Kite's color notation: Difference between revisions

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|gu 2nd

|g2

|-

|15/14

|119¢

|ruyo unison

|ry1

|-

|10/9

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|gu 7th

|g7

|-

|28/15

|1081¢

|zogu octave

|zg8

|-

|15/8

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|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), it's not unique (there are other major thirds available), and quality isn't used with color names (see [[#Color Names for Higher Primes]] below for why). Instead of augmented and diminished, remote intervals are '''large''' (fifthward) and '''small''' (fourthward), written L and s, and sometimes abbreviated '''la''' and '''sa''' (especially in temperament names). '''Central''', the default, means neither large nor small. The '''magnitude''' is the sum all the monzo exponents except the first one, divided by 7, and rounded off. 0 = central, 1 = large, 2 = double large, etc. 81/64 = Lw3, 135/128 = Ly1. Unfortunately, magnitudes do not add up predictably like colors and degrees do: w2 + w2 = Lw3.

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), it's not unique (there are other major thirds available), and quality isn't used with color names (see [[#Color Names for Higher Primes]] below for why). Instead of augmented and diminished, remote intervals are '''large''' (fifthward) and '''small''' (fourthward), written L and s, and sometimes abbreviated '''la''' and '''sa''' (especially in temperament names). '''Central''', the default, means neither large nor small. The general term for large/small/central/etc. is '''magnitude'''. A ratio's magnitude is found from the sum all the monzo exponents except the first one, divided by 7, and rounded off. 0 = central, 1 = large, 2 = double large, etc. 81/64 = Lw3, 135/128 = Ly1. Unfortunately, magnitudes do not add up predictably like colors and degrees do: w2 + w2 = Lw3.

Colors can be doubled or tripled: 25/16 = yoyo 5th = yy5 and 128/125 = triple gu 2nd = g32. Double and triple are often abbreviated '''bi-''' and '''tri-''', especially in temperament names such as Biruyo (50/49) and Trigu (128/125). Bi- is only used if it shortens the name: yoyo not biyo. Quadruple and quintuple are abbreviated '''quad-''' and '''quin-''', as in quadyo or quingu. For sextuple, etc., see [[#Temperament Names]] below.

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The double-large wa negative 2nd (LLw-2, the pyth comma) is simply called the wa comma. 3-limit commas such as L3w-2 = (-30, 19) can be abbreviated as w-19, the wa-19 comma.

Compound, abbreviated '''co-''' or '''c''', is a conventional term that means widened by an octave. 15/4 is a compound yo 7th = coyo 7th = cy7. 5/1 is a double-compound yo 3rd = cocoyo 3rd = ccy3. More examples in the [[Gallery of just intervals#Intervals larger than an octave|Gallery of just intervals]]. Mnemonic: co- as in co-pilot means auxiliary, thus a 9th is a co-2nd.

Compound, abbreviated '''co-''' or '''c''', is a conventional term that means widened by an octave. 15/4 is a compound yo 7th = coyo 7th = cy7. 5/1 is a double-compound yo 3rd = cocoyo 3rd = ccy3. More examples in the [[Gallery of just intervals#Intervals larger than an octave|Gallery of just intervals]]. Mnemonic: co- as in co-pilot means auxiliary, thus a 9th is a co-2nd. See [[#Prime Subgroup Names]] below for another mnemonic.

== Note Names ==

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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. '''Nowaca''' means without 2 or 3, thus 5.7.11 is yazala nowaca. Clear/ca is only ever used in the terms noca and nowaca. However, ~~a good~~ mnemonic for "co-" (compound, widened by an octave) is "clear-over".

Prime 2 (even more colorless than wa) is '''clear''', abbreviated '''ca''', and yaza '''noca''' = 3.5.7 = [[Bohlen-Pierce]]. 2-limit intervals like 2/1 are called wa not clear, for simplicity. '''Nowaca''' means without 2 or 3, thus 5.7.11 is yazala nowaca. Clear/ca is only ever used in the terms noca and nowaca. However, an additional mnemonic for "co-" (compound, widened by an octave) is "clear-over", in the sense that the ratio's numerator is multiplied by 2.

