Kite's ups and downs notation: Difference between revisions

Line 1:

<h2>IMPORTED REVISION FROM WIKISPACES</h2>

This is an imported revision from Wikispaces. The revision metadata is included below for reference:

: This revision was by author [[User:TallKite|TallKite]] and made on <tt>2015-09-01 06:47:12 UTC</tt>.

: This revision was by author [[User:TallKite|TallKite]] and made on <tt>2015-09-01 16:20:28 UTC</tt>.

: The original revision id was <tt>~~557878737~~</tt>.

: The original revision id was <tt>557941697</tt>.

: The revision comment was: <tt></tt>

The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.

Line 8:

<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">="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.

Ups and Downs is a notation system developed by [[KiteGiedraitis|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.

Line 76:

__**Other EDOs**__

~~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!)

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:

Line 127:

Ups and downs allow us to name any chord easily. First we need an exact definition of major, minor, perfect, etc. that works with all edos. The quality of an interval is defined by its position on the chain of 5ths. Perfect is 0-1 steps away, major/minor are 2-5 steps away, aug/dim are 6-12 steps away, etc.

There are 3 special cases to be addressed. The first is when the edo's 5th is narrower than 4\7, as in 16edo. Major is defined as ~~always~~ wider than minor, so major is not fifthwards but fourthwards:

There are 3 special cases to be addressed. The first is when the edo's 5th is narrower than 4\7, as in 16edo. Major is defined as wider than minor, so major is not fifthwards but fourthwards:

The fourthwards chain of fifths in superflat aka Mavila EDOs (3/2 maps to less than 4\7):

Line 140:

Eb + m3 --> E# + M3 = G## --> Gbb

The second special case is when the edo's fifth equals 4\7, as in 7edo, 14edo, 21edo, 28edo, and 35edo. 42edo, 49edo, etc. have a fifth wider than 4\7. In these edos, there are zero keys per sharp/flat, and all intervals are perfect.

The second special case is when the edo's fifth equals 4\7, as in 7edo, 14edo, 21edo, 28edo, and 35edo. (42edo, 49edo, etc. have a fifth wider than 4\7.) In these five edos, there are zero keys per sharp/flat, and all intervals are perfect.

The chain of fifths in heptatonic EDOs (3/2 maps to 4\7):

P2 - P6 - P3 - P7 - P4 - P1 - P5 - P2 - P6 - P3 - P7 etc.

F - C - G - D - A - E - B - F - C - G - D - A - E - B etc.

21edo: P1 - A1 - d2 - P2 - A2 - d3 - P3 - A3 - d4 - P4 - A4 - d5 - P5 - A5 - d6 - P6 - A6 - D7 - P7 - A7 - d8 - P8

21edo: P1 - ^P1 - vP2 - P2 - ^P2 - vP3 - P3 - ^P3 - vP4 - P4 - ^P4 - vP5 - P5 - ^P5 - vP6 - P6 - ^P6 - vP7 - P7 - ^P7 - vP8 - P8

Because everything is perfect, the quality can be omitted:

21edo: 1 - ^1 - v2 - 2 - ^2 - v3 - 3 - ^3 - v4 - 4 - ^4 - v5 - 5 - ^5 - v6 - 6 - ^6 - v7 - 7 - ^7 - v8 - 8

21edo: C - C^ - Dv - D - D^ - Ev - E - E^ - Fv - F - F^ - Gv - G - G^ - Av - A - A^ - Bv - B - B^ - Cv - C

Just as ups and downs aren't needed in 19edo, sharps and flats aren't needed in 21edo~~. However they can be used for familiarity's sake: an A major chord can be written A - C#^ - E~~.

Just as ups and downs aren't needed in 19edo, sharps and flats aren't needed in 21edo.

The 3rd special case is when the edo's fifth is wider than 3\5, as in 8edo, 13edo, 18edo and 23edo. Heptatonic fifth-based notation is impossible in these cases, ~~because~~ the ~~chain~~ of ~~7 fifths isn't~~ a ~~MOS scale~~. Such EDOs are dealt with below.

The 3rd special case is when the edo's fifth is wider than 3\5, as in 8edo, 13edo, 18edo and 23edo. Heptatonic fifth-based notation is impossible in these cases. The minor 2nd, which is the sum of five 4ths minus two 8ves, becomes a descending interval. Thus the major 3rd is wider than the perfect 4th, etc. Such EDOs are dealt with below.

Chord names are based entirely on the ups/downs interval names, not on JI ratios. This avoids identifying one EDOstep with multiple ratios, as happens in 22edo when 0-7-18 implies 4:5:7 but 0-9-18 implies 9:12:16. 18\22 is neither 7/4 nor 16/9, it's 18\22!

Line 182:

Line 184:

These are pronounced "downmajor second", "upminor third", etc. For 4ths and 5ths, "perfect" is implied and can be omitted: ^P4 = "up-four" and vP5 = "down-five". In larger edos there may be "down-octave", "up-unison", etc.

0-7-13-18 in C is "C vM,m7", pronounced "C downmajor, minor seventh". The ~~space~~ between the C and the down symbol is needed because Cv is a note, and "Cv M,m7" is a different chord. That chord is pronounced "C down, major, minor 7th", so one has to "speak the ~~space~~"~~. Alternatively, a comma could be used: C,vM,m7 vs. Cv,M,m7~~. The extra ~~space/~~comma isn't needed when there's no ups or downs immediately after the note name, e.g. Cm.

0-7-13-18 in C is "C,vM,m7", pronounced "C downmajor, minor seventh". The comma between the C and the down symbol is needed because Cv is a note, and "Cv,M,m7" is a different chord. That chord is pronounced "C down, major, minor 7th", so one has to "speak the comma". The extra comma isn't needed when there's no ups or downs immediately after the note name, e.g. Cm.

The conventional chord naming system uses a lot of "shorthand" like dom7 for M3,m7 and min6 for m3,M6. This causes problems in 22edo where there are so many choices for the 3rd, the 6th, the 7th and the 9th. For example, min6 could mean m3,vM6 = approximate 6:7:9:10 chord, or it could mean ^m3,M6 = approximate 1/1-6/5-3/2-12/7 chord. Larger edos would present even greater problems. Furthermore there's some ambiguity in the shorthand, e.g. in 12edo, both 0-3-6 and 0-3-6-9 are called dim chords.

