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"].

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

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

Every prime above 3 has two ~~color names~~, ~~one for~~ '''over''' (prime in the numerator) and ~~one for~~ '''under''' (prime in the denominator). Over colors end with -o, and under colors with -u. ~~Here~~'~~s the colors 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

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'''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. ~~Azure is used instead of~~ blue because b looks like a flat sign. Mnemonic: Z looks like 7 with an extra line on the bottom.

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.

== Interval Names ==

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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|~~731x731px~~]]

[[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 ~~so much~~ higher.

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.

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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.

[[File:Lattice51.png|frameless|~~810x810px~~]]

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

== Prime Subgroup Names ==

Just as wa means 3-all or 3-limit, '''ya''' means 5-all and includes wa, yo, gu, yoyo, gugu, etc. Ya = the 2.3.5 prime subgroup = 5-limit. '''Za''' = 7-all = 2.3.7. Yaza = 2.3.5.7 = 7-limit. '''Nowa''' means without wa, and yaza nowa = 2.5.7.

Just as wa means 3-all or 3-limit, '''ya''' means 5-all and includes wa, yo, gu, yoyo, gugu, etc. Ya = the 2.3.5 prime subgroup = 5-limit. '''Za''' = 7-all = 2.3.7. Yaza = 2.3.5.7 = the full 7-limit. '''Nowa''' means without wa, and yaza nowa = 2.5.7.

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.

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Colors for primes greater than 7 are named after the number itself:

'''Lova''' = 11-over, '''lu''' = 11-under, and '''la''' = 11-all = 2.3.11. (Lova not lo, because "lo C" sounds like "low C".) Lova and lu are abbreviated to '''1o''' and '''1u''' on the score and in interval names and chord names, e.g. lova A = 1oA, lova 4th = 1o4 = 11/8 and C lova-7 = C1o7 = 1/1 - 11/9 - 3/2 - 11/6. The associated color is lavender (mnemonic: "e-leven-der"), which refers to both lova and lu, since they are only 7.1¢ apart ~~(implying~~ the [http://x31eq.com/cgi-bin/rt.cgi?ets=24_17&limit=2_3_11 Neuter] temperament). ~~More precisely, lova~~ notes could be called lovender, and lu notes could be called luvender. Both are shades of lavender.

'''Lova''' = 11-over, '''lu''' = 11-under, and '''la''' = 11-all = 2.3.11. (Lova not lo, because "lo C" sounds like "low C".) Lova and lu are abbreviated to '''1o''' and '''1u''' on the score and in interval names and chord names, e.g. lova A = 1oA, lova 4th = 1o4 = 11/8 and C lova-7 = C1o7 = 1/1 - 11/9 - 3/2 - 11/6. The associated color is lavender (mnemonic: "e-leven-der"), which refers to both lova 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. Lova 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.

'''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 use '''tro''', '''tru''' and '''tra'''.

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.

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.

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 3oA♭, but 13/8 is only 3o6. This is the rationale for using large/small rather than major/minor. Intervals names and chord names become unambiguous for la and tha intervals. Also, commonly used intervals and chords get concise names: gu 3rd not gu minor 3rd, Ag not Agm, etc. 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.

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 3oA♭, but 13/8 is only 3o6. This is the rationale for using large/small rather than major/minor. Intervals names and chord names become unambiguous for la and tha intervals. Also, commonly used intervals and chords get concise names: gu 3rd not gu minor 3rd, Ag not Agm, etc.

'''So''' = 17-over, '''su''' = 17-under, and '''sa''' = 17-all, abbreviated as '''17o''' and '''17u'''. '''Sova''' is an alternate form of so, to distinguish it from the solfege syllable Sol.

'''Nova''' = 19-over, '''nunda''' = 19-under, '''na''' = 19-all, abbreviated as '''19o''' and '''19u'''. Nova because "no 3rd" could mean either 19/16 or thirdless. Nunda because "the nu key" sounds like "the new key". 12edo implies yasana = 2.3.5.17.19.