== 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:

'''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. La when by itself may become '''ila''', to avoid confusion with the solfege note La, and also with large. 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 ~~Lulu aka~~ [http://x31eq.com/cgi-bin/rt.cgi?ets=24_17&limit=2_3_11 Neutral] 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. La when by itself may become '''ila''', to avoid confusion with the solfege note La, and also with large. 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 Lulu aka Neutral] 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, 14/13 = 3uz2 = thuzo 2nd.

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'''Ino''' = 19-over, '''nu''' = 19-under, and '''na''' = 19-all, abbreviated as '''19o''', '''19u''' and '''19a'''. Ino because "no 3rd" could mean either 19/16 or thirdless. '''Inu''' is an alternate form of nu, to distinguish "the nu key" from "the new key". 12edo implies yasana = 2.3.5.17.19.

'''Twetho''' = 23-over, '''twethu''' = 23-under, '''~~twentha~~''' =23-all, abbreviated as '''23o''', '''23u''' and '''23a'''. 2.3.5.7.23 = yaza23a = yazatwetha. 23/16 = 23o5 = twetho 5th, and 23/22 = 23o1u2 = twetholu 2nd. 529/512 = bitwetho 2nd (not twethotho, because that means a ratio that's both 23-over and 13-over).

'''Twetho''' = 23-over, '''twethu''' = 23-under, and '''twetha''' = 23-all, abbreviated as '''23o''', '''23u''' and '''23a'''. 2.3.5.7.23 = yaza23a = yazatwetha. 23/16 = 23o5 = twetho 5th, and 23/22 = 23o1u2 = twetholu 2nd. 529/512 = bitwetho 2nd (not twethotho, because that means a ratio that's both 23-over and 13-over).

Similarly, '''tweno/-nu/-na''' = 29o/29u/29a, '''thiwo/-wu/-wa''' = 31o/31u/31a, etc. The abbreviations are '''twe-, thi-, fo-, fi- and si-'''. Unfortunately seventy can't become se- because that already means 17-exponent (see "Temperament Names" below). Setho means 1317-over, so it can't mean 73-over. So starting at 71, the longer form is used: 71o is seventy-wo, 73o is seventy-tho, etc.

Similarly, '''tweno/-nu/-na''' = 29o/29u/29a, '''thiwo/-wu/-wa''' = 31o/31u/31a, etc. The abbreviations are '''twe-, thi-, fo-, fi- and si-'''. Unfortunately seventy can't become se- because that already means 17-exponent (see [[#Temperament Names]] below). Setho means 1317-over, so it can't mean 73-over. So starting at 71, the longer form is used: 71o is seventy-wo, 73o is seventy-tho, etc.

{| class="wikitable"

!prime

|5o

|7o

|11o

|13o

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|-

!word

|yo

|zo

|(i)lo

|tho

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|siso

|}

The prefix i- is only used when confusion is possible. Thus 19/15 = nogu 4th, not inogu 4th, and 2.3.5.17.19 is yasana.

The prefix i- is only used when confusion is possible. Thus 19/15 = nogu 4th, not inogu 4th, and 2.3.5.17.19 is yasana not yasaina.

For any prime P, the degree of the ratio P/1 is chosen to minimize negative intervals. It 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 alternative method ~~is to~~ use the 7edo [[edomapping]], but that requires using every other 14edostep as boundaries, harder to remember and much less convenient than the 24edo boundaries used here.)

For any prime P, the degree of the ratio P/1 is chosen to minimize negative intervals. It is determined by its 8ve-reduced cents, and how it relates to 12edo:

{| class="wikitable"

!unison

!2nd

!3rd

!4th

!5th

!6th

!7th

!8ve

|-

|0-50¢

|50-250¢

|250-450¢

|450-600¢

|600-750¢

|750-950¢

|950-1150¢

|1150-1200¢

|}

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 37...]. An alternative method would use the actual 7edo [[edomapping]], but that requires using every other 14edostep as boundaries, harder to remember and much less convenient than the 24edo boundaries used here. Since negative intervals will arise no matter what, convenience is prioritized. For the first 26 primes, the 24edo-based degrees correspond to 7klmrs-edo.

== Converting a Ratio to/from a Color Name ==

Often a ratio can be converted by breaking it down into simpler, ~~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 not summed, and must be found either visually from the lattices above, or from the monzo directly. 45/32 = [-5 2 1>, and (2+1)/7 rounds to 0, so it's central, and 45/32 = y4.

