Kite's ups and downs notation: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>

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: This revision was by author [[User:TallKite|TallKite]] and made on <tt>2015-07-~~28 17~~:05:16 UTC</tt>.

: This revision was by author [[User:TallKite|TallKite]] and made on <tt>2015-08-31 19:54:31 UTC</tt>.

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alternate spellings: A1=vm2, ^m2=vM2, ^M3=vP4, ^P4=vA4, etc.

In C: C C^ Dbv Db Db^ D D^ Ebv Eb Eb^ E E^ Fv F F^ F# Gb Gb^ G etc.

JI associations: Perfect = white, major = yellow or fifthward white, minor = green or fourthward white, downminor = blue, upmajor = red, downmajor = upminor = jade or amber (same as 24-EDO).</pre></div>

JI associations: Perfect = white, major = yellow or fifthward white, minor = green or fourthward white, downminor = blue, upmajor = red, downmajor = upminor = jade or amber (same as 24-EDO).

=__Naming Chords__=

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. Major is always wider than minor, so if the edo's 5th is narrower than 4\7, as is in 16edo, major is not fifthwards but fourthwards:

The chain of fifths in fourthwards EDOs:

M2 - M6 - M3 - M7 - P4 - P1 - P5 - m2 - m6 - m3 - m7 - A4 - A1 etc.

F# - C# - G# - D# - A# - E# - B# - F - C - G - D - A - E - B - Fb - Cb - Gb - Db - Ab - Eb - Bb - Fbb etc.

16edo: P1 - A1/d2 - m2 - M2 - m3 - M3 - A3/d4 - P4 - A4/d5 - P5 - A5/d6 - m6 - M6 - m7 - M7 - A7/d8 - P8

16edo: C - C#/Db - D - D#/Eb - E - E# - Fb - F - F#/Gb - G - G#/Ab - A - A#/Bb - B - B# - Cb - C

In other words, sharp/flat, major/minor, and aug/dim all retain their melodic meaning but are flipped harmonically. Perfect and natural are unaffected. Interval arithmetic in fourthwards edos: First flip the meaning, then perform normal arithmetic, then flip the meaning again:

M2 + M2 --> m2 + m2 = dim3 --> aug3

D to F# --> D to Fb = dim3 --> aug3

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

==__22edo chord names__==

Chord names are based entirely on the ups/downs interval names:

0\22 = P1

1\22 = m2

2\22 = ^m2

3\22 = vM2

4\22 = M2

5\22 = m3

6\22 = ^m3

7\22 = vM3

8\22 = M3

9\22 = P4

10\22 = ^P4, d5

11\22 = vA4, ^d5

12\22 = A4, vP5

13\22 = P5

14\22 = m6

15\22 = ^m6

16\22 = vM6

17\22 = M6

18\22 = m7

19\22 = ^m7

20\22 = vM7

21\22 = M7

22\22 = P8

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 you have to "speak the space". I see the need for a space as a small drawback, but can't think of a good way to avoid it. Alternatively, a comma could be used: C,vM,m7 vs. Cv,M,m7. The extra space/comma isn't needed when there's no usp 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. I think this would cause 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 utonal chord. And larger edos would present even greater problems. Plus there's some ambiguity in the shorthand, e.g. in 12edo, both 0-3-6 and 0-3-6-9 are called dim chords.

So I propose abandoning the shorthand and explicitly spelling out all the components of the chord, 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.

Sus chords: "sus" means the 3rd is replaced by the named note, a 2nd or 4th. "Sus4" means a perfect 4th, and sus^4 means an up-perfect 4th. Some edos would have susv4, susvv4, etc. "Sus2" means a major 2nd. In most edos, M2 is always a perfect 4th below the perfect 5th, see 16edo below for an exception.

