Kite's color notation: Difference between revisions

Line 156:

|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 "Higher Primes" below for why). Instead of augmented and diminished, remote intervals are '''large''' (fifthward) and '''small''' (fourthward), ~~abbreviated~~ L and s. '''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 "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.

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 and trigu. Quadruple and quintuple are abbreviated '''quad-''' and '''quin-''', as in quadyo or ~~quinlarge~~. For sextuple, etc., see "Temperament Names" below.

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 and trigu. Quadruple and quintuple are abbreviated '''quad-''' and '''quin-''', as in quadyo or quinla. For sextuple, etc., see "Temperament Names" below.

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

Line 181:

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 ~~(see "Temperament names" below)~~. Lo and lu are abbreviated to '''1o''' and '''1u''' on the score and in interval names and chord names, e.g. ilo A = 1oA, ilo 4th = 1o4 = 11/8, and C ilo seven = C1o7 = 1/1 - 11/9 - 3/2 - 11/6 on C. Lolo is 1oo, triple-lu is 1u3, etc. The associated color is lavender (mnemonic: "e-leven-der"), which refers to both ilo and lu, since they are only 7.1¢ apart. Lavender is a '''pseudocolor''' that implies the [http://x31eq.com/cgi-bin/rt.cgi?ets=24_17&limit=2_3_11 Neuter] temperament. IIo notes could be called lovender, and lu notes could be called luvender. Both are "shades" of lavender.

'''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 Neuter] temperament. IIo notes could be called lovender, and lu notes could be called luvender. Both are "shades" of lavender.

'''Tho''' = 13-over, '''thu''' = 13-under, and '''tha''' = 13-all. Tho and thu are abbreviated as '''3o''' and '''3u''' on the score and in interval names, e.g. 13/8 = 3o6 = tho 6th, 14/13 = 3uz2 = thuzo 2nd.

Line 189:

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''' and '''17u'''. '''Iso''' is an alternate form of so, to distinguish it from the solfege syllable So. 17/12 = 17o5 = iso So.

'''So''' = 17-over, '''su''' = 17-under, and '''sa''' = 17-all, abbreviated as '''17o''' and '''17u'''. '''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.

'''Ino''' = 19-over, '''nu''' = 19-under, and '''na''' = 19-all, abbreviated as '''19o''' and '''19u'''. 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 197:

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

The prefix i- is only ~~needed~~ when confusion is possible. Thus 19/15 = nogu 4th, not inogu 4th, and 29o = twenty-no, not twenty-ino.

The prefix i- is only used when confusion is possible. Thus 19/15 = nogu 4th, not inogu 4th, and 29o = twenty-no, not twenty-ino.

For any prime P, the degree of the ratio P/1 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 alternate method is to use the 7edo [[edomapping]], but that requires using every other 14edostep as boundaries, less convenient than the 24edo boundaries used here.)

== 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 ~~y4 is~~ central, and 45/32 = y4.

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.

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

Line 212:

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.

Example: interval = sgg2, S = 2 - 1 = 1 step, M = small = -1, monzo = |a b -2>, X = <7 11 16| dot |0 0 -2> = -32, b = (2·1 - 2·(-32) + 3) mod 7 + 7·(-1) - 3 = 69 mod 7 - 7 - 3 = -4, a = (1 - (-32) - 11·(-4)) / 7 = 77/7 = 11, monzo = |11 -4 -2>, ratio = 2048/2025.

Example: interval = sgg2, S = 2 - 1 = 1 step, M = small = -1, monzo = |a b -2>, X = <7 11 16| dot |0 0 -2> = -32, b = (2·1 - 2·(-32) + 3) mod 7 + 7·(-1) - 3 = 69 mod 7 - 7 - 3 = 6 - 10 = -4, a = (1 - (-32) - 11·(-4)) / 7 = 77/7 = 11, monzo = |11 -4 -2>, ratio = 2048/2025.