Thus the shorthand should be largely abandoned and all the components of the chord should be explicitly spelled out, with a few exceptions: 1) The root, obviously. 2) The perfect 5th is assumed present unless otherwise specified. Thus 0-7-18 is "C vM,m7,-5" and 0-6-11 is "C ^m,^d5". 3) The 3rd is also assumed to be present, and is implied by a quality with no degree. Thus 0-7-13 is "C vM". 4) The 3rd isn't spelled out if the 6th or 7th has the same quality as the 3rd. Thus 0-7-13-16 is "C vM6", but 0-7-13-17 is "C vM,M6". Thirdless chords: 0-13-18 is either "Cm7,-3" or "C5,m7".

Thus the shorthand should be largely abandoned and all the components of the chord should be explicitly spelled out, with a few exceptions: 1) The root, obviously. 2) The perfect 5th is assumed present unless otherwise specified. Thus 0-7-18 is C,vM,m7,-5 and 0-6-11 is C,^m,^d5. 3) The 3rd is also assumed to be present, and is implied by a quality with no degree. Thus 0-7-13 is C,vM. 4) The 3rd isn't spelled out if the 6th or 7th has the same quality as the 3rd. Thus 0-7-13-16 is C,vM6, but 0-7-13-17 is C,vM,M6. Thirdless chords: 0-13-18 is either Cm7,-3 or C5,m7.

The 6th, the 7th, the 9th, the 11th, etc. are explicitly written out, including their qualities. Thus the 9th isn't assumed to be major, and the presence of a 9th doesn't imply the presence of a 7th.

Line 220:

Line 222:

You can write out chord progressions using the ups/downs notation for note names. Here's the first 4 chords of Paul Erlich's 22edo composition Tibia:

G vM7,-5 = "G downmajor seven, no five""

G,vM7,-5 = "G downmajor seven, no five""

Eb^ vM,M9 = "E flat up, downmajor, major nine"

Eb^,vM,M9 = "E flat up, downmajor, major nine"

Gm7,-5 (no ~~space~~ needed) = "G minor seven, no five"

Gm7,-5 (no comma needed) = "G minor seven, no five"

A vM,m7 = "A downmajor, minor seven"

A,vM,m7 = "A downmajor, minor seven"

To use relative notation, first write out all possible 22edo chord roots relatively. This is equivalent to the interval notation with Roman numerals substituted for Arabic, # for aug, and b for minor. Dim from perfect is b, but dim from minor is bb. Enharmonic equivalents like ^I = bII are used in certain chord progressions like Im - ^IIIM - ^VIIM - ^IVm - ^Im.

Line 229:

Line 231:

These are pronounced "down-two", "up-flat-three", "down-sharp-four", etc.

Here's the Tibia chords. No ~~spaces are~~ needed because ups and downs are always leading, never trailing.

Here's the Tibia chords. No comma is needed after the root because ups and downs are always leading, never trailing.

IvM7,-5 = "one downmajor seven, no five"

^bVIvM,M9 = "up-flat six downmajor, major nine"

Line 237:

Line 239:

==__Chord names in other EDOs__==

15edo: 3 keys per #/b, so ~~^/v is~~ needed.

15edo: 3 keys per #/b, so ups and downs are needed.

keyboard/fretboard: D * * E/F * * G * * A * * B/C * * D

(the chain of fifths is always centered on D)

Line 248:

Line 250:

0-5-9-12 = vM,m7

16edo: D * E * * F * G * A * B * * C * D, 1 key per #/b, ~~^/v~~ not needed. # is fourthward.

16edo: D * E * * F * G * A * B * * C * D, 1 key per #/b, ups and downs not needed. # is fourthward.

chord components: P1 d2 m2 M2 m3 M3 A3/d4 P4 A4/d5 P5 d6 m6 M6/d7 m7 M7 A7 P8

chord roots: I #I/bbII bII II bIII III #III/vIV IV #IV/bV V #V/bbVI bVI VI bVII VII #VII/bI

Line 271:

Line 273:

Alternatively, one could replace downmajor with n = neutral or somesuch.

19edo: D * * E * F * * G * * A * * B * C * * D, ~~^/v~~ not needed.

19edo: D * * E * F * * G * * A * * B * C * * D, ups and downs not needed.

chord components: P1 d2 m2 M2 d3 m3 M3 A3 P4 A4 d5 P5 d6 m6 M6 d7 m7 M7 A7 P8

chord roots: I v#I/bII #I/vII II bIII vIII III IV ^IV/bV #IV/vV V #V/bVI vVI VI bVII vVII VII

Line 293:

Line 295:

0-3-12 = sus2

0-4-12 = vv or sus^2

0-5-12 = v (a down chord, e.g. "C down")

0-5-12 = v (a down chord, e.g. C,v = "C down")

0-6-12 = ~ (e.g. "D mid")

0-6-12 = ~ (e.g. D,~ = "D mid")

0-7-12 = ^ (e.g. "E flat up")

0-7-12 = ^ (e.g. Eb,^ = "E flat up")

0-8-12 = ^^ or susv4

0-9-12 = sus4

Line 422:

Line 424:

<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>Ups and Downs Notation</title></head><body><h1 id="toc0"><a name="x&quot;Ups and Downs&quot; Notation"></a>&quot;Ups and Downs&quot; Notation</h1>

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 &quot;^&quot; and the down symbol &quot;v&quot;. There's also the mid symbol &quot;~&quot; which undoes ups and downs.

Ups and Downs is a notation system developed by <a class="wiki_link" href="/KiteGiedraitis">Kite</a> 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 &quot;^&quot; and the down symbol &quot;v&quot;. There's also the mid symbol &quot;~&quot; 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.

Line 490:

Line 492:

Other EDOs

~~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!)

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:

Line 541:

Line 543:

Ups and downs allow us to name any chord easily. First we need an exact definition of major, minor, perfect, etc. that works with all edos. The quality of an interval is defined by its position on the chain of 5ths. Perfect is 0-1 steps away, major/minor are 2-5 steps away, aug/dim are 6-12 steps away, etc.