0-5-13 = m

0-6-13 = ^m

0-7-13 = vM

0-8-13 = M

0-9-13 = sus4

0-10-13 = sus^4

0-4-13 = sus2

0-3-13 = susvM2

0-5-11 = m,^d5

0-5-12 = m,vP5 (or possibly m,A4)

0-5-11-14 = m6,^d5

0-6-11-15 = ^m6,^d5

0-7-13-16 = vM6

0-8-13-17 = M6

0-5-13-18 = m7

0-6-13-19 = ^m7

0-7-13-20 = vM7

0-8-13-21 = M7

0-5-13-16 = m,vM6

0-8-13-19 = M,^m7

0-7-13-18-26 = vM,m7,M9

0-7-13-18-26-32 = vM,m7,M9,^P11

You can write out chord progressions using the ups/downs notation for note names. Here's the first 2 bars of Tibia:

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

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

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

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

To use relative notation, first write out all possible 22edo chord roots relatively. This is just the interval notation with Roman numerals instead of Arabic, # for aug, and b for minor. Dim from perfect is b, but dim from minor is bb. I've also included more enharmonic equivalents like ^I = bII.

I ^I/bII v#I/^bII #I/vII II ^II/bIII v#II/^bIII #II/vIII III IV ^IV/bV v#IV/^bV #IV/vV

V ^V/bVI v#V/^bVI #V/vVI VI ^VI/bVII v#VI/^bVII #VI/vVII VII

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.

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

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

Im7,-5 = "one minor seven, no five"

IIvM,m7 = "two downmajor, minor seven"</pre></div>

<h4>Original HTML content:</h4>

<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>

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alternate spellings: A1=vm2, ^m2=vM2, ^M3=vP4, ^P4=vA4, etc.

In C: C C^ Dbv Db Db^ D D^ Ebv Eb Eb^ E E^ Fv F F^ F# Gb Gb^ G etc.

JI associations: Perfect = white, major = yellow or fifthward white, minor = green or fourthward white, downminor = blue, upmajor = red, downmajor = upminor = jade or amber (same as 24-EDO).</body></html></pre></div>

JI associations: Perfect = white, major = yellow or fifthward white, minor = green or fourthward white, downminor = blue, upmajor = red, downmajor = upminor = jade or amber (same as 24-EDO).

<h1 id="toc1"><a name="Naming Chords"></a>Naming Chords</h1>

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. Major is always wider than minor, so if the edo's 5th is narrower than 4\7, as is in 16edo, major is not fifthwards but fourthwards:

The chain of fifths in fourthwards EDOs:

M2 - M6 - M3 - M7 - P4 - P1 - P5 - m2 - m6 - m3 - m7 - A4 - A1 etc.

F# - C# - G# - D# - A# - E# - B# - F - C - G - D - A - E - B - Fb - Cb - Gb - Db - Ab - Eb - Bb - Fbb etc.

16edo: P1 - A1/d2 - m2 - M2 - m3 - M3 - A3/d4 - P4 - A4/d5 - P5 - A5/d6 - m6 - M6 - m7 - M7 - A7/d8 - P8

16edo: C - C#/Db - D - D#/Eb - E - E# - Fb - F - F#/Gb - G - G#/Ab - A - A#/Bb - B - B# - Cb - C

In other words, sharp/flat, major/minor, and aug/dim all retain their melodic meaning but are flipped harmonically. Perfect and natural are unaffected. Interval arithmetic in fourthwards edos: First flip the meaning, then perform normal arithmetic, then flip the meaning again:

M2 + M2 --&gt; m2 + m2 = dim3 --&gt; aug3

D to F# --&gt; D to Fb = dim3 --&gt; aug3

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

<h2 id="toc2"><a name="Naming Chords-22edo chord names"></a>22edo chord names</h2>

Chord names are based entirely on the ups/downs interval names:

0\22 = P1

1\22 = m2

2\22 = ^m2

3\22 = vM2

4\22 = M2

5\22 = m3

6\22 = ^m3

7\22 = vM3

8\22 = M3

9\22 = P4

10\22 = ^P4, d5

11\22 = vA4, ^d5

12\22 = A4, vP5

13\22 = P5

14\22 = m6

15\22 = ^m6

16\22 = vM6

17\22 = M6

18\22 = m7

19\22 = ^m7

20\22 = vM7

21\22 = M7

22\22 = P8

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 you have to &quot;speak the space&quot;. I see the need for a space as a small drawback, but can't think of a good way to avoid it. Alternatively, a comma could be used: C,vM,m7 vs. Cv,M,m7. The extra space/comma isn't needed when there's no usp 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. I think this would cause 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 utonal chord. And larger edos would present even greater problems. Plus there's some ambiguity in the shorthand, e.g. in 12edo, both 0-3-6 and 0-3-6-9 are called dim chords.