== Staff notation ==

Line 259:

== 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-.

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-.

[[Meantone]] = the Gu temperament = gT. [[Diaschismic]] = Sagugu = sggT. [[Porcupine]] = Triyo = y3T. [[Porcupine family|7-limit Porcupine]] = Triyo and Ru = y3&rT. Each variety of porcupine has a different name, thus color names provide more information than standard temperament names.

Line 265:

Untempered primes can be included with '''plus'''. The 2.3.5.7 subgroup with 81/80 tempered out is g+zT = gu plus za.

See the [[Comma]] lists for more ~~examples~~. Temperament names are further explained here: [[Color notation/Temperament Names]].

See the [[Comma]] lists for more example names. Temperament names are further explained here: [[Color notation/Temperament Names]].

== Ups and Downs, Lifts and Drops, Plain and Mid ==

Line 276:

Rank-2 temperaments can be notated with ups and downs as well. Plain and mid are also used in this context. Some temperaments require an additional pair of virtual colors, '''lifts''' and '''drops''' (/ and \). Notes are named lift C = /C, downdrop F sharp = v\F#, etc. Intervals are named drop 4th = \4, uplift major 3rd = ^/M3, etc. Plain means neither up nor down nor lifted nor dropped. There may be upmid or liftmid intervals. Chords are named C-up lift-seven = C^,/7 = C ^E G /Bb, C uplift-seven = C^/7 = C ^/E G ^/Bb, etc. See [[Pergen|pergens]].

