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| == Ups-and-Downs-based notation == | | == Ups-and-Downs-based notation == |
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| Another system proposed by [[User:TallKite|TallKite]] involves simpler notation, with as few extra accidental pairs as possible. One could do with only one extra pair, only ups and downs (that is, arrows), but one would need at least septuple ups, and in practice octuple or more, rendering such a system impractical. As a result, this system has two extra pairs of accidentals. | | Another system proposed by [[User:TallKite|TallKite]] uses ups and downs (^ v), with quintuple arrows notated as quip and quid (> <). |
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| According to this system, 159edo would be notated with a combination of ups/downs and lifts/drops. The latter (referred to as "slants" here) are written / and \. The ups and downs are used as in 53edo, so one up is 3 edosteps. One lift is 1 edostep. Double-arrows are called dup and dud. Triple-arrows are trup and trud. Double-slants are dublift and dubdrop.
| | * 1\159 = ^ = up |
| | * 2\159 = ^^ = dup |
| | * 3\159 = ^^^ = trup |
| | * 4\159 = v> = quup |
| | * 5\159 = > = quip |
| | * 6\159 = ^> = upquip |
| | * 7\159 = ^^> = dupquip or vvv<# = trudquidsharp |
| | * 8\159 = ^^^> = trupquip or vv<# = dudquidsharp |
| | * 9\159 = v>> = quupquip or v<# = downquidsharp |
| | * 10\159 = <# = quidsharp |
| | * 11\159 = ^<# = quudsharp |
| | * 12\159 = vvv# = trudsharp |
| | * 13\159 = vv# = dudsharp |
| | * 14\159 = v# = downsharp |
| | * 15\159 = # = sharp |
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| <tt>
| | Notes flatter than natural can be deduced by symmetry, i.e. C vC vvC vvvC ^<C <C etc. Notes beyond sharp just run through the same list, but adding "sharp": sharp, upsharp, dupsharp, quupsharp, quipsharp... going to double-sharp eventually. |
| 0 natural
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| 1 / lift
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| 2 ^\ updrop
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| // (dublift)
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| 3 ^ up
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| 4 ^/ uplift
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| 5 ^^\ dupdrop
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| ^// (up dublift)
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| 6 ^^ dup
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| vvv# (trudsharp)
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| 7 ^^/ duplift
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| vvv/# (trudlift sharp)
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| 8 ^^^\ trupdrop
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| ^^// (dup dublift)
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| vv\# duddrop sharp
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| 9 ^^^ trup
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| vv# dudsharp
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| 10 ^^^/ truplift
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| vv/# dudlift sharp
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| v\\# (down dubdrop sharp)
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| 11 v\# downdrop sharp
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| 12 v# downsharp
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| 13 v/# downlift sharp
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| \\# (dubdrop sharp)
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| 14 \# dropsharp
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| 15 # sharp
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| </tt>
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| Notes flatter than natural can be deduced by symmetry, i.e. C \C v/C vC v\C etc. Notes beyond sharp just run through the same list, but adding "sharp": | |
| sharp, liftsharp, updrop sharp (or dublift sharp), upsharp, uplift sharp... | |
| going to double-sharp eventually. | |
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| Instead of ^^^ one could put an actual numeral 3 right on the score, like ^3. If someone actually used just arrows and no slants, they would really need to write ^7 and not ^^^^^^^.
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| The spectrum of qualities looks like this: | | The spectrum of qualities looks like this: |
| <tt>
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| -6 vvm dudminor (same as dupmajor of the next lower degree)
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| -5 vv/m dudlift minor
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| -4 v\m downdrop minor
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| -3 vm dropminor
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| -2 v/m downlift minor
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| \\m (dubdrop minor)
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| -1 \m dropminor
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| 0 m minor
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| 1 /m liftminor
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| 2 ^\m updrop minor
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| //m (dublift minor)
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| 3 ^m upminor
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| 4 ^/m uplift minor
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| 5 ^^\m dupdrop minor
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| ^//m (up dublift minor)
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| 6 ^^m dupminor
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| vvvM (trudmajor)
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| 7 ^^/m duplift minor
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| vvv/M (trudlift major)
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| 8 ^^^\m trupdrop minor
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| ^^//m (dup dublift minor)
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| vv\M duddrop major
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| 9 ^^^m trupminor
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| vvM dudmajor
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| 10 ^^^/m truplift minor
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| vv/M dudlift major
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| v\\M (down dubdrop major)
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| 11 v\M downdrop major
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| 12 vM downmajor
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| 13 v/M downlift major
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| \\M (dubdrop major)
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| 14 \M dropmajor
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| 15 M major
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| 16 /M liftmajor
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| 17 ^\M updrop major
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| //M (dublift major)
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| 18 ^M upmajor
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| 19 ^/M uplift major
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| 20 ^^\M dupdrop major
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| 21 ^^M dupmajor (same as dudminor of the next higher degree)
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| </tt>
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| Thus 4:5:6:7:9:11 = P1 vM3 P5 v\m7 M9 v/~11 = C vE G v\Bb D ^^/F = Cv9(v\7)^^/11 = C down-9 downdrop-7 duplift-11
| | * -6 = v<m = downquidminor (same as upquipmajor of the next lower degree) |
| | * -5 = <m = quidminor |
| | * -4 = ^<m = quudminor |
| | * -3 = vvvm = trudminor |
| | * -2 = vvm = dudminor |
| | * -1 = vm = downminor |
| | * 0 = m = minor |
| | * 1 = ^m = upminor |
| | * 2 = ^^m = dupminor |
| | * 3 = ^^^m = trupminor |
| | * 4 = v>m = quupminor |
| | * 5 = >m = quipminor = <<M = quidquidmajor |
| | * 6 = ^>m = upquipminor = ^<<M = quudquidmajor |
| | * 7 = ^^>m = dupquipminor = vvv<M = trudquidmajor |
| | * 8 = ^^^>m = trupquipminor = vv<M = dudquidmajor |
| | * 9 = v>>m = quudquipminor = v<M = downquidmajor |
| | * 10 = >>m = quipquipminor = <M = quidmajor |
| | * 11= ^<M = quudmajor |
| | * 12 = vvvM = trudmajor |
| | * 13 = vvM = dudmajor |
| | * 14 = vM = downmajor |
| | * 15 = M = major |
| | * 16 = ^M = upmajor |
| | * 17 = ^^M = dupmajor |
| | * 18 = ^^^M = trupmajor |
| | * 19 = v>M = quupmajor |
| | * 20 = >M = quipmajor |
| | * 21 = ^>M = upquipmajor (same as downquidminor of the next higher degree) |
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| This system uses both arrows and slants for larger EDOs only when the EDO is multi-ring- that is, the circle of 5ths doesn't include every note- and each ring requires ups and downs. For example 205edo is 5 rings of 41edo, but 124edo is not 4 rings of 31edo. The lifts and drops label the rings. In 159edo, there's a lift ring, a drop ring, and a plain ring. The lift ring is also a double-drop ring, and the drop ring is also a double-lift ring.
| | Thus 4:5:6:7:9:11 = P1 vvvM3 P5 ^<m7 M9 ^^>11 = C vvvE G ^<Bb D ^^>F = Cvvv9(^<7)^^>11 = C trud-9 quud-7 dupquip-11 |
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| ===Advantages and disadvantages=== | | ===Advantages and disadvantages=== |