There are 3 special cases to be addressed. The first is when the edo's 5th is narrower than 4\7, as in 16edo. Major is defined as ~~always~~ wider than minor, so major is not fifthwards but fourthwards:

There are 3 special cases to be addressed. The first is when the edo's 5th is narrower than 4\7, as in 16edo. Major is defined as wider than minor, so major is not fifthwards but fourthwards:

The fourthwards chain of fifths in superflat aka Mavila EDOs (3/2 maps to less than 4\7):

Line 554:

Line 556:

Eb + m3 --&gt; E# + M3 = G## --&gt; Gbb

The second special case is when the edo's fifth equals 4\7, as in 7edo, 14edo, 21edo, 28edo, and 35edo. 42edo, 49edo, etc. have a fifth wider than 4\7. In these edos, there are zero keys per sharp/flat, and all intervals are perfect.

The second special case is when the edo's fifth equals 4\7, as in 7edo, 14edo, 21edo, 28edo, and 35edo. (42edo, 49edo, etc. have a fifth wider than 4\7.) In these five edos, there are zero keys per sharp/flat, and all intervals are perfect.

The chain of fifths in heptatonic EDOs (3/2 maps to 4\7):

P2 - P6 - P3 - P7 - P4 - P1 - P5 - P2 - P6 - P3 - P7 etc.

F - C - G - D - A - E - B - F - C - G - D - A - E - B etc.

21edo: P1 - A1 - d2 - P2 - A2 - d3 - P3 - A3 - d4 - P4 - A4 - d5 - P5 - A5 - d6 - P6 - A6 - D7 - P7 - A7 - d8 - P8

21edo: P1 - ^P1 - vP2 - P2 - ^P2 - vP3 - P3 - ^P3 - vP4 - P4 - ^P4 - vP5 - P5 - ^P5 - vP6 - P6 - ^P6 - vP7 - P7 - ^P7 - vP8 - P8

Because everything is perfect, the quality can be omitted:

21edo: 1 - ^1 - v2 - 2 - ^2 - v3 - 3 - ^3 - v4 - 4 - ^4 - v5 - 5 - ^5 - v6 - 6 - ^6 - v7 - 7 - ^7 - v8 - 8

21edo: C - C^ - Dv - D - D^ - Ev - E - E^ - Fv - F - F^ - Gv - G - G^ - Av - A - A^ - Bv - B - B^ - Cv - C

Just as ups and downs aren't needed in 19edo, sharps and flats aren't needed in 21edo~~. However they can be used for familiarity's sake: an A major chord can be written A - C#^ - E~~.

Just as ups and downs aren't needed in 19edo, sharps and flats aren't needed in 21edo.

The 3rd special case is when the edo's fifth is wider than 3\5, as in 8edo, 13edo, 18edo and 23edo. Heptatonic fifth-based notation is impossible in these cases, ~~because~~ the ~~chain~~ of ~~7 fifths isn't~~ a ~~MOS scale~~. Such EDOs are dealt with below.

The 3rd special case is when the edo's fifth is wider than 3\5, as in 8edo, 13edo, 18edo and 23edo. Heptatonic fifth-based notation is impossible in these cases. The minor 2nd, which is the sum of five 4ths minus two 8ves, becomes a descending interval. Thus the major 3rd is wider than the perfect 4th, etc. Such EDOs are dealt with below.

Chord names are based entirely on the ups/downs interval names, not on JI ratios. This avoids identifying one EDOstep with multiple ratios, as happens in 22edo when 0-7-18 implies 4:5:7 but 0-9-18 implies 9:12:16. 18\22 is neither 7/4 nor 16/9, it's 18\22!

Line 596:

Line 600:

These are pronounced &quot;downmajor second&quot;, &quot;upminor third&quot;, etc. For 4ths and 5ths, &quot;perfect&quot; is implied and can be omitted: ^P4 = &quot;up-four&quot; and vP5 = &quot;down-five&quot;. In larger edos there may be &quot;down-octave&quot;, &quot;up-unison&quot;, etc.

0-7-13-18 in C is &quot;C vM,m7&quot;, pronounced &quot;C downmajor, minor seventh&quot;. The ~~space~~ between the C and the down symbol is needed because Cv is a note, and &quot;Cv M,m7&quot; is a different chord. That chord is pronounced &quot;C down, major, minor 7th&quot;, so one has to &quot;speak the ~~space~~&quot;~~. Alternatively, a comma could be used: C,vM,m7 vs. Cv,M,m7~~. The extra ~~space/~~comma isn't needed when there's no ups or downs immediately after the note name, e.g. Cm.

0-7-13-18 in C is &quot;C,vM,m7&quot;, pronounced &quot;C downmajor, minor seventh&quot;. The comma between the C and the down symbol is needed because Cv is a note, and &quot;Cv,M,m7&quot; is a different chord. That chord is pronounced &quot;C down, major, minor 7th&quot;, so one has to &quot;speak the comma&quot;. The extra comma isn't needed when there's no ups or downs immediately after the note name, e.g. Cm.

The conventional chord naming system uses a lot of &quot;shorthand&quot; like dom7 for M3,m7 and min6 for m3,M6. This causes problems in 22edo where there are so many choices for the 3rd, the 6th, the 7th and the 9th. For example, min6 could mean m3,vM6 = approximate 6:7:9:10 chord, or it could mean ^m3,M6 = approximate 1/1-6/5-3/2-12/7 chord. Larger edos would present even greater problems. Furthermore there's some ambiguity in the shorthand, e.g. in 12edo, both 0-3-6 and 0-3-6-9 are called dim chords.

Thus the shorthand should be largely abandoned and all the components of the chord should be explicitly spelled out, with a few exceptions: 1) The root, obviously. 2) The perfect 5th is assumed present unless otherwise specified. Thus 0-7-18 is ~~&quot;~~C vM,m7,-5~~&quot;~~ and 0-6-11 is ~~&quot;~~C ^m,^d5~~&quot;~~. 3) The 3rd is also assumed to be present, and is implied by a quality with no degree. Thus 0-7-13 is ~~&quot;~~C vM~~&quot;~~. 4) The 3rd isn't spelled out if the 6th or 7th has the same quality as the 3rd. Thus 0-7-13-16 is ~~&quot;~~C vM6~~&quot;~~, but 0-7-13-17 is ~~&quot;~~C vM,M6~~&quot;~~. Thirdless chords: 0-13-18 is either ~~&quot;~~Cm7,-3~~&quot;~~ or ~~&quot;~~C5,m7~~&quot;~~.