==Translations==

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

@@ Line 156: / Line 156: @@
 |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 "Higher Primes" below for why). Instead of augmented and diminished, remote intervals are '''large''' (fifthward) and '''small''' (fourthward), abbreviated L and s. '''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 "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.
-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 and trigu. Quadruple and quintuple are abbreviated '''quad-''' and '''quin-''', as in quadyo or quinlarge. For sextuple, etc., see "Temperament Names" below.
+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 and trigu. Quadruple and quintuple are abbreviated '''quad-''' and '''quin-''', as in quadyo or quinla. For sextuple, etc., see "Temperament Names" below.
 [[File:Lattice41a.png|833x833px]]
@@ Line 181: / Line 181: @@
 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 (see "Temperament names" below). Lo and lu are abbreviated to '''1o''' and '''1u''' on the score and in interval names and chord names, e.g. ilo A = 1oA, ilo 4th = 1o4 = 11/8, and C ilo seven = C1o7 = 1/1 - 11/9 - 3/2 - 11/6 on C. Lolo is 1oo, triple-lu is 1u<sup>3</sup>, etc. The associated color is lavender (mnemonic: "e-leven-der"), which refers to both ilo and lu, since they are only 7.1¢ apart. Lavender is a '''pseudocolor''' that implies the [http://x31eq.com/cgi-bin/rt.cgi?ets=24_17&limit=2_3_11 Neuter] temperament. IIo notes could be called lovender, and lu notes could be called luvender. Both are "shades" of lavender.
+'''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 Neuter] temperament. IIo notes could be called lovender, and lu notes could be called luvender. Both are "shades" of lavender.
 '''Tho''' = 13-over, '''thu''' = 13-under, and '''tha''' = 13-all. Tho and thu are abbreviated as '''3o''' and '''3u''' on the score and in interval names, e.g. 13/8 = 3o6 = tho 6th, 14/13 = 3uz2 = thuzo 2nd.
@@ Line 189: / Line 189: @@
 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''' and '''17u'''. '''Iso''' is an alternate form of so, to distinguish it from the solfege syllable So. 17/12 = 17o5 = iso So.
+'''So''' = 17-over, '''su''' = 17-under, and '''sa''' = 17-all, abbreviated as '''17o''' and '''17u'''. '''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.
 '''Ino''' = 19-over, '''nu''' = 19-under, and '''na''' = 19-all, abbreviated as '''19o''' and '''19u'''. 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 197: / Line 197: @@
 Similarly, '''twenty-no/-nu/-na''' = 29o/29u/29a, '''thirty-wo/-wu/-wa''' = 31o/31u/31a, '''thirty-so/-su/-sa''' = 37o/37u/37a, etc.
-The prefix i- is only needed when confusion is possible. Thus 19/15 = nogu 4th, not inogu 4th, and 29o = twenty-no, not twenty-ino.
+The prefix i- is only used when confusion is possible. Thus 19/15 = nogu 4th, not inogu 4th, and 29o = twenty-no, not twenty-ino.
 For any prime P, the degree of the ratio P/1 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 alternate method is to use the 7edo [[edomapping]], but that requires using every other 14edostep as boundaries, less convenient than the 24edo boundaries used here.)
 == 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 y4 is central, and 45/32 = y4.
+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.
 For more complex ratios, a more direct method is used:
@@ Line 212: / Line 212: @@
 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.
-Example: interval = sgg2, S = 2 - 1 = 1 step, M = small = -1, monzo = |a b -2>, X = <7 11 16| dot |0 0 -2> = -32, b = (2·1 - 2·(-32) + 3) mod 7 + 7·(-1) - 3 = 69 mod 7 - 7 - 3 = -4, a = (1 - (-32) - 11·(-4)) / 7 = 77/7 = 11, monzo = |11 -4 -2>, ratio = 2048/2025.
+Example: interval = sgg2, S = 2 - 1 = 1 step, M = small = -1, monzo = |a b -2>, X = <7 11 16| dot |0 0 -2> = -32, b = (2·1 - 2·(-32) + 3) mod 7 + 7·(-1) - 3 = 69 mod 7 - 7 - 3 = 6 - 10 = -4, a = (1 - (-32) - 11·(-4)) / 7 = 77/7 = 11, monzo = |11 -4 -2>, ratio = 2048/2025.
 == Staff notation ==
@@ Line 259: / Line 259: @@
 == 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-.
+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-.
 [[Meantone]] = the Gu temperament = gT.  [[Diaschismic]] = Sagugu = sggT. [[Porcupine]] = Triyo = y<sup>3</sup>T. [[Porcupine family|7-limit Porcupine]] = Triyo and Ru = y<sup>3</sup>&rT. Each variety of porcupine has a different name, thus color names provide more information than standard temperament names.
@@ Line 265: / Line 265: @@
 Untempered primes can be included with '''plus'''. The 2.3.5.7 subgroup with 81/80 tempered out is g+zT = gu plus za.
-See the [[Comma]] lists for more examples. Temperament names are further explained here: [[Color notation/Temperament Names]].
+See the [[Comma]] lists for more example names. Temperament names are further explained here: [[Color notation/Temperament Names]].
 == Ups and Downs, Lifts and Drops, Plain and Mid ==
@@ Line 276: / Line 276: @@
 Rank-2 temperaments can be notated with ups and downs as well. Plain and mid are also used in this context. Some temperaments require an additional pair of virtual colors, '''lifts''' and '''drops''' (/ and \). Notes are named lift C = /C, downdrop F sharp = v\F#, etc. Intervals are named drop 4th = \4, uplift major 3rd = ^/M3, etc. Plain means neither up nor down nor lifted nor dropped. There may be upmid or liftmid intervals. Chords are named C-up lift-seven = C^,/7 = C ^E G /Bb, C uplift-seven = C^/7 = C ^/E G ^/Bb, etc. See [[Pergen|pergens]].
 ==Translations==
-:''For translations of color notation terms into other languages, see [[Color notation/Translations]].''             [[Category:color_notation]]             [[Category:ji]]             [[Category:notation]]
+:''For translations of color notation terms into other languages, see [[Color notation/Translations]].''              [[Category:color_notation]]              [[Category:ji]]              [[Category:notation]]