Often a ratio can be converted by breaking it down into simpler ratios with familiar color names, then adding. 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 not summed, and must be found either visually from the lattices above, or from the monzo directly. 45/32 = [-5 2 1>, and (2+1)/7 rounds to 0, so it's central, and 45/32 = y4.

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

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== Staff Notation ==

Notes on the staff default to wa. Non-wa notes have a color accidental like g, ry, etc. Like conventional sharp/flat accidentals, they apply to every such note in the measure and in the same octave. Unlike conventional accidentals which apply to a note (e.g. A), color accidentals only apply to one specific "version" of that note (e.g. A flat or A natural). For example, the yo accidental in the first chord applies to all the D naturals in that measure, but not to the D flats.

Notes on the staff default to wa. Non-wa notes have a color accidental like g, ry, etc. Like conventional sharp/flat accidentals, they apply to every such note in the measure and in the same octave. Unlike conventional accidentals which apply to a note (e.g. A), color accidentals only apply to one specific "version" of that note (e.g. A flat or A natural). For example, the yo accidental in the first chord applies to all the D-naturals in that measure, but not to the D-flats.

[[File:Notation example 1.png|frameless|781x781px]]

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Color notation can optionally be made more similar to Sagittal notation by including two more accidentals, '''p''' and '''q''' (long forms '''po''' and '''qu''' = "ku"), to indicate raising/lowering by a pythagorean comma. (See [http://tallkite.com/misc_files/Sagittal-JI-Translated-To-Colors.png Sagittal-JI-Translated-To-Colors.png].) For example, yF# = ypGb, and zEb = zqD#. This allows trills to always be written as a 2nd, less cluttered.[[File:Notation example 5a.png|992x992px]]

L and s never appear on the staff. Tripled colors are written as y3 ~~not~~ yyy. In MuseScore, color accidentals are made by adding fingerings to the notes, then editing the fingering text. The font used here is Arial Black.

L and s never appear on the staff. Tripled colors are written as y3 not y3 or yyy. In MuseScore, color accidentals are made by adding fingerings to the notes, then editing the fingering text. This text can be copied and pasted. The font used here is Arial Black.

== Chord Names ==

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Alterations are always in parentheses, additions never are, e.g. z7(zg5) and z,y6. An alteration's degree must match a note in the chord, e.g. Cz7(y6) is invalid. But an exception is made for sus chords, where degree 2 or 4 alter the 3rd: C(z4) = w1 z4 w5. The sus note defaults to wa: Cy9(4) = w1 w4 w5 y7 w9.

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.

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 called the h7 chord ("har-seven"), because it's part of the harmonic series. Ch9 = Cy,z7,w9 and Ch11 = Cy,z7,w9,1o11. The s7 ("sub-seven") chord is part of the subharmonic series. It's the first 7 subharmonics, with the 7th subharmonic becoming the root. Cs9 = Cr,g7,w9 and Cs11 = C1o11(1or5,1og9). Note that s9 is not s7 plus a 9th, but a completely different chord. Usually the 9th ascends from the root, but in a sub9 chord it descends from the top note, and becomes the new root.

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| style="text-align:center" | +

|add an untempered prime to the temperament

|Blackwood = 2.3.5 with 256/243 tempered out = ~~5-edo~~ + ya

|Blackwood = 2.3.5 with 256/243 tempered out = Sawa + ya

|-

| colspan="2" |nowa

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|lowered by some other comma

|-

| ~~colspan="2"~~ |~~plain~~

|plain

|♢

|neither up nor down nor lifted nor dropped

|-

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==Translations==

:''For translations of color notation terms into other languages, see [[Color notation/Translations]].''

:For translations of color notation terms into other languages, see [[Color notation/Translations]].