Thus the shorthand should be largely abandoned and all the components of the chord should be explicitly spelled out, with a few exceptions: 1) The root, obviously. 2) The perfect 5th is assumed present unless otherwise specified. Thus 0-7-18 is C,vM,m7,-5 and 0-6-11 is C,^m,^d5. 3) The 3rd is also assumed to be present, and is implied by a quality with no degree. Thus 0-7-13 is C,vM. 4) The 3rd isn't spelled out if the 6th or 7th has the same quality as the 3rd. Thus 0-7-13-16 is C,vM6, but 0-7-13-17 is C,vM,M6. Thirdless chords: 0-13-18 is either Cm7,-3 or C5,m7.

The 6th, the 7th, the 9th, the 11th, etc. are explicitly written out, including their qualities. Thus the 9th isn't assumed to be major, and the presence of a 9th doesn't imply the presence of a 7th.

Line 634:

Line 638:

You can write out chord progressions using the ups/downs notation for note names. Here's the first 4 chords of Paul Erlich's 22edo composition Tibia:

G vM7,-5 = &quot;G downmajor seven, no five&quot;&quot;

G,vM7,-5 = &quot;G downmajor seven, no five&quot;&quot;

Eb^ vM,M9 = &quot;E flat up, downmajor, major nine&quot;

Eb^,vM,M9 = &quot;E flat up, downmajor, major nine&quot;

Gm7,-5 (no ~~space~~ needed) = &quot;G minor seven, no five&quot;

Gm7,-5 (no comma needed) = &quot;G minor seven, no five&quot;

A vM,m7 = &quot;A downmajor, minor seven&quot;

A,vM,m7 = &quot;A downmajor, minor seven&quot;

To use relative notation, first write out all possible 22edo chord roots relatively. This is equivalent to the interval notation with Roman numerals substituted for Arabic, # for aug, and b for minor. Dim from perfect is b, but dim from minor is bb. Enharmonic equivalents like ^I = bII are used in certain chord progressions like Im - ^IIIM - ^VIIM - ^IVm - ^Im.

Line 643:

Line 647:

These are pronounced &quot;down-two&quot;, &quot;up-flat-three&quot;, &quot;down-sharp-four&quot;, etc.

Here's the Tibia chords. No ~~spaces are~~ needed because ups and downs are always leading, never trailing.

Here's the Tibia chords. No comma is needed after the root because ups and downs are always leading, never trailing.

IvM7,-5 = &quot;one downmajor seven, no five&quot;

^bVIvM,M9 = &quot;up-flat six downmajor, major nine&quot;

Line 651:

Line 655:

<h2 id="toc3"><a name="Naming Chords-Chord names in other EDOs"></a>Chord names in other EDOs</h2>

15edo: 3 keys per #/b, so ~~^/v is~~ needed.

15edo: 3 keys per #/b, so ups and downs are needed.

keyboard/fretboard: D * * E/F * * G * * A * * B/C * * D

(the chain of fifths is always centered on D)

Line 662:

Line 666:

0-5-9-12 = vM,m7

16edo: D * E * * F * G * A * B * * C * D, 1 key per #/b, ~~^/v~~ not needed. # is fourthward.

16edo: D * E * * F * G * A * B * * C * D, 1 key per #/b, ups and downs not needed. # is fourthward.

chord components: P1 d2 m2 M2 m3 M3 A3/d4 P4 A4/d5 P5 d6 m6 M6/d7 m7 M7 A7 P8

chord roots: I #I/bbII bII II bIII III #III/vIV IV #IV/bV V #V/bbVI bVI VI bVII VII #VII/bI

Line 685:

Line 689:

Alternatively, one could replace downmajor with n = neutral or somesuch.

19edo: D * * E * F * * G * * A * * B * C * * D, ~~^/v~~ not needed.

19edo: D * * E * F * * G * * A * * B * C * * D, ups and downs not needed.

chord components: P1 d2 m2 M2 d3 m3 M3 A3 P4 A4 d5 P5 d6 m6 M6 d7 m7 M7 A7 P8

chord roots: I v#I/bII #I/vII II bIII vIII III IV ^IV/bV #IV/vV V #V/bVI vVI VI bVII vVII VII

Line 707:

Line 711:

0-3-12 = sus2

0-4-12 = vv or sus^2

0-5-12 = v (a down chord, e.g. &quot;C down&quot;)

0-5-12 = v (a down chord, e.g. C,v = &quot;C down&quot;)

0-6-12 = ~ (e.g. &quot;D mid&quot;)

0-6-12 = ~ (e.g. D,~ = &quot;D mid&quot;)

0-7-12 = ^ (e.g. &quot;E flat up&quot;)

0-7-12 = ^ (e.g. Eb,^ = &quot;E flat up&quot;)

