Kite's color notation: Difference between revisions

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|w8

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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.

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 as L and s, and abbreviated as '''la''' and '''sa'''. '''Central''', the default, means neither large nor small. The general term for large/small/central/etc. is '''magnitude'''. When discussing magnitudes in general (e.g. tempering out a large comma usually flattens the 5th), the full words large and small are used to avoid confusion with solfege's La and saregam's Sa. A ratio's magnitude is the sum of 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. Only intervals have a magnitude, notes never do, and L and s never appear on the staff.

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.

Colors can be doubled or tripled, which are abbreviated '''bi-''' and '''tri-''': 49/25= bizogu 9th = zzgg9 and 128/125 = trigu 2nd = g32. Bi- is only used if it shortens the name: 25/16 = yoyo 5th not biyo 5th. Quadruple and quintuple are abbreviated '''quad-''' and '''quin-''', as in quadyo or quingu. Likewise with magnitudes: lala, trisa, quadla, etc. For sextuple, etc., see [[#Temperament Names]] below.

Colors using only one prime above 3 are called '''primary''' colors. Thus gu and yoyo are primary and ruyo is non-primary.

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[[File:Lattice41a.png|833x833px]]

Degrees can be negative: 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. There are also diminished unisons, which raise the pitch but diminish the quality. For example, if 11/8 is a P4, two of them are a m7 of 121/64 = 1102¢. Going from a yo M7 = 1088¢ up to this m7 raises the pitch, and 121/120 is a dim unison.

Degrees can be negative: 50/49 = biruyo 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. There are also diminished unisons, which raise the pitch but diminish the quality. For example, if 11/8 is notated as a P4, two of them are a m7 of 121/64 = 1102¢. Going from a yo M7 = 1088¢ up to this m7 raises the pitch, and 121/120 is a dim unison.

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.

The lalawa negative 2nd (LLw-2, the [[Pythagorean comma|pythagorean or 12-edo comma]]) is simply called the wa comma. The [[256/243|5-edo comma]] is the sawa comma, and the [[2187/2048|7-edo comma]] is the lawa comma. All other 3-limit commas such as L3w-2 = (-30, 19) are named 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. See [[#Prime Subgroup Names]] below for another mnemonic.

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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. 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.

'''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 becomes '''ila''', to avoid confusion with the solfege note La, and also with la for 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, trilu 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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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).

'''So''' = 17-over, '''su''' = 17-under, and '''sa''' = 17-all, abbreviated as '''17o''', '''17u''' and '''17a'''. '''Iso''' is an alternate form of so, to distinguish it from the solfege syllable So. 17/12 = 17o5 = iso So. '''Isa''' is an alternate form of sa, to distinguish it from small, and from the Indian saregam syllable Sa.

'''So''' = 17-over, '''su''' = 17-under, and '''sa''' = 17-all, abbreviated as '''17o''', '''17u''' and '''17a'''. '''Iso''' is an alternate form of so, to distinguish it from the solfege syllable So. 17/12 = 17o5 = iso So. '''Isa''' is an alternate form of sa, to distinguish it from sa for small, and from the Indian saregam syllable Sa.

'''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.

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== Temperament Names ==

Temperaments are named after the color of the comma(s) they temper out. ~~Many words are abbreviated~~. ~~Large becomes la~~ and ~~small becomes sa~~. ~~Double, triple, etc, become bi-, tri~~-, ~~quad- and quin-. Sextuple~~ is ~~tribi~~-, and ~~septuple~~ is ~~sep-~~. Eleven-fold is le- = "e'''l'''even '''e'''xponent".

Temperaments are named after the color of the comma(s) they temper out. The degree is omitted. Sextuple is tribi- and septuple is sep-. Eightfold is quadbi-, ninefold is tritri-, and tenfold is quinbi. Eleven-fold is le- = "e'''l'''even '''e'''xponent".

[[Meantone]] is the Gu temperament. [[Srutal]] is Sagugu. [[Porcupine]] is Triyo. Some multi-comma temperaments have multiple commas in their name, and some don't. [[Meantone family#Septimal meantone|Septimal Meantone]] is Gu, but [[Meantone family#Dominant|Dominant Meantone]] is Gu & Rugu. Untempered primes are included with a plus sign. The 2.3.5.7 prime subgroup with 81/80 tempered out is Gu + za.

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|as a suffix, 2nd smallest comma in the row segment

