Kite's ups and downs notation
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="Ups and Downs" Notation=
Ups and Downs is a notation system developed by Kite that works very well with almost all EDOs and rank 2 tunings. It only adds 3 symbols to standard notation, so it's very easy to learn. The name comes from the up symbol "^" and the down symbol "v". There's also the mid symbol "~" which undoes ups and downs.
To understand the ups and downs notation, let's start with an EDO that doesn't need it. 19-EDO is easy to notate because 7 fifths adds up to one EDO-step. So C# is right next to C, and your keyboard runs C C# Db D D# Eb E etc. Conventional notation works perfectly with 19-EDO as long as you remember that C# and Db are different notes.
But 22-EDO is hard to notate because 7 fifths are __three__ EDO-steps, and if you set up the usual chain of fifths Eb-Bb-F-C-G-D-A-E-B-F#-C# etc., you get C Db B# C# D Eb Fb D# E F. And that's very confusing. For example a 4:5:6 chord is C-D#-G. Some people forgo the chain of fifths and do something like C _ _ D _ _ E _ _ F _ _ _ G _ _ A _ _ B _ _ C. But that's confusing too because G-D and A-E are dim 5ths. And if your piece is in G or A, that's really bad. A notation system should work in every key!
The solution is to use the sharp symbol to mean raised by 7 fifths, and to use the up symbol "^" to mean sharpened by one EDO-step. 22-EDO can be written C-Db-Db^-Dv-D-Eb-Eb^-Ev-E-F etc. The notes are pronounced "D-flat-up, D-down", etc. The names change depending on the key, just like in conventional notation where F# in D major becomes Gb in Db major. So in B, we get B-C-C^-C#v-C#-D-D^-D#v-D#-E etc.
The basic pattern for 22-EDO is P1-m2-^m2-vM2-M2-m3-^m3-vM3-M3-P4-d5-^d5-vP5-P5 etc. That's pronounced "upminor 2nd, downmajor 3rd", etc. The ups and downs are leading in relative notation but trailing in absolute notation.
You can loosely relate the ups and downs to JI: major = red or fifthward white, downmajor = yellow, upminor = green, minor = blue or fourthwards white. Or simply up = green, down = yellow, and mid = white, blue or red. (See [[Kite's color notation]] for an explanation of the colors.) These correlations are for 22-EDO only, other EDOs have other correlations.
Conventionally, in C you use D# instead of Eb when you have a Gaug chord. You have the freedom to spell your notes how you like, to make your chords look right. Likewise, in 22-EDO, Db can be spelled C^ or B#v or even B^^ ("B double-up").
The interval arithmetic works out very neatly. Ups and downs are just added in:
C + M3 = E, C + vM3 = Ev, C^ + M3 = E^
D-F# = M3, D-F#v = vM3, Dv-F#v = M3
M2 + m2 = m3, M2 + ^m2 = ^m3, vM2 + m2 = vm3
Staff notation is a breeze, just put an up or down to the left of the note and any standard accidental it might have. All 22 possible keys can be written out. The tonic is usually a mid note, i.e. not up or down. Some of the key signatures have double-sharps or double-flats in them.
So that's 22-EDO. This notation works for almost every EDO. 9, 11, 16, and 23 have weird interval arithmetic because of the narrow fifth, but they can be notated. 13 and 18 are best notated using the narrower of the 2 possible fifths, which makes them like 9, 11, 16 and 23. 8-EDO is hard. It works with pentatonic notation, if you don't mind learning pentatonic interval arithmetic. (Big if!)