0-8-12 = ^^ or susv4

0-9-12 = sus4

@@ Line 1: / Line 1: @@
 <h2>IMPORTED REVISION FROM WIKISPACES</h2>
 This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
-: This revision was by author [[User:TallKite|TallKite]] and made on <tt>2015-09-01 06:47:12 UTC</tt>.<br>
+: This revision was by author [[User:TallKite|TallKite]] and made on <tt>2015-09-01 16:20:28 UTC</tt>.<br>
-: The original revision id was <tt>557878737</tt>.<br>
+: The original revision id was <tt>557941697</tt>.<br>
 : The revision comment was: <tt></tt><br>
 The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
@@ Line 8: / Line 8: @@
 <div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">="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.
+Ups and Downs is a notation system developed by [[KiteGiedraitis|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.
@@ Line 76: / Line 76: @@
 __**Other EDOs**__
-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!)
+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:
@@ Line 127: / Line 127: @@
 Ups and downs allow us to name any chord easily. First we need an exact definition of major, minor, perfect, etc. that works with all edos. The quality of an interval is defined by its position on the chain of 5ths. Perfect is 0-1 steps away, major/minor are 2-5 steps away, aug/dim are 6-12 steps away, etc.
-There are 3 special cases to be addressed. The first is when the edo's 5th is narrower than 4\7, as in 16edo. Major is defined as always wider than minor, so major is not fifthwards but fourthwards:
+There are 3 special cases to be addressed. The first is when the edo's 5th is narrower than 4\7, as in 16edo. Major is defined as wider than minor, so major is not fifthwards but fourthwards:
 The fourthwards chain of fifths in superflat aka Mavila EDOs (3/2 maps to less than 4\7):
@@ Line 140: / Line 140: @@
 Eb + m3 --&gt; E# + M3 = G## --&gt; Gbb
-The second special case is when the edo's fifth equals 4\7, as in 7edo, 14edo, 21edo, 28edo, and 35edo. 42edo, 49edo, etc. have a fifth wider than 4\7. In these edos, there are zero keys per sharp/flat, and all intervals are perfect.
+The second special case is when the edo's fifth equals 4\7, as in 7edo, 14edo, 21edo, 28edo, and 35edo. (42edo, 49edo, etc. have a fifth wider than 4\7.) In these five edos, there are zero keys per sharp/flat, and all intervals are perfect.
 The chain of fifths in heptatonic EDOs (3/2 maps to 4\7):
 P2 - P6 - P3 - P7 - P4 - P1 - P5 - P2 - P6 - P3 - P7 etc.
 F - C - G - D - A - E - B - F - C - G - D - A - E - B etc.
-edo: P1 - A1 - d2 - P2 - A2 - d3 - P3 - A3 - d4 - P4 - A4 - d5 - P5 - A5 - d6 - P6 - A6 - D7 - P7 - A7 - d8 - P8
+edo: P1 - ^P1 - vP2 - P2 - ^P2 - vP3 - P3 - ^P3 - vP4 - P4 - ^P4 - vP5 - P5 - ^P5 - vP6 - P6 - ^P6 - vP7 - P7 - ^P7 - vP8 - P8
+Because everything is perfect, the quality can be omitted:
+edo: 1 - ^1 - v2 - 2 - ^2 - v3 - 3 - ^3 - v4 - 4 - ^4 - v5 - 5 - ^5 - v6 - 6 - ^6 - v7 - 7 - ^7 - v8 - 8
 edo: C - C^ - Dv - D - D^ - Ev - E - E^ - Fv - F - F^ - Gv - G - G^ - Av - A - A^ - Bv - B - B^ - Cv - C
-Just as ups and downs aren't needed in 19edo, sharps and flats aren't needed in 21edo. However they can be used for familiarity's sake: an A major chord can be written A - C#^ - E.
+Just as ups and downs aren't needed in 19edo, sharps and flats aren't needed in 21edo.
-The 3rd special case is when the edo's fifth is wider than 3\5, as in 8edo, 13edo, 18edo and 23edo. Heptatonic fifth-based notation is impossible in these cases, because the chain of 7 fifths isn't a MOS scale. Such EDOs are dealt with below.
+The 3rd special case is when the edo's fifth is wider than 3\5, as in 8edo, 13edo, 18edo and 23edo. Heptatonic fifth-based notation is impossible in these cases. The minor 2nd, which is the sum of five 4ths minus two 8ves, becomes a descending interval. Thus the major 3rd is wider than the perfect 4th, etc. Such EDOs are dealt with below.
 Chord names are based entirely on the ups/downs interval names, not on JI ratios. This avoids identifying one EDOstep with multiple ratios, as happens in 22edo when 0-7-18 implies 4:5:7 but 0-9-18 implies 9:12:16. 18\22 is neither 7/4 nor 16/9, it's 18\22!
@@ Line 182: / Line 184: @@
 These are pronounced "downmajor second", "upminor third", etc. For 4ths and 5ths, "perfect" is implied and can be omitted: ^P4 = "up-four" and vP5 = "down-five". In larger edos there may be "down-octave", "up-unison", etc.
--7-13-18 in C is "C vM,m7", pronounced "C downmajor, minor seventh". The space between the C and the down symbol is needed because Cv is a note, and "Cv M,m7" is a different chord. That chord is pronounced "C down, major, minor 7th", so one has to "speak the space". Alternatively, a comma could be used: C,vM,m7 vs. Cv,M,m7. The extra space/comma isn't needed when there's no ups or downs immediately after the note name, e.g. Cm.
+-7-13-18 in C is "C,vM,m7", pronounced "C downmajor, minor seventh". The comma between the C and the down symbol is needed because Cv is a note, and "Cv,M,m7" is a different chord. That chord is pronounced "C down, major, minor 7th", so one has to "speak the comma". The extra comma isn't needed when there's no ups or downs immediately after the note name, e.g. Cm.