'''Nova''' = 19-over, '''nunda''' = 19-under, and '''na''' = 19-all, abbreviated as '''19o''' and '''19u'''. Nova because "no 3rd" could mean either 19/16 or thirdless. Nunda because "the nu key" sounds like "the new key". 12edo implies yasana = 2.3.5.17.19.

'''Twenty-tho''' = 23-over, '''twenty-thu''' = 23-under, '''twenty-tha''' =23-all, abbreviated as '''23o''', '''23u''' and '''23a'''. 2.3.5.7.23 = yaza23a = "yaza-twenty-tha".

'''~~Twenty~~-no/-nu/-na''' = 29o/29u/29a, '''thirty-wo/-wu/-wa''' = 31o/31u/31a, '''thirty-so/-su/-sa''' = 37o/37u/37a, etc.

Similarly, '''twenty-no/-nu/-na''' = 29o/29u/29a, '''thirty-wo/-wu/-wa''' = 31o/31u/31a, '''thirty-so/-su/-sa''' = 37o/37u/37a, etc.

The alternate forms with -ova or -unda are only needed when the color word appears alone, and confusion is possible. Thus 11/7 = loru 5th, not lovaru 5th, and 29o = twenty-no, not twenty-nova.

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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. There are h9 chords, s11 chords, etc.

Alterations are in parentheses, additions never are~~. Example: Ch7(zg5)zg9 = C yE zgG♭ zB♭ zgD♭~~. Omissions are indicated by "no", as in Ch11no3. In harmonic and subharmonic chords, the 3 refers to the degree, not the 3rd harmonic. However numbers ≥ 15 always refer to (sub)harmonics, as in Ch15.

Alterations are always in parentheses, additions never are. Omissions are indicated by "no", as in Ch11no3. The Hendrix chord might be Ch7,z10no5. In harmonic and subharmonic chords, the 3 refers to the degree, not the 3rd harmonic. However numbers ≥ 15 always refer to (sub)harmonics, as in Ch15.

An 11th implies a 3rd, 5th, 7th and 9th. A 13th implies all these plus an 11th. The 5th, 9th and/or 13th default to wa. The 6th, 7th, and/or 11th defaults to the color of the 3rd. Thus a y13 chord = w1 y3 w5 y7 w9 y11 w13. However, an add 11 chord defaults to a wa 11: Cz7,11 = w1 z3 w5 z7 w11

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== Chord Progressions, Keys and Modulations ==

The tonic is always wa. The root of each chord has a color, which defaults to wa. C - Am - F - ~~G would~~ be Cy - yAg - Fy - Gy.

The tonic is always wa. The root of each chord has a color, which defaults to wa. C - Am - F - G7 might be Cy - yAg - Fy - Gy,w7.

In relative notation, the I, IV and V chords default to a wa root. II, III, VI and VII must have an explicit root-color. gCy - gGy - Ag becomes gIIIy - gVIIy - Ig.

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== Ups and Downs, Lifts and Drops ==

Color notation merely renames ratios ~~in a~~ more ~~convenient form~~, and strictly speaking, it only applies to just intonation. However, just as ratios can loosely describe edo notes, colors can be loosely applied to edos as well. A more precise application is to use ups and downs (^ and v) as "virtual colors" that always map to exactly one edostep.

Color notation merely renames ratios more conveniently, and strictly speaking, it only applies to just intonation. However, just as ratios can loosely describe edo notes, colors can be loosely applied to edos as well. A more precise application is to use ups and downs (^ and v) as "virtual colors", accidentals that always map to exactly one edostep. Notes are named up C sharp = ^C#, or C sharp up = C#^. Ups and downs are used on the score just like color accidentals are. Intervals are named upmajor 3rd = ^M3, down 4th = v4, etc. Chords are named upminor 7th = ^m7, etc.

Rank-2 temperaments can be notated with ups and downs as well. Some require another accidental pair, lifts and drops (/ and \). See the [[Pergen|pergens]] page.