[[Category:Color notation| ]]

[[Category:Just intonation]]

[[Category:Notation]]

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 |gu 2nd
 |g2
+|-
+|15/14
+|119¢
+|ruyo unison
+|ry1
 |-
 |10/9
@@ Line 178: / Line 183: @@
 |gu 7th
 |g7
+|-
+|28/15
+|1081¢
+|zogu octave
+|zg8
 |-
 |15/8
@@ Line 194: / Line 204: @@
 |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), it's not unique (there are other major thirds available), and quality isn't used with color names (see [[#Color Names for Higher Primes]] below for why). Instead of augmented and diminished, remote intervals are '''large''' (fifthward) and '''small''' (fourthward), written L and s, and sometimes abbreviated '''la''' and '''sa''' (especially in temperament names). '''Central''', the default, means neither large nor small. The '''magnitude''' is the sum all the monzo exponents except the first one, divided by 7, and rounded off. 0 = central, 1 = large, 2 = double large, etc. 81/64 = Lw3, 135/128 = Ly1. Unfortunately, magnitudes do not add up predictably like colors and degrees do: w2 + w2 = Lw3.
+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), it's not unique (there are other major thirds available), and quality isn't used with color names (see [[#Color Names for Higher Primes]] below for why). Instead of augmented and diminished, remote intervals are '''large''' (fifthward) and '''small''' (fourthward), written L and s, and sometimes abbreviated '''la''' and '''sa''' (especially in temperament names). '''Central''', the default, means neither large nor small. The general term for large/small/central/etc. is '''magnitude'''. A ratio's magnitude is found from the sum all the monzo exponents except the first one, divided by 7, and rounded off. 0 = central, 1 = large, 2 = double large, etc. 81/64 = Lw3, 135/128 = Ly1. Unfortunately, magnitudes do not add up predictably like colors and degrees do: w2 + w2 = Lw3.
 Colors can be doubled or tripled: 25/16 = yoyo 5th = yy5 and 128/125 = triple gu 2nd = g<sup>3</sup>2. Double and triple are often abbreviated '''bi-''' and '''tri-''', especially in temperament names such as Biruyo (50/49) and Trigu (128/125). Bi- is only used if it shortens the name: yoyo not biyo. Quadruple and quintuple are abbreviated '''quad-''' and '''quin-''', as in quadyo or quingu. For sextuple, etc., see [[#Temperament Names]] below.
@@ Line 206: / Line 216: @@
 The double-large wa negative 2nd (LLw-2, the pyth comma) is simply called the wa comma. 3-limit commas such as L<sup>3</sup>w-2 = (-30, 19) can be abbreviated as w-19, the wa-19 comma.
-Compound, abbreviated '''co-''' or '''c''', is a conventional term that means widened by an octave. 15/4 is a compound yo 7th = coyo 7th = cy7. 5/1 is a double-compound yo 3rd = cocoyo 3rd = ccy3. More examples in the [[Gallery of just intervals#Intervals larger than an octave|Gallery of just intervals]]. Mnemonic: co- as in co-pilot means auxiliary, thus a 9th is a co-2nd.
+Compound, abbreviated '''co-''' or '''c''', is a conventional term that means widened by an octave. 15/4 is a compound yo 7th = coyo 7th = cy7. 5/1 is a double-compound yo 3rd = cocoyo 3rd = ccy3. More examples in the [[Gallery of just intervals#Intervals larger than an octave|Gallery of just intervals]]. Mnemonic: co- as in co-pilot means auxiliary, thus a 9th is a co-2nd. See [[#Prime Subgroup Names]] below for another mnemonic.
 == Note Names ==
@@ Line 216: / Line 226: @@
 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. '''Nowaca''' means without 2 or 3, thus 5.7.11 is yazala nowaca. Clear/ca is only ever used in the terms noca and nowaca. However, a good mnemonic for "co-" (compound, widened by an octave) is "clear-over".
+Prime 2 (even more colorless than wa) is '''clear''', abbreviated '''ca''', and yaza '''noca''' = 3.5.7 = [[Bohlen-Pierce]]. 2-limit intervals like 2/1 are called wa not clear, for simplicity. '''Nowaca''' means without 2 or 3, thus 5.7.11 is yazala nowaca. Clear/ca is only ever used in the terms noca and nowaca. However, an additional mnemonic for "co-" (compound, widened by an octave) is "clear-over", in the sense that the ratio's numerator is multiplied by 2.