 The conventional chord naming system uses a lot of "shorthand" like dom7 for M3,m7 and min6 for m3,M6. This causes problems in 22edo where there are so many choices for the 3rd, the 6th, the 7th and the 9th. For example, min6 could mean m3,vM6 = approximate 6:7:9:10 chord, or it could mean ^m3,M6 = approximate 1/1-6/5-3/2-12/7 chord. Larger edos would present even greater problems. Furthermore there's some ambiguity in the shorthand, e.g. in 12edo, both 0-3-6 and 0-3-6-9 are called dim chords.
-Thus the shorthand should be largely abandoned and all the components of the chord should be explicitly spelled out, with a few exceptions: 1) The root, obviously. 2) The perfect 5th is assumed present unless otherwise specified. Thus 0-7-18 is "C vM,m7,-5" and 0-6-11 is "C ^m,^d5". 3) The 3rd is also assumed to be present, and is implied by a quality with no degree. Thus 0-7-13 is "C vM". 4) The 3rd isn't spelled out if the 6th or 7th has the same quality as the 3rd. Thus 0-7-13-16 is "C vM6", but 0-7-13-17 is "C vM,M6". Thirdless chords: 0-13-18 is either "Cm7,-3" or "C5,m7".
+Thus the shorthand should be largely abandoned and all the components of the chord should be explicitly spelled out, with a few exceptions: 1) The root, obviously. 2) The perfect 5th is assumed present unless otherwise specified. Thus 0-7-18 is C,vM,m7,-5 and 0-6-11 is C,^m,^d5. 3) The 3rd is also assumed to be present, and is implied by a quality with no degree. Thus 0-7-13 is C,vM. 4) The 3rd isn't spelled out if the 6th or 7th has the same quality as the 3rd. Thus 0-7-13-16 is C,vM6, but 0-7-13-17 is C,vM,M6. Thirdless chords: 0-13-18 is either Cm7,-3 or C5,m7.
 The 6th, the 7th, the 9th, the 11th, etc. are explicitly written out, including their qualities. Thus the 9th isn't assumed to be major, and the presence of a 9th doesn't imply the presence of a 7th.
@@ Line 220: / Line 222: @@
 You can write out chord progressions using the ups/downs notation for note names. Here's the first 4 chords of Paul Erlich's 22edo composition Tibia:
-G vM7,-5 = "G downmajor seven, no five""
+G,vM7,-5 = "G downmajor seven, no five""
-Eb^ vM,M9 = "E flat up, downmajor, major nine"
+Eb^,vM,M9 = "E flat up, downmajor, major nine"
-Gm7,-5 (no space needed) = "G minor seven, no five"
+Gm7,-5 (no comma needed) = "G minor seven, no five"
-A vM,m7 = "A downmajor, minor seven"
+A,vM,m7 = "A downmajor, minor seven"
 To use relative notation, first write out all possible 22edo chord roots relatively. This is equivalent to the interval notation with Roman numerals substituted for Arabic, # for aug, and b for minor. Dim from perfect is b, but dim from minor is bb. Enharmonic equivalents like ^I = bII are used in certain chord progressions like Im - ^IIIM - ^VIIM - ^IVm - ^Im.
@@ Line 229: / Line 231: @@
 These are pronounced "down-two", "up-flat-three", "down-sharp-four", etc.
-Here's the Tibia chords. No spaces are needed because ups and downs are always leading, never trailing.
+Here's the Tibia chords. No comma is needed after the root because ups and downs are always leading, never trailing.
 IvM7,-5 = "one downmajor seven, no five"
 ^bVIvM,M9 = "up-flat six downmajor, major nine"
@@ Line 237: / Line 239: @@
 ==__Chord names in other EDOs__==
-edo: 3 keys per #/b, so ^/v is needed.
+edo: 3 keys per #/b, so ups and downs are needed.
 keyboard/fretboard: D * * E/F * * G * * A * * B/C * * D
 (the chain of fifths is always centered on D)
@@ Line 248: / Line 250: @@
 -5-9-12 = vM,m7
-edo: D * E * * F * G * A * B * * C * D, 1 key per #/b, ^/v not needed. # is fourthward.
+edo: D * E * * F * G * A * B * * C * D, 1 key per #/b, ups and downs not needed. # is fourthward.
 chord components: P1 d2 m2 M2 m3 M3 A3/d4 P4 A4/d5 P5 d6 m6 M6/d7 m7 M7 A7 P8
 chord roots: I #I/bbII bII II bIII III #III/vIV IV #IV/bV V #V/bbVI bVI VI bVII VII #VII/bI
@@ Line 271: / Line 273: @@
 Alternatively, one could replace downmajor with n = neutral or somesuch.
-edo: D * * E * F * * G * * A * * B * C * * D, ^/v not needed.
+edo: D * * E * F * * G * * A * * B * C * * D, ups and downs not needed.
 chord components: P1 d2 m2 M2 d3 m3 M3 A3 P4 A4 d5 P5 d6 m6 M6 d7 m7 M7 A7 P8
 chord roots: I v#I/bII #I/vII II bIII vIII III IV ^IV/bV #IV/vV V #V/bVI vVI VI bVII vVII VII
@@ Line 293: / Line 295: @@
 -3-12 = sus2
 -4-12 = vv or sus^2
--5-12 = v (a down chord, e.g. "C down")
+-5-12 = v (a down chord, e.g. C,v = "C down")
--6-12 = ~ (e.g. "D mid")
+-6-12 = ~ (e.g. D,~ = "D mid")
--7-12 = ^ (e.g. "E flat up")
+-7-12 = ^ (e.g. Eb,^ = "E flat up")
 -8-12 = ^^ or susv4
 -9-12 = sus4
@@ Line 422: / Line 424: @@
 <div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html">&lt;html&gt;&lt;head&gt;&lt;title&gt;Ups and Downs Notation&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="x&amp;quot;Ups and Downs&amp;quot; Notation"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;&amp;quot;Ups and Downs&amp;quot; Notation&lt;/h1&gt;
   &lt;br /&gt;
-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 &amp;quot;^&amp;quot; and the down symbol &amp;quot;v&amp;quot;. There's also the mid symbol &amp;quot;~&amp;quot; which undoes ups and downs.&lt;br /&gt;
+Ups and Downs is a notation system developed by &lt;a class="wiki_link" href="/KiteGiedraitis"&gt;Kite&lt;/a&gt; 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 &amp;quot;^&amp;quot; and the down symbol &amp;quot;v&amp;quot;. There's also the mid symbol &amp;quot;~&amp;quot; which undoes ups and downs.&lt;br /&gt;
 &lt;br /&gt;
 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.&lt;br /&gt;
@@ Line 490: / Line 492: @@
 &lt;br /&gt;
 &lt;u&gt;&lt;strong&gt;Other EDOs&lt;/strong&gt;&lt;/u&gt;&lt;br /&gt;
-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!)&lt;br /&gt;