So I propose abandoning the shorthand and explicitly spelling out all the components of the chord, 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;.

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.

Sus chords: &quot;sus&quot; means the 3rd is replaced by the named note, a 2nd or 4th. &quot;Sus4&quot; means a perfect 4th, and sus^4 means an up-perfect 4th. Some edos would have susv4, susvv4, etc. &quot;Sus2&quot; means a major 2nd. In most edos, M2 is always a perfect 4th below the perfect 5th, see 16edo below for an exception.

0-5-13 = m

0-6-13 = ^m

0-7-13 = vM

0-8-13 = M

0-9-13 = sus4

0-10-13 = sus^4

0-4-13 = sus2

0-3-13 = susvM2

0-5-11 = m,^d5

0-5-12 = m,vP5 (or possibly m,A4)

0-5-11-14 = m6,^d5

0-6-11-15 = ^m6,^d5

0-7-13-16 = vM6

0-8-13-17 = M6

0-5-13-18 = m7

0-6-13-19 = ^m7

0-7-13-20 = vM7

0-8-13-21 = M7

0-5-13-16 = m,vM6

0-8-13-19 = M,^m7

0-7-13-18-26 = vM,m7,M9

0-7-13-18-26-32 = vM,m7,M9,^P11

You can write out chord progressions using the ups/downs notation for note names. Here's the first 2 bars of Tibia:

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

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

Gm7,-5 (no space needed) = &quot;G minor seven, no five&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 just the interval notation with Roman numerals instead of Arabic, # for aug, and b for minor. Dim from perfect is b, but dim from minor is bb. I've also included more enharmonic equivalents like ^I = bII.

I ^I/bII v#I/^bII #I/vII II ^II/bIII v#II/^bIII #II/vIII III IV ^IV/bV v#IV/^bV #IV/vV

V ^V/bVI v#V/^bVI #V/vVI VI ^VI/bVII v#VI/^bVII #VI/vVII VII

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.

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

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

Im7,-5 = &quot;one minor seven, no five&quot;

