'''
+!'''cents'''
+!'''color & degree'''
+!'''shorthand'''
+|-
+|1/1
+|0¢
+|wa unison
+|w1
+|-
+|21/20
+|84¢
+|zogu 2nd
+|zg2
+|-
+|16/15
+|112¢
+|gu 2nd
+|g2
+|-
+|10/9
+|182¢
+|yo 2nd
+|y2
+|-
+|9/8
+|204¢
+|wa 2nd
+|w2
+|-
+|8/7
+|231¢
+|ru 2nd
+|r2
+|-
+|7/6
+|267¢
+|zo 3rd
+|z3
+|-
+|32/27
+|294¢
+|wa 3rd
+|w3
+|-
+|6/5
+|316¢
+|gu 3rd
+|g3
+|-
+|5/4
+|386¢
+|yo 3rd
+|y3
+|-
+|9/7
+|435¢
+|ru 3rd
+|r3
+|-
+|21/16
+|471¢
+|zo 4th
+|z4
+|-
+|4/3
+|498¢
+|wa 4th
+|w4
+|-
+|27/20
+|520¢
+|gu 4th
+|g4
+|-
+|7/5
+|583¢
+|zogu 5th
+|zg5
+|-
+|45/32
+|590¢
+|yo 4th
+|y4
+|-
+|64/45
+|610¢
+|gu 5th
+|g5
+|-
+|10/7
+|617¢
+|ruyo 4th
+|ry4
+|-
+|40/27
+|680¢
+|yo 5th
+|y5
+|-
+|3/2
+|702¢
+|wa 5th
+|w5
+|-
+|32/21
+|729¢
+|ru 5th
+|r5
+|-
+|14/9
+|765¢
+|zo 6th
+|z6
+|-
+|8/5
+|814¢
+|gu 6th
+|g6
+|-
+|5/3
+|884¢
+|yo 6th
+|y6
+|-
+|27/16
+|906¢
+|wa 6th
+|w6
+|-
+|12/7
+|933¢
+|ru 6th
+|r6
+|-
+|7/4
+|969¢
+|zo 7th
+|z7
+|-
+|16/9
+|996¢
+|wa 7th
+|w7
+|-
+|9/5
+|1018¢
+|gu 7th
+|g7
+|-
+|15/8
+|1088¢
+|yo 7th
+|y7
+|-
+|40/21
+|1116¢
+|ruyo 7th
+|ry7
+|-
+|2/1
+|1200¢
+|wa octave
+|w8
+|}
+Yo and ru intervals tend to be major, and gu and zo ones tend to be minor. But interval quality is redundant (if a third is yo, it must be major) and not unique (there are other major thirds available). See the "Higher Primes" section below for why quality isn't used with color names. Instead of augmented and diminished, remote intervals are '''large''' (fifthward) and '''small''' (fourthward), abbreviated L and s. '''Central''' means neither large nor small. The '''magnitude''' is found by adding up all the monzo exponents except the first one, dividing by 7, and rounding off. 0 = central, 1 = large, 2 = double large, etc. 81/64 = Lw3, 135/128 = Ly1. Magnitudes do not add up predictably like colors and degrees do: w2 + w2 = Lw3.
 [[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 (the pyth comma) is simply the wa comma. 81/80 = g1 is the gu comma. LLg-2 = g1 + 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.
-See the [[Gallery of Just Intervals]] for more examples of interval names.
 == Note Names ==
-Notes are named zE♭, 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. Thus D + y3 = yF#, and from yE to ryF# = r2.
 [[File:Lattice51.png|frameless|962x962px]]
@@ Line 44: / Line 203: @@
 Prime 2 (even more colorless than wa) is clear, abbreviated '''ca''', and yaza noca = 3.5.7. 2-limit intervals like 2/1 are called wa not clear, for simplicity.
+Subgroups which omit 5 or 7 are '''noya''' or '''noza''', and those which omit both are '''noyaza'''. Unlike nowa, these terms aren't used in actual subgroup names. They are general descriptive terms, e.g. zala, latha and zalatha are all noya.
 == Color Names for Higher Primes ==
 Colors for primes greater than 7 are named after the number itself, using the prefix i- for disambiguation as needed:
-'''ilo''' = 11-over, '''lu''' = 11-under, and '''la''' = 11-all = 2.3.11 (ilo not lo, because "lo C" sounds like "low C"). ilo 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. 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. ilo notes could be called lovender, and lu notes could be called luvender. Both are "shades" of lavender.
+'''ilo''' ("ee-LOW") = 11-over, '''lu''' = 11-under, and '''la''' = 11-all = 2.3.11 (ilo not lo, because "lo C" sounds like "low C"). ilo 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. 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. ilo 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.
+'''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.
@@ Line 66: / Line 227: @@
 The disambiguation prefix i- is only needed when the color word appears alone, and confusion is possible. Thus 11/7 = loru 5th, not iloru 5th, and 29o = twenty-no, not twenty-ino.
-== Converting a monzo to/from a color name ==
+== Converting a ratio to/from a color name ==
-Converting a [[Monzos|monzo]]: to find the degree, first find the dot product of the monzo with the 7edo [[patent val]] or edomapping <7 11 16 20 24 26 29 30|. Then add 1, or subtract 1 if the answer is negative. To find the color, combine all the appropriate colors for each prime, highest prime first. To find the magnitude, add up all the monzo exponents except the first one, divide by 7, and round off.
+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.
+Example: ratio = 63/40, monzo = |-3 2 -1 1>, color = zg, stepspan = -21+22-16+20 = 5, degree = 5+1 = 6, magnitude = round [(2-1+1)/7] = round (2/7) = 0, interval = zg6.
+Converting a color name: 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 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 7edo edomapping. Then b = (2S - 2X + 3) mod 7 + 7M - 3, and a = (S - X - 11b) / 7. Convert the monzo to a ratio.
-Converting a color name: The colors directly give you all the monzo entries except the first two. (more to come...)
+Example: interval = sgg2, S = 2-1 = 1, M = -1, monzo = |a b -2>, X = <7 11 16| dot |0 0 -2> = -32, b = (2-(-64)+3) mod 7 + 7(-1) - 3 = 6-7-3 = -4, a = (1-(-32)-(-44))/7 = 77/7 = 11, monzo = |11 -4 -1>, ratio = 2048/2025.
 == Chord Names ==