EDOs come in 5 categories, based on the size of the fifth:
supersharp EDOs, with fifths wider than 720¢
pentatonic EDOs, with a fifth = 720¢
"sweet" EDOs, so-called because the fifth hits the "sweet spot" between 720¢ and 4\7 = 686¢
heptatonic EDOs,Original HTML content:
<html><head><title>Ups and Downs Notation</title></head><body><!-- ws:start:WikiTextHeadingRule:0:<h1> --><h1 id="toc0"><a name="x"Ups and Downs" Notation"></a><!-- ws:end:WikiTextHeadingRule:0 -->"Ups and Downs" Notation</h1> <br /> Ups and Downs is a notation system developed by Kite that works very well with almost all EDOs and rank 2 tunings. It only adds 3 symbols to standard notation, so it's very easy to learn. The name comes from the up symbol "^" and the down symbol "v". There's also the mid symbol "~" which undoes ups and downs.<br /> <br /> To understand the ups and downs notation, let's start with an EDO that doesn't need it. 19-EDO is easy to notate because 7 fifths adds up to one EDO-step. So C# is right next to C, and your keyboard runs C C# Db D D# Eb E etc. Conventional notation works perfectly with 19-EDO as long as you remember that C# and Db are different notes. <br /> <br /> But 22-EDO is hard to notate because 7 fifths are <u>three</u> EDO-steps, and if you set up the usual chain of fifths Eb-Bb-F-C-G-D-A-E-B-F#-C# etc., you get C Db B# C# D Eb Fb D# E F. And that's very confusing. For example a 4:5:6 chord is C-D#-G. Some people forgo the chain of fifths and do something like C _ _ D _ _ E _ _ F _ _ _ G _ _ A _ _ B _ _ C. But that's confusing too because G-D and A-E are dim 5ths. And if your piece is in G or A, that's really bad. A notation system should work in every key!<br /> <br /> The solution is to use the sharp symbol to mean raised by 7 fifths, and to use the up symbol "^" to mean sharpened by one EDO-step. 22-EDO can be written C-Db-Db^-Dv-D-Eb-Eb^-Ev-E-F etc. The notes are pronounced "D-flat-up, D-down", etc. The names change depending on the key, just like in conventional notation where F# in D major becomes Gb in Db major. So in B, we get B-C-C^-C#v-C#-D-D^-D#v-D#-E etc.<br /> <br /> The basic pattern for 22-EDO is P1-m2-^m2-vM2-M2-m3-^m3-vM3-M3-P4-d5-^d5-vP5-P5 etc. That's pronounced "upminor 2nd, downmajor 3rd", etc. The ups and downs are leading in relative notation but trailing in absolute notation.<br /> <br /> You can loosely relate the ups and downs to JI: major = red or fifthward white, downmajor = yellow, upminor = green, minor = blue or fourthwards white. Or simply up = green, down = yellow, and mid = white, blue or red. (See <a class="wiki_link" href="/Kite%27s%20color%20notation">Kite's color notation</a> for an explanation of the colors.) These correlations are for 22-EDO only, other EDOs have other correlations.<br /> <br /> Conventionally, in C you use D# instead of Eb when you have a Gaug chord. You have the freedom to spell your notes how you like, to make your chords look right. Likewise, in 22-EDO, Db can be spelled C^ or B#v or even B^^ ("B double-up").<br /> <br /> The interval arithmetic works out very neatly. Ups and downs are just added in:<br /> C + M3 = E, C + vM3 = Ev, C^ + M3 = E^<br /> D-F# <!-- ws:start:WikiTextHeadingRule:2:<h1> --><h1 id="toc1"><a name="M3, D-F#v"></a><!-- ws:end:WikiTextHeadingRule:2 --> M3, D-F#v </h1> vM3, Dv-F#v = M3<br /> M2 + m2 = m3, M2 + ^m2 = ^m3, vM2 + m2 = vm3<br /> <br /> Staff notation is a breeze, just put an up or down to the left of the note and any standard accidental it might have. All 22 possible keys can be written out. The tonic is usually a mid note, i.e. not up or down. Some of the key signatures have double-sharps or double-flats in them.<br /> <br /> So that's 22-EDO. This notation works for almost every EDO. 9, 11, 16, and 23 have weird interval arithmetic because of the narrow fifth, but they can be notated. 13 and 18 are best notated using the narrower of the 2 possible fifths, which makes them like 9, 11, 16 and 23. 8-EDO is hard. It works with pentatonic notation, if you don't mind learning pentatonic interval arithmetic. (Big if!)<br /> <br /> EDOs come in 5 categories, based on the size of the fifth:<br /> supersharp EDOs, with fifths wider than 720¢<br /> pentatonic EDOs, with a fifth = 720¢<br /> "sweet" EDOs, so-called because the fifth hits the "sweet spot" between 720¢ and 4\7 = 686¢<br /> heptatonic EDOs,</body></html>