IIvM,m7 = &quot;two downmajor, minor seven&quot;</body></html></pre></div>

@@ 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>2015-07-28 17:05:16 UTC</tt>.<br>
+: This revision was by author [[User:TallKite|TallKite]] and made on <tt>2015-08-31 19:54:31 UTC</tt>.<br>
-: The original revision id was <tt>555869645</tt>.<br>
+: The original revision id was <tt>557847281</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 115: / Line 115: @@
 alternate spellings: A1=vm2, ^m2=vM2, ^M3=vP4, ^P4=vA4, etc.
 In C: C C^ Dbv Db Db^ D D^ Ebv Eb Eb^ E E^ Fv F F^ F# Gb Gb^ G etc.
-JI associations: Perfect = white, major = yellow or fifthward white, minor = green or fourthward white, downminor = blue, upmajor = red, downmajor = upminor = jade or amber (same as 24-EDO).</pre></div>
+JI associations: Perfect = white, major = yellow or fifthward white, minor = green or fourthward white, downminor = blue, upmajor = red, downmajor = upminor = jade or amber (same as 24-EDO).
+=__Naming Chords__=
+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. Major is always wider than minor, so if the edo's 5th is narrower than 4\7, as is in 16edo, major is not fifthwards but fourthwards:
+The chain of fifths in fourthwards EDOs:
+M2 - M6 - M3 - M7 - P4 - P1 - P5 - m2 - m6 - m3 - m7 - A4 - A1 etc.
+F# - C# - G# - D# - A# - E# - B# - F - C - G - D - A - E - B - Fb - Cb - Gb - Db - Ab - Eb - Bb - Fbb etc.
+edo: P1 - A1/d2 - m2 - M2 - m3 - M3 - A3/d4 - P4 - A4/d5 - P5 - A5/d6 - m6 - M6 - m7 - M7 - A7/d8 - P8
+edo: C - C#/Db - D - D#/Eb - E - E# - Fb - F - F#/Gb - G - G#/Ab - A - A#/Bb - B - B# - Cb - C
+In other words, sharp/flat, major/minor, and aug/dim all retain their melodic meaning but are flipped harmonically. Perfect and natural are unaffected. Interval arithmetic in fourthwards edos: First flip the meaning, then perform normal arithmetic, then flip the meaning again:
+M2 + M2 --&gt; m2 + m2 = dim3 --&gt; aug3
+D to F# --&gt; D to Fb = dim3 --&gt; aug3
+Eb + m3 --&gt; E# + M3 = Gx --&gt; Gbb
+==__22edo chord names__==
+Chord names are based entirely on the ups/downs interval names:
+\22 = P1
+\22 = m2
+\22 = ^m2
+\22 = vM2
+\22 = M2
+\22 = m3
+\22 = ^m3
+\22 = vM3
+\22 = M3
+\22 = P4
+\22 = ^P4, d5
+\22 = vA4, ^d5
+\22 = A4, vP5
+\22 = P5
+\22 = m6
+\22 = ^m6
+\22 = vM6
+\22 = M6
+\22 = m7
+\22 = ^m7
+\22 = vM7
+\22 = M7
+\22 = P8
+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 you have to "speak the space". I see the need for a space as a small drawback, but can't think of a good way to avoid it. Alternatively, a comma could be used: C,vM,m7 vs. Cv,M,m7. The extra space/comma isn't needed when there's no usp 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. I think this would cause 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 utonal chord. And larger edos would present even greater problems. Plus there's some ambiguity in the shorthand, e.g. in 12edo, both 0-3-6 and 0-3-6-9 are called dim chords.
+So I propose abandoning the shorthand and explicitly spelling out all the components of the chord, 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.
+Sus chords: "sus" means the 3rd is replaced by the named note, a 2nd or 4th. "Sus4" means a perfect 4th, and sus^4 means an up-perfect 4th. Some edos would have susv4, susvv4, etc. "Sus2" means a major 2nd. In most edos, M2 is always a perfect 4th below the perfect 5th, see 16edo below for an exception.
+-5-13 = m
+-6-13 = ^m
+-7-13 = vM
+-8-13 = M
+-9-13 = sus4
+-10-13 = sus^4
+-4-13 = sus2
+-3-13 = susvM2
+-5-11 = m,^d5
+-5-12 = m,vP5 (or possibly m,A4)
+-5-11-14 = m6,^d5