|Meantone = 81/80 = Gu = gT, Father = 16/15 = Gubi = g#2T

|-

~~|large~~

~~| style="text-align:center" |L~~

~~|augmented by 2187/2048 from the central ratio~~

~~|32/27 = (central) wa 3rd = w3, 81/64 = large wa 3rd = Lw3~~

|-

~~|small~~

~~| style="text-align:center" |s~~

~~|diminished by 2187/2048 from the central ratio~~

~~|27/16 = (central) wa 6th = w6, 128/81 = small wa 6th = sw6~~

|-

|la

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

|large, ~~used in temperament & comma names~~

|large, augmented by 2187/2048 from the central ratio

|~~Schismatic~~ = ~~(-15 8 1)~~ = ~~Layo~~ = ~~LyT~~

|32/27 = wa 3rd = w3, 81/64 = lawa 3rd = Lw3

|-

|sa

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

|small, ~~used in temperament & comma names~~

|small, diminished by 2187/2048 from the central ratio

|~~Srutal~~ = ~~2048~~/~~2025~~ = ~~Sagugu~~ = ~~sggT~~

|27/16 = wa 6th = w6, 128/81 = sawa 6th = sw6

|-

|plus

@@ Line 204: / 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 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.
+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 as L and s, and abbreviated as '''la''' and '''sa'''. '''Central''', the default, means neither large nor small. The general term for large/small/central/etc. is '''magnitude'''. When discussing magnitudes in general (e.g. tempering out a large comma usually flattens the 5th), the full words large and small are used to avoid confusion with solfege's La and saregam's Sa. A ratio's magnitude is the sum of 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. Only intervals have a magnitude, notes never do, and L and s never appear on the staff.
-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.
+Colors can be doubled or tripled, which are abbreviated '''bi-''' and '''tri-''': 49/25= bizogu 9th = zzgg9 and 128/125 = trigu 2nd = g<sup>3</sup>2. Bi- is only used if it shortens the name: 25/16 = yoyo 5th not biyo 5th. Quadruple and quintuple are abbreviated '''quad-''' and '''quin-''', as in quadyo or quingu. Likewise with magnitudes: lala, trisa, quadla, etc. For sextuple, etc., see [[#Temperament Names]] below.
 Colors using only one prime above 3 are called '''primary''' colors. Thus gu and yoyo are primary and ruyo is non-primary.
@@ Line 212: / Line 212: @@
 [[File:Lattice41a.png|833x833px]]
-Degrees can be negative: 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. There are also diminished unisons, which raise the pitch but diminish the quality. For example, if 11/8 is a P4, two of them are a m7 of 121/64 = 1102¢. Going from a yo M7 = 1088¢ up to this m7 raises the pitch, and 121/120 is a dim unison.
+Degrees can be negative: 50/49 = biruyo 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. There are also diminished unisons, which raise the pitch but diminish the quality. For example, if 11/8 is notated as a P4, two of them are a m7 of 121/64 = 1102¢. Going from a yo M7 = 1088¢ up to this m7 raises the pitch, and 121/120 is a dim unison.
-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.
+The lalawa negative 2nd (LLw-2, the [[Pythagorean comma|pythagorean or 12-edo comma]]) is simply called the wa comma. The [[256/243|5-edo comma]] is the sawa comma, and the [[2187/2048|7-edo comma]] is the lawa comma. All other 3-limit commas such as L<sup>3</sup>w-2 = (-30, 19) are named 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. See [[#Prime Subgroup Names]] below for another mnemonic.
@@ Line 231: / Line 231: @@
 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 [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.
+'''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 becomes '''ila''', to avoid confusion with the solfege note La, and also with la for 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, trilu 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 239: / Line 239: @@
 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).
-'''So''' = 17-over, '''su''' = 17-under, and '''sa''' = 17-all, abbreviated as '''17o''', '''17u''' and '''17a'''. '''Iso''' is an alternate form of so, to distinguish it from the solfege syllable So. 17/12 = 17o5 = iso So. '''Isa''' is an alternate form of sa, to distinguish it from small, and from the Indian saregam syllable Sa.
+'''So''' = 17-over, '''su''' = 17-under, and '''sa''' = 17-all, abbreviated as '''17o''', '''17u''' and '''17a'''. '''Iso''' is an alternate form of so, to distinguish it from the solfege syllable So. 17/12 = 17o5 = iso So. '''Isa''' is an alternate form of sa, to distinguish it from sa for small, and from the Indian saregam syllable Sa.
 '''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.
@@ Line 377: / Line 377: @@
 == Temperament Names ==
-Temperaments are named after the color of the comma(s) they temper out. Many words are abbreviated. Large becomes la and small becomes sa. Double, triple, etc, become bi-, tri-, quad- and quin-. Sextuple is tribi-, and septuple is sep-. Eleven-fold is le- = "e'''<u>l</u>'''even '''<u>e</u>'''xponent".
+Temperaments are named after the color of the comma(s) they temper out. The degree is omitted. Sextuple is tribi- and septuple is sep-. Eightfold is quadbi-, ninefold is tritri-, and tenfold is quinbi. Eleven-fold is le- = "e'''<u>l</u>'''even '''<u>e</u>'''xponent".
 [[Meantone]] is the Gu temperament. [[Srutal]] is Sagugu. [[Porcupine]] is Triyo. Some multi-comma temperaments have multiple commas in their name, and some don't. [[Meantone family#Septimal meantone|Septimal Meantone]] is Gu, but [[Meantone family#Dominant|Dominant Meantone]] is Gu & Rugu. Untempered primes are included with a plus sign. The 2.3.5.7 prime subgroup with 81/80 tempered out is Gu + za.
@@ Line 509: / Line 509: @@
 |as a suffix, 2nd smallest comma in the row segment
 |Meantone = 81/80 = Gu = gT, Father = 16/15 = Gubi = g#2T
-|-
-|large
-| style="text-align:center" |L
-|augmented by 2187/2048 from the central ratio
-|32/27 = (central) wa 3rd = w3, 81/64 = large wa 3rd = Lw3
-|-
-|small
-| style="text-align:center" |s
-|diminished by 2187/2048 from the central ratio
-|27/16 = (central) wa 6th = w6, 128/81 = small wa 6th = sw6
 |-
 |la
 | style="text-align:center" |L
-|large, used in temperament & comma names
+|large, augmented by 2187/2048 from the central ratio
-|Schismatic = (-15 8 1) = Layo = LyT
+|32/27 = wa 3rd = w3, 81/64 = lawa 3rd = Lw3
 |-
 |sa
 | style="text-align:center" |s
-|small, used in temperament & comma names
+|small, diminished by 2187/2048 from the central ratio
-|Srutal = 2048/2025 = Sagugu = sggT
+|27/16 = wa 6th = w6, 128/81 = sawa 6th = sw6
 |-
 |plus