+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!)&lt;br /&gt;
 &lt;br /&gt;
 EDOs come in 5 categories, based on the size of the fifth:&lt;br /&gt;
@@ Line 541: / Line 543: @@
 Ups and downs allow us to name any chord easily. First we need an exact definition of major, minor, perfect, etc. that works with all edos. The quality of an interval is defined by its position on the chain of 5ths. Perfect is 0-1 steps away, major/minor are 2-5 steps away, aug/dim are 6-12 steps away, etc.&lt;br /&gt;
 &lt;br /&gt;
-There are 3 special cases to be addressed. The first is when the edo's 5th is narrower than 4\7, as in 16edo. Major is defined as always wider than minor, so major is not fifthwards but fourthwards:&lt;br /&gt;
+There are 3 special cases to be addressed. The first is when the edo's 5th is narrower than 4\7, as in 16edo. Major is defined as wider than minor, so major is not fifthwards but fourthwards:&lt;br /&gt;
 &lt;br /&gt;
 The fourthwards chain of fifths in superflat aka Mavila EDOs (3/2 maps to less than 4\7):&lt;br /&gt;
@@ Line 554: / Line 556: @@
 Eb + m3 --&amp;gt; E# + M3 = G## --&amp;gt; Gbb&lt;br /&gt;
 &lt;br /&gt;
-The second special case is when the edo's fifth equals 4\7, as in 7edo, 14edo, 21edo, 28edo, and 35edo. 42edo, 49edo, etc. have a fifth wider than 4\7. In these edos, there are zero keys per sharp/flat, and all intervals are perfect.&lt;br /&gt;
+The second special case is when the edo's fifth equals 4\7, as in 7edo, 14edo, 21edo, 28edo, and 35edo. (42edo, 49edo, etc. have a fifth wider than 4\7.) In these five edos, there are zero keys per sharp/flat, and all intervals are perfect.&lt;br /&gt;
 &lt;br /&gt;
 The chain of fifths in heptatonic EDOs (3/2 maps to 4\7):&lt;br /&gt;
 P2 - P6 - P3 - P7 - P4 - P1 - P5 - P2 - P6 - P3 - P7 etc.&lt;br /&gt;
 F - C - G - D - A - E - B - F - C - G - D - A - E - B etc.&lt;br /&gt;
-edo: P1 - A1 - d2 - P2 - A2 - d3 - P3 - A3 - d4 - P4 - A4 - d5 - P5 - A5 - d6 - P6 - A6 - D7 - P7 - A7 - d8 - P8&lt;br /&gt;
+edo: P1 - ^P1 - vP2 - P2 - ^P2 - vP3 - P3 - ^P3 - vP4 - P4 - ^P4 - vP5 - P5 - ^P5 - vP6 - P6 - ^P6 - vP7 - P7 - ^P7 - vP8 - P8&lt;br /&gt;
+Because everything is perfect, the quality can be omitted:&lt;br /&gt;
+edo: 1 - ^1 - v2 - 2 - ^2 - v3 - 3 - ^3 - v4 - 4 - ^4 - v5 - 5 - ^5 - v6 - 6 - ^6 - v7 - 7 - ^7 - v8 - 8&lt;br /&gt;
 edo: C - C^ - Dv - D - D^ - Ev - E - E^ - Fv - F - F^ - Gv - G - G^ - Av - A - A^ - Bv - B - B^ - Cv - C&lt;br /&gt;
-Just as ups and downs aren't needed in 19edo, sharps and flats aren't needed in 21edo. However they can be used for familiarity's sake: an A major chord can be written A - C#^ - E.&lt;br /&gt;
+Just as ups and downs aren't needed in 19edo, sharps and flats aren't needed in 21edo.&lt;br /&gt;
 &lt;br /&gt;
-The 3rd special case is when the edo's fifth is wider than 3\5, as in 8edo, 13edo, 18edo and 23edo. Heptatonic fifth-based notation is impossible in these cases, because the chain of 7 fifths isn't a MOS scale. Such EDOs are dealt with below.&lt;br /&gt;
+The 3rd special case is when the edo's fifth is wider than 3\5, as in 8edo, 13edo, 18edo and 23edo. Heptatonic fifth-based notation is impossible in these cases. The minor 2nd, which is the sum of five 4ths minus two 8ves, becomes a descending interval. Thus the major 3rd is wider than the perfect 4th, etc. Such EDOs are dealt with below.&lt;br /&gt;
 &lt;br /&gt;
 Chord names are based entirely on the ups/downs interval names, not on JI ratios. This avoids identifying one EDOstep with multiple ratios, as happens in 22edo when 0-7-18 implies 4:5:7 but 0-9-18 implies 9:12:16. 18\22 is neither 7/4 nor 16/9, it's 18\22!&lt;br /&gt;
@@ Line 596: / Line 600: @@
 These are pronounced &amp;quot;downmajor second&amp;quot;, &amp;quot;upminor third&amp;quot;, etc. For 4ths and 5ths, &amp;quot;perfect&amp;quot; is implied and can be omitted: ^P4 = &amp;quot;up-four&amp;quot; and vP5 = &amp;quot;down-five&amp;quot;. In larger edos there may be &amp;quot;down-octave&amp;quot;, &amp;quot;up-unison&amp;quot;, etc.&lt;br /&gt;
 &lt;br /&gt;
--7-13-18 in C is &amp;quot;C vM,m7&amp;quot;, pronounced &amp;quot;C downmajor, minor seventh&amp;quot;. The space between the C and the down symbol is needed because Cv is a note, and &amp;quot;Cv M,m7&amp;quot; is a different chord. That chord is pronounced &amp;quot;C down, major, minor 7th&amp;quot;, so one has to &amp;quot;speak the space&amp;quot;. Alternatively, a comma could be used: C,vM,m7 vs. Cv,M,m7. The extra space/comma isn't needed when there's no ups or downs immediately after the note name, e.g. Cm.&lt;br /&gt;
+-7-13-18 in C is &amp;quot;C,vM,m7&amp;quot;, pronounced &amp;quot;C downmajor, minor seventh&amp;quot;. The comma between the C and the down symbol is needed because Cv is a note, and &amp;quot;Cv,M,m7&amp;quot; is a different chord. That chord is pronounced &amp;quot;C down, major, minor 7th&amp;quot;, so one has to &amp;quot;speak the comma&amp;quot;. The extra comma isn't needed when there's no ups or downs immediately after the note name, e.g. Cm.&lt;br /&gt;
 &lt;br /&gt;
 The conventional chord naming system uses a lot of &amp;quot;shorthand&amp;quot; like dom7 for M3,m7 and min6 for m3,M6. This causes problems in 22edo where there are so many choices for the 3rd, the 6th, the 7th and the 9th. For example, min6 could mean m3,vM6 = approximate 6:7:9:10 chord, or it could mean ^m3,M6 = approximate 1/1-6/5-3/2-12/7 chord. Larger edos would present even greater problems. Furthermore there's some ambiguity in the shorthand, e.g. in 12edo, both 0-3-6 and 0-3-6-9 are called dim chords.&lt;br /&gt;