=='''FULL EXPLANATION:'''==

@@ 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"].
-== Color Names for 3, 5 and 7 ==
+== Color Names for Primes 3, 5 and 7 ==
-Every prime above 3 has two color names, one for '''over''' (prime in the numerator) and one for '''under''' (prime in the denominator). Over colors end with -o, and under colors with -u. Here's the colors 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
@@ Line 14: / Line 14: @@
 '''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. Azure is used instead of blue because b looks like a flat sign. Mnemonic: Z looks like 7 with an extra line on the bottom.
+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.
 == Interval Names ==
@@ Line 27: / Line 27: @@
 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|731x731px]]
+[[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 so much higher.
+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.
@@ Line 36: / Line 36: @@
 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.
-[[File:Lattice51.png|frameless|810x810px]]
+[[File:Lattice51.png|frameless|962x962px]]
 == Prime Subgroup Names ==
-Just as wa means 3-all or 3-limit, '''ya''' means 5-all and includes wa, yo, gu, yoyo, gugu, etc. Ya = the 2.3.5 prime subgroup = 5-limit. '''Za''' = 7-all = 2.3.7. Yaza = 2.3.5.7 = 7-limit. '''Nowa''' means without wa, and yaza nowa = 2.5.7.
+Just as wa means 3-all or 3-limit, '''ya''' means 5-all and includes wa, yo, gu, yoyo, gugu, etc. Ya = the 2.3.5 prime subgroup = 5-limit. '''Za''' = 7-all = 2.3.7. Yaza = 2.3.5.7 = the full 7-limit. '''Nowa''' means without wa, and yaza nowa = 2.5.7.
 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.
@@ Line 46: / Line 46: @@
 Colors for primes greater than 7 are named after the number itself:
-'''Lova''' = 11-over, '''lu''' = 11-under, and '''la''' = 11-all = 2.3.11. (Lova not lo, because "lo C" sounds like "low C".) Lova and lu are abbreviated to '''1o''' and '''1u''' on the score and in interval names and chord names, e.g. lova A = 1oA, lova 4th = 1o4 = 11/8 and C lova-7 = C1o7 = 1/1 - 11/9 - 3/2 - 11/6. The associated color is lavender (mnemonic: "e-leven-der"), which refers to both lova and lu, since they are only 7.1¢ apart (implying the [http://x31eq.com/cgi-bin/rt.cgi?ets=24_17&limit=2_3_11 Neuter] temperament). More precisely, lova notes could be called lovender, and lu notes could be called luvender. Both are shades of lavender.
+'''Lova''' = 11-over, '''lu''' = 11-under, and '''la''' = 11-all = 2.3.11. (Lova not lo, because "lo C" sounds like "low C".) Lova and lu are abbreviated to '''1o''' and '''1u''' on the score and in interval names and chord names, e.g. lova A = 1oA, lova 4th = 1o4 = 11/8 and C lova-7 = C1o7 = 1/1 - 11/9 - 3/2 - 11/6. The associated color is lavender (mnemonic: "e-leven-der"), which refers to both lova 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. Lova 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.
+'''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 use '''tro''', '''tru''' and '''tra'''.
-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.
+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.
-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 3oA♭, but 13/8 is only 3o6. <u>This is the rationale for using large/small rather than major/minor</u>. Intervals names and chord names become unambiguous for la and tha intervals. Also, commonly used intervals and chords get concise names: gu 3rd not gu minor 3rd, Ag not Agm, etc. 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.
+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 3oA♭, but 13/8 is only 3o6. <u>This is the rationale for using large/small rather than major/minor</u>. Intervals names and chord names become unambiguous for la and tha intervals. Also, commonly used intervals and chords get concise names: gu 3rd not gu minor 3rd, Ag not Agm, etc.