 == 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:
-'''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. La when by itself may become '''ila''', to avoid confusion with the solfege note La, and also with large. 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 Lulu aka [http://x31eq.com/cgi-bin/rt.cgi?ets=24_17&limit=2_3_11 Neutral] 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. La when by itself may become '''ila''', to avoid confusion with the solfege note La, and also with large. 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 Lulu aka Neutral] 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, 14/13 = 3uz2 = thuzo 2nd.
@@ Line 233: / Line 243: @@
 '''Ino''' = 19-over, '''nu''' = 19-under, and '''na''' = 19-all, abbreviated as '''19o''', '''19u''' and '''19a'''. Ino because "no 3rd" could mean either 19/16 or thirdless. '''Inu''' is an alternate form of nu, to distinguish "the nu key" from "the new key". 12edo implies yasana = 2.3.5.17.19.
-'''Twetho''' = 23-over, '''twethu''' = 23-under, '''twentha''' =23-all, abbreviated as '''23o''', '''23u''' and '''23a'''. 2.3.5.7.23 = yaza23a = yazatwetha. 23/16 = 23o5 = twetho 5th, and 23/22 = 23o1u2 = twetholu 2nd. 529/512 = bitwetho 2nd (not twethotho, because that means a ratio that's both 23-over and 13-over).
+'''Twetho''' = 23-over, '''twethu''' = 23-under, and '''twetha''' = 23-all, abbreviated as '''23o''', '''23u''' and '''23a'''. 2.3.5.7.23 = yaza23a = yazatwetha. 23/16 = 23o5 = twetho 5th, and 23/22 = 23o1u2 = twetholu 2nd. 529/512 = bitwetho 2nd (not twethotho, because that means a ratio that's both 23-over and 13-over).
-Similarly, '''tweno/-nu/-na''' = 29o/29u/29a, '''thiwo/-wu/-wa''' = 31o/31u/31a, etc. The abbreviations are '''twe-, thi-, fo-, fi- and si-'''. Unfortunately seventy can't become se- because that already means 17-exponent (see "Temperament Names" below). Setho means 13<sup>17</sup>-over, so it can't mean 73-over. So starting at 71, the longer form is used: 71o is seventy-wo, 73o is seventy-tho, etc.
+Similarly, '''tweno/-nu/-na''' = 29o/29u/29a, '''thiwo/-wu/-wa''' = 31o/31u/31a, etc. The abbreviations are '''twe-, thi-, fo-, fi- and si-'''. Unfortunately seventy can't become se- because that already means 17-exponent (see [[#Temperament Names]] below). Setho means 13<sup>17</sup>-over, so it can't mean 73-over. So starting at 71, the longer form is used: 71o is seventy-wo, 73o is seventy-tho, etc.
 {| class="wikitable"
 !prime
+|5o
+|7o
 |11o
 |13o
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 |-
 !word
+|yo
+|zo
 |(i)lo
 |tho
@@ Line 271: / Line 285: @@
 |siso
 |}
-The prefix i- is only used when confusion is possible. Thus 19/15 = nogu 4th, not inogu 4th, and 2.3.5.17.19 is yasana.
+The prefix i- is only used when confusion is possible. Thus 19/15 = nogu 4th, not inogu 4th, and 2.3.5.17.19 is yasana not yasaina.
-For any prime P, the degree of the ratio P/1 is chosen to minimize negative intervals. It 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 alternative method is to use the 7edo [[edomapping]], but that requires using every other 14edostep as boundaries, harder to remember and much less convenient than the 24edo boundaries used here.)
+For any prime P, the degree of the ratio P/1 is chosen to minimize negative intervals. It is determined by its 8ve-reduced cents, and how it relates to 12edo:
+{| class="wikitable"
+!unison
+!2nd
+!3rd
+!4th
+!5th
+!6th
+!7th
+!8ve
+|-
+|0-50¢
+|50-250¢
+|250-450¢
+|450-600¢
+|600-750¢
+|750-950¢
+|950-1150¢
+|1150-1200¢
+|}
+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 37...]. An alternative method would use the actual 7edo [[edomapping]], but that requires using every other 14edostep as boundaries, harder to remember and much less convenient than the 24edo boundaries used here. Since negative intervals will arise no matter what, convenience is prioritized. For the first 26 primes, the 24edo-based degrees correspond to 7klmrs-edo.
 == Converting a Ratio to/from a Color Name ==
-Often a ratio can be converted by breaking it down into simpler, 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)/7 rounds to 0, so it's central, and 45/32 = y4.