+-6-11-15 = ^m6,^d5
+-7-13-16 = vM6
+-8-13-17 = M6
+-5-13-18 = m7
+-6-13-19 = ^m7
+-7-13-20 = vM7
+-8-13-21 = M7
+-5-13-16 = m,vM6
+-8-13-19 = M,^m7
+-7-13-18-26 = vM,m7,M9
+-7-13-18-26-32 = vM,m7,M9,^P11
+You can write out chord progressions using the ups/downs notation for note names. Here's the first 2 bars of Tibia:
+G vM7,-5 = "G downmajor seven, no five""
+Eb^ vM,M9 = "E flat up, downmajor, major nine"
+Gm7,-5 (no space needed) = "G minor seven, no five"
+A vM,m7 = "A downmajor, minor seven"
+To use relative notation, first write out all possible 22edo chord roots relatively. This is just the interval notation with Roman numerals instead of Arabic, # for aug, and b for minor. Dim from perfect is b, but dim from minor is bb. I've also included more enharmonic equivalents like ^I = bII.
+I ^I/bII v#I/^bII #I/vII II ^II/bIII v#II/^bIII #II/vIII III IV ^IV/bV v#IV/^bV #IV/vV
+V ^V/bVI v#V/^bVI #V/vVI VI ^VI/bVII v#VI/^bVII #VI/vVII VII
+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.
+IvM7,-5 = "one downmajor seven, no five"
+^bVIvM,M9 = "up-flat six downmajor, major nine"
+Im7,-5 = "one minor seven, no five"
+IIvM,m7 = "two downmajor, minor seven"</pre></div>
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 <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;
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 alternate spellings: A1=vm2, ^m2=vM2, ^M3=vP4, ^P4=vA4, etc.&lt;br /&gt;
 In C: C C^ Dbv Db Db^ D D^ Ebv Eb Eb^ E E^ Fv F F^ F# Gb Gb^ G etc.&lt;br /&gt;
-JI associations: Perfect = white, major = yellow or fifthward white, minor = green or fourthward white, downminor = blue, upmajor = red, downmajor = upminor = jade or amber (same as 24-EDO).&lt;/body&gt;&lt;/html&gt;</pre></div>
+JI associations: Perfect = white, major = yellow or fifthward white, minor = green or fourthward white, downminor = blue, upmajor = red, downmajor = upminor = jade or amber (same as 24-EDO).&lt;br /&gt;
+&lt;br /&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc1"&gt;&lt;a name="Naming Chords"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;&lt;u&gt;Naming Chords&lt;/u&gt;&lt;/h1&gt;
+ &lt;br /&gt;
+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.&lt;br /&gt;
+&lt;br /&gt;
+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. Major is always wider than minor, so if the edo's 5th is narrower than 4\7, as is in 16edo, major is not fifthwards but fourthwards:&lt;br /&gt;
+&lt;br /&gt;
+The chain of fifths in fourthwards EDOs:&lt;br /&gt;
+M2 - M6 - M3 - M7 - P4 - P1 - P5 - m2 - m6 - m3 - m7 - A4 - A1 etc.&lt;br /&gt;
+F# - C# - G# - D# - A# - E# - B# - F - C - G - D - A - E - B - Fb - Cb - Gb - Db - Ab - Eb - Bb - Fbb etc.&lt;br /&gt;
+edo: P1 - A1/d2 - m2 - M2 - m3 - M3 - A3/d4 - P4 - A4/d5 - P5 - A5/d6 - m6 - M6 - m7 - M7 - A7/d8 - P8&lt;br /&gt;
+edo: C - C#/Db - D - D#/Eb - E - E# - Fb - F - F#/Gb - G - G#/Ab - A - A#/Bb - B - B# - Cb - C&lt;br /&gt;
+&lt;br /&gt;
+In other words, sharp/flat, major/minor, and aug/dim all retain their melodic meaning but are flipped harmonically. Perfect and natural are unaffected. Interval arithmetic in fourthwards edos: First flip the meaning, then perform normal arithmetic, then flip the meaning again:&lt;br /&gt;
+M2 + M2 --&amp;gt; m2 + m2 = dim3 --&amp;gt; aug3&lt;br /&gt;
+D to F# --&amp;gt; D to Fb = dim3 --&amp;gt; aug3&lt;br /&gt;
+Eb + m3 --&amp;gt; E# + M3 = Gx --&amp;gt; Gbb&lt;br /&gt;
+&lt;br /&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc2"&gt;&lt;a name="Naming Chords-22edo chord names"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;&lt;u&gt;22edo chord names&lt;/u&gt;&lt;/h2&gt;