 &lt;br /&gt;
-Thus the shorthand should be largely abandoned and all the components of the chord should be explicitly spelled out, with a few exceptions: 1) The root, obviously. 2) The perfect 5th is assumed present unless otherwise specified. Thus 0-7-18 is &amp;quot;C vM,m7,-5&amp;quot; and 0-6-11 is &amp;quot;C ^m,^d5&amp;quot;. 3) The 3rd is also assumed to be present, and is implied by a quality with no degree. Thus 0-7-13 is &amp;quot;C vM&amp;quot;. 4) The 3rd isn't spelled out if the 6th or 7th has the same quality as the 3rd. Thus 0-7-13-16 is &amp;quot;C vM6&amp;quot;, but 0-7-13-17 is &amp;quot;C vM,M6&amp;quot;. Thirdless chords: 0-13-18 is either &amp;quot;Cm7,-3&amp;quot; or &amp;quot;C5,m7&amp;quot;.&lt;br /&gt;
+Thus the shorthand should be largely abandoned and all the components of the chord should be explicitly spelled out, with a few exceptions: 1) The root, obviously. 2) The perfect 5th is assumed present unless otherwise specified. Thus 0-7-18 is C,vM,m7,-5 and 0-6-11 is C,^m,^d5. 3) The 3rd is also assumed to be present, and is implied by a quality with no degree. Thus 0-7-13 is C,vM. 4) The 3rd isn't spelled out if the 6th or 7th has the same quality as the 3rd. Thus 0-7-13-16 is C,vM6, but 0-7-13-17 is C,vM,M6. Thirdless chords: 0-13-18 is either Cm7,-3 or C5,m7.&lt;br /&gt;
 &lt;br /&gt;
 The 6th, the 7th, the 9th, the 11th, etc. are explicitly written out, including their qualities. Thus the 9th isn't assumed to be major, and the presence of a 9th doesn't imply the presence of a 7th.&lt;br /&gt;
@@ Line 634: / Line 638: @@
 &lt;br /&gt;
 You can write out chord progressions using the ups/downs notation for note names. Here's the first 4 chords of Paul Erlich's 22edo composition Tibia:&lt;br /&gt;
-G vM7,-5 = &amp;quot;G downmajor seven, no five&amp;quot;&amp;quot;&lt;br /&gt;
+G,vM7,-5 = &amp;quot;G downmajor seven, no five&amp;quot;&amp;quot;&lt;br /&gt;
-Eb^ vM,M9 = &amp;quot;E flat up, downmajor, major nine&amp;quot;&lt;br /&gt;
+Eb^,vM,M9 = &amp;quot;E flat up, downmajor, major nine&amp;quot;&lt;br /&gt;
-Gm7,-5 (no space needed) = &amp;quot;G minor seven, no five&amp;quot;&lt;br /&gt;
+Gm7,-5 (no comma needed) = &amp;quot;G minor seven, no five&amp;quot;&lt;br /&gt;
-A vM,m7 = &amp;quot;A downmajor, minor seven&amp;quot;&lt;br /&gt;
+A,vM,m7 = &amp;quot;A downmajor, minor seven&amp;quot;&lt;br /&gt;
 &lt;br /&gt;
 To use relative notation, first write out all possible 22edo chord roots relatively. This is equivalent to the interval notation with Roman numerals substituted for Arabic, # for aug, and b for minor. Dim from perfect is b, but dim from minor is bb. Enharmonic equivalents like ^I = bII are used in certain chord progressions like Im - ^IIIM - ^VIIM - ^IVm - ^Im.&lt;br /&gt;
@@ Line 643: / Line 647: @@
 These are pronounced &amp;quot;down-two&amp;quot;, &amp;quot;up-flat-three&amp;quot;, &amp;quot;down-sharp-four&amp;quot;, etc.&lt;br /&gt;
 &lt;br /&gt;
-Here's the Tibia chords. No spaces are needed because ups and downs are always leading, never trailing.&lt;br /&gt;
+Here's the Tibia chords. No comma is needed after the root because ups and downs are always leading, never trailing.&lt;br /&gt;
 IvM7,-5 = &amp;quot;one downmajor seven, no five&amp;quot;&lt;br /&gt;
 ^bVIvM,M9 = &amp;quot;up-flat six downmajor, major nine&amp;quot;&lt;br /&gt;
@@ Line 651: / Line 655: @@
 &lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc3"&gt;&lt;a name="Naming Chords-Chord names in other EDOs"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;&lt;u&gt;Chord names in other EDOs&lt;/u&gt;&lt;/h2&gt;
   &lt;br /&gt;
-edo: 3 keys per #/b, so ^/v is needed.&lt;br /&gt;
+edo: 3 keys per #/b, so ups and downs are needed.&lt;br /&gt;
 keyboard/fretboard: D * * E/F * * G * * A * * B/C * * D&lt;br /&gt;
 (the chain of fifths is always centered on D)&lt;br /&gt;
@@ Line 662: / Line 666: @@
 -5-9-12 = vM,m7&lt;br /&gt;
 &lt;br /&gt;
-edo: D * E * * F * G * A * B * * C * D, 1 key per #/b, ^/v not needed. # is fourthward.&lt;br /&gt;
+edo: D * E * * F * G * A * B * * C * D, 1 key per #/b, ups and downs not needed. # is fourthward.&lt;br /&gt;
 chord components: P1 d2 m2 M2 m3 M3 A3/d4 P4 A4/d5 P5 d6 m6 M6/d7 m7 M7 A7 P8&lt;br /&gt;
 chord roots: I #I/bbII bII II bIII III #III/vIV IV #IV/bV V #V/bbVI bVI VI bVII VII #VII/bI&lt;br /&gt;
@@ Line 685: / Line 689: @@
 Alternatively, one could replace downmajor with n = neutral or somesuch.&lt;br /&gt;
 &lt;br /&gt;
-edo: D * * E * F * * G * * A * * B * C * * D, ^/v not needed.&lt;br /&gt;
+edo: D * * E * F * * G * * A * * B * C * * D, ups and downs not needed.&lt;br /&gt;
 chord components: P1 d2 m2 M2 d3 m3 M3 A3 P4 A4 d5 P5 d6 m6 M6 d7 m7 M7 A7 P8&lt;br /&gt;
 chord roots: I v#I/bII #I/vII II bIII vIII III IV ^IV/bV #IV/vV V #V/bVI vVI VI bVII vVII VII&lt;br /&gt;
@@ Line 707: / Line 711: @@
 -3-12 = sus2&lt;br /&gt;
 -4-12 = vv or sus^2&lt;br /&gt;
--5-12 = v (a down chord, e.g. &amp;quot;C down&amp;quot;)&lt;br /&gt;
+-5-12 = v (a down chord, e.g. C,v = &amp;quot;C down&amp;quot;)&lt;br /&gt;
--6-12 = ~ (e.g. &amp;quot;D mid&amp;quot;)&lt;br /&gt;
+-6-12 = ~ (e.g. D,~ = &amp;quot;D mid&amp;quot;)&lt;br /&gt;
--7-12 = ^ (e.g. &amp;quot;E flat up&amp;quot;)&lt;br /&gt;
+-7-12 = ^ (e.g. Eb,^ = &amp;quot;E flat up&amp;quot;)&lt;br /&gt;
 -8-12 = ^^ or susv4&lt;br /&gt;
 -9-12 = sus4&lt;br /&gt;