+Often a ratio can be converted by breaking it down into simpler ratios with familiar color names, then adding. 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)/7 rounds to 0, so it's central, and 45/32 = y4.
 For more complex ratios, a more direct method is used:
@@ Line 289: / Line 323: @@
 == Staff Notation ==
-Notes on the staff default to wa. Non-wa notes have a color accidental like g, ry, etc. Like conventional sharp/flat accidentals, they apply to every such note in the measure and in the same octave. Unlike conventional accidentals which apply to a note (e.g. A), color accidentals only apply to one specific "version" of that note (e.g. A flat or A natural). For example, the yo accidental in the first chord applies to all the D naturals in that measure, but not to the D flats.
+Notes on the staff default to wa. Non-wa notes have a color accidental like g, ry, etc. Like conventional sharp/flat accidentals, they apply to every such note in the measure and in the same octave. Unlike conventional accidentals which apply to a note (e.g. A), color accidentals only apply to one specific "version" of that note (e.g. A flat or A natural). For example, the yo accidental in the first chord applies to all the D-naturals in that measure, but not to the D-flats.
 [[File:Notation example 1.png|frameless|781x781px]]
@@ Line 299: / Line 333: @@
 Color notation can optionally be made more similar to Sagittal notation by including two more accidentals, '''p''' and '''q''' (long forms '''po''' and '''qu''' = "ku"), to indicate raising/lowering by a pythagorean comma. (See [http://tallkite.com/misc_files/Sagittal-JI-Translated-To-Colors.png Sagittal-JI-Translated-To-Colors.png].) For example, yF# = ypGb, and zEb = zqD#. This allows trills to always be written as a 2nd, less cluttered.[[File:Notation example 5a.png|992x992px]]
-L and s never appear on the staff. Tripled colors are written as y<sup>3</sup> not yyy. In MuseScore, color accidentals are made by adding fingerings to the notes, then editing the fingering text. The font used here is Arial Black.
+L and s never appear on the staff. Tripled colors are written as y3 not y<sup>3</sup> or yyy. In MuseScore, color accidentals are made by adding fingerings to the notes, then editing the fingering text. This text can be copied and pasted. The font used here is Arial Black.
 == Chord Names ==
@@ Line 316: / Line 350: @@
 <u>Alterations are always in parentheses</u>, additions never are, e.g. z7(zg5) and z,y6. An alteration's degree must match a note in the chord, e.g. Cz7(y6) is invalid. But an exception is made for sus chords, where degree 2 or 4 alter the 3rd: C(z4) = w1 z4 w5. The sus note defaults to wa: Cy9(4) = w1 w4 w5 y7 w9.
-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.
+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 called the h7 chord ("har-seven"), because it's part of the harmonic series. Ch9 = Cy,z7,w9 and Ch11 = Cy,z7,w9,1o11. The s7 ("sub-seven") chord is part of the subharmonic series. It's the first 7 subharmonics, with the 7th subharmonic becoming the root. Cs9 = Cr,g7,w9 and Cs11 = C1o11(1or5,1og9). Note that s9 is not s7 plus a 9th, but a completely different chord. Usually the 9th ascends from the root, but in a sub9 chord it descends from the top note, and becomes the new root.
@@ Line 492: / Line 526: @@
 | style="text-align:center" | +
 |add an untempered prime to the temperament
-|Blackwood = 2.3.5 with 256/243 tempered out = 5-edo + ya
+|Blackwood = 2.3.5 with 256/243 tempered out = Sawa + ya
 |-
 | colspan="2" |nowa
@@ Line 571: / Line 605: @@
 |lowered by some other comma
 |-
-| colspan="2" |plain
+|plain
+|♢
 |neither up nor down nor lifted nor dropped
 |-
@@ Line 581: / Line 616: @@
 ==Translations==
-:''For translations of color notation terms into other languages, see [[Color notation/Translations]].''
+:For translations of color notation terms into other languages, see [[Color notation/Translations]].
 [[Category:Color notation| ]] <!-- main article -->
 [[Category:Just intonation]]
 [[Category:Notation]]