+ &lt;br /&gt;
+Chord names are based entirely on the ups/downs interval names:&lt;br /&gt;
+&lt;br /&gt;
+\22 = P1&lt;br /&gt;
+\22 = m2&lt;br /&gt;
+\22 = ^m2&lt;br /&gt;
+\22 = vM2&lt;br /&gt;
+\22 = M2&lt;br /&gt;
+\22 = m3&lt;br /&gt;
+\22 = ^m3&lt;br /&gt;
+\22 = vM3&lt;br /&gt;
+\22 = M3&lt;br /&gt;
+\22 = P4&lt;br /&gt;
+\22 = ^P4, d5&lt;br /&gt;
+\22 = vA4, ^d5&lt;br /&gt;
+\22 = A4, vP5&lt;br /&gt;
+\22 = P5&lt;br /&gt;
+\22 = m6&lt;br /&gt;
+\22 = ^m6&lt;br /&gt;
+\22 = vM6&lt;br /&gt;
+\22 = M6&lt;br /&gt;
+\22 = m7&lt;br /&gt;
+\22 = ^m7&lt;br /&gt;
+\22 = vM7&lt;br /&gt;
+\22 = M7&lt;br /&gt;
+\22 = P8&lt;br /&gt;
+&lt;br /&gt;
+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 you have to &amp;quot;speak the space&amp;quot;. I see the need for a space as a small drawback, but can't think of a good way to avoid it. Alternatively, a comma could be used: C,vM,m7 vs. Cv,M,m7. The extra space/comma isn't needed when there's no usp 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. I think this would cause 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 utonal chord. And larger edos would present even greater problems. Plus 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;
+So I propose abandoning the shorthand and explicitly spelling out all the components of the chord, 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;
+&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;
+&lt;br /&gt;
+Sus chords: &amp;quot;sus&amp;quot; means the 3rd is replaced by the named note, a 2nd or 4th. &amp;quot;Sus4&amp;quot; means a perfect 4th, and sus^4 means an up-perfect 4th. Some edos would have susv4, susvv4, etc. &amp;quot;Sus2&amp;quot; means a major 2nd. In most edos, M2 is always a perfect 4th below the perfect 5th, see 16edo below for an exception.&lt;br /&gt;
+&lt;br /&gt;
+-5-13 = m&lt;br /&gt;
+-6-13 = ^m&lt;br /&gt;
+-7-13 = vM&lt;br /&gt;
+-8-13 = M&lt;br /&gt;
+-9-13 = sus4&lt;br /&gt;
+-10-13 = sus^4&lt;br /&gt;
+-4-13 = sus2&lt;br /&gt;
+-3-13 = susvM2&lt;br /&gt;
+&lt;br /&gt;
+-5-11 = m,^d5&lt;br /&gt;
+-5-12 = m,vP5 (or possibly m,A4)&lt;br /&gt;
+&lt;br /&gt;
+-5-11-14 = m6,^d5&lt;br /&gt;
+-6-11-15 = ^m6,^d5&lt;br /&gt;
+-7-13-16 = vM6&lt;br /&gt;
+-8-13-17 = M6&lt;br /&gt;
+&lt;br /&gt;
+-5-13-18 = m7&lt;br /&gt;
+-6-13-19 = ^m7&lt;br /&gt;
+-7-13-20 = vM7&lt;br /&gt;
+-8-13-21 = M7&lt;br /&gt;
+&lt;br /&gt;
+-5-13-16 = m,vM6&lt;br /&gt;
+-8-13-19 = M,^m7&lt;br /&gt;
+-7-13-18-26 = vM,m7,M9&lt;br /&gt;
+-7-13-18-26-32 = vM,m7,M9,^P11&lt;br /&gt;
+&lt;br /&gt;
+You can write out chord progressions using the ups/downs notation for note names. Here's the first 2 bars of Tibia:&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;
+Gm7,-5 (no space 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;
+&lt;br /&gt;
+To use relative notation, first write out all possible 22edo chord roots relatively. This is just the interval notation with Roman numerals instead of Arabic, # for aug, and b for minor. Dim from perfect is b, but dim from minor is bb. I've also included more enharmonic equivalents like ^I = bII.&lt;br /&gt;
+I ^I/bII v#I/^bII #I/vII II ^II/bIII v#II/^bIII #II/vIII III IV ^IV/bV v#IV/^bV #IV/vV&lt;br /&gt;
+V ^V/bVI v#V/^bVI #V/vVI VI ^VI/bVII v#VI/^bVII #VI/vVII VII&lt;br /&gt;
+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;
+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;
+Im7,-5 = &amp;quot;one minor seven, no five&amp;quot;&lt;br /&gt;
+IIvM,m7 = &amp;quot;two downmajor, minor seven&amp;quot;&lt;/body&gt;&lt;/html&gt;</pre></div>