 '''So''' = 17-over, '''su''' = 17-under, and '''sa''' = 17-all, abbreviated as '''17o''' and '''17u'''. '''Sova''' is an alternate form of so, to distinguish it from the solfege syllable Sol.
-'''Nova''' = 19-over, '''nunda''' = 19-under, '''na''' = 19-all, abbreviated as '''19o''' and '''19u'''. Nova because "no 3rd" could mean either 19/16 or thirdless. Nunda because "the nu key" sounds like "the new key". 12edo implies yasana = 2.3.5.17.19.
+'''Nova''' = 19-over, '''nunda''' = 19-under, and '''na''' = 19-all, abbreviated as '''19o''' and '''19u'''. Nova because "no 3rd" could mean either 19/16 or thirdless. Nunda because "the nu key" sounds like "the new key". 12edo implies yasana = 2.3.5.17.19.
 '''Twenty-tho''' = 23-over, '''twenty-thu''' = 23-under, '''twenty-tha''' =23-all, abbreviated as '''23o''', '''23u''' and '''23a'''. 2.3.5.7.23 = yaza23a = "yaza-twenty-tha".
-'''Twenty-no/-nu/-na''' = 29o/29u/29a, '''thirty-wo/-wu/-wa''' = 31o/31u/31a, '''thirty-so/-su/-sa''' = 37o/37u/37a, etc.
+Similarly, '''twenty-no/-nu/-na''' = 29o/29u/29a, '''thirty-wo/-wu/-wa''' = 31o/31u/31a, '''thirty-so/-su/-sa''' = 37o/37u/37a, etc.
 The alternate forms with -ova or -unda are only needed when the color word appears alone, and confusion is possible. Thus 11/7 = loru 5th, not lovaru 5th, and 29o = twenty-no, not twenty-nova.
@@ Line 75: / Line 75: @@
 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. There are h9 chords, s11 chords, etc.
-<u>Alterations are in parentheses</u>, additions never are. Example: Ch7(zg5)zg9 = C yE zgG♭ zB♭ zgD♭. Omissions are indicated by "no", as in Ch11no3. In harmonic and subharmonic chords, the 3 refers to the degree, not the 3rd harmonic. However numbers ≥ 15 always refer to (sub)harmonics, as in Ch15.
+<u>Alterations are always in parentheses</u>, additions never are. Omissions are indicated by "no", as in Ch11no3. The Hendrix chord might be Ch7,z10no5. In harmonic and subharmonic chords, the 3 refers to the degree, not the 3rd harmonic. However numbers ≥ 15 always refer to (sub)harmonics, as in Ch15.
 An 11th implies a 3rd, 5th, 7th and 9th. A 13th implies all these plus an 11th. The 5th, 9th and/or 13th default to wa. The 6th, 7th, and/or 11th defaults to the color of the 3rd. Thus a y13 chord = w1 y3 w5 y7 w9 y11 w13. However, an add 11 chord defaults to a wa 11: Cz7,11 = w1 z3 w5 z7 w11
@@ Line 91: / Line 91: @@
 == Chord Progressions, Keys and Modulations ==
-The tonic is always wa. The root of each chord has a color, which defaults to wa. C - Am - F - G would be Cy - yAg - Fy - Gy.
+The tonic is always wa. The root of each chord has a color, which defaults to wa. C - Am - F - G7 might be Cy - yAg - Fy - Gy,w7.
 In relative notation, the I, IV and V chords default to a wa root. II, III, VI and VII <u>must</u> have an explicit root-color. gCy - gGy - Ag becomes gIIIy - gVIIy - Ig.
@@ Line 107: / Line 107: @@
 == Ups and Downs, Lifts and Drops ==
-Color notation merely renames ratios in a more convenient form, and strictly speaking, it only applies to just intonation. However, just as ratios can loosely describe edo notes, colors can be loosely applied to edos as well. A more precise application is to use ups and downs (^ and v) as "virtual colors" that always map to exactly one edostep.
+Color notation merely renames ratios more conveniently, and strictly speaking, it only applies to just intonation. However, just as ratios can loosely describe edo notes, colors can be loosely applied to edos as well. A more precise application is to use ups and downs (^ and v) as "virtual colors", accidentals that always map to exactly one edostep. Notes are named up C sharp = ^C#, or C sharp up = C#^. Ups and downs are used on the score just like color accidentals are. Intervals are named upmajor 3rd = ^M3, down 4th = v4, etc. Chords are named upminor 7th = ^m7, etc.
+Rank-2 temperaments can be notated with ups and downs as well. Some require another accidental pair, lifts and drops (/ and \). See the [[Pergen|pergens]] page.
 =='''<u>FULL EXPLANATION</u>:'''==