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>2015-08-31 20:44:07 UTC</tt>.

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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.

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.

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.

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 utonal 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.

~~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".

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.

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.

Sus chords: as usual, "sus" means the 3rd is replaced by the named note, a 2nd or 4th. "Sus4" implies a perfect 4th, and other 4ths are specified explicitly as sus^4 for an up-perfect 4th, etc. Some larger edos would have susv4, susvv4, etc. "Sus2" implies a major 2nd. In most edos, this M2 is always a perfect 4th below the perfect 5th, implying an approximate 8:9:12 chord. See 16edo below for an exception.

0-5-13 = m

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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:

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""

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

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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.

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. Enharmonic equivalents like ^I = bII are used in certain chord progressions like Im - ^IIIM - ^VIIM - ^IVm - ^Im.

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

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

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

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==__Chord names in other EDOs__==

15edo: ~~use 3/2 as a notation generator,~~ 3 keys per #/b, so ^/v is needed.

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

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

(the chain of ~~generators~~ is always centered on D)

(the chain of fifths is always centered on D)

chord components: P1 ^m2 vM2 M2/m3 ^m3 vM3 P4 ^P4 vP5 P5 ^m6 vM6 M6/m7 ^m7 vM7 P8

chord roots: I ^bII vII II/bIII ^bIII vIII IV ^IV vV V ^bVI vVI VI/bVII ^bVII vVII

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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

0-2-9 = ~~sus2~~

0-2-9 = susm2

0-3-9 = susM2

0-4-9 = m

0-5-9 = M

0-5-10 = M,A5 (aug chord)

0-5-10 = M,A5 (the conventional aug chord)

0-6-9 = A3

0-6-9 = A (aug 3rd, perfect 5th)

0-7-9 = sus4

0-4-8-12 = m,d5,d7 (dim tetrad)

0-4-8-12 = m,d5,d7 (the conventional dim tetrad)

17edo: D * * E F * * G * * A * * B C * * D, 2 keys per #/b.

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0-5-10-15 = vM7

0-6-10-16 = M7

~~Sure~~, we could replace downmajor with n = neutral~~, but that spoils the economy -- two new words up & down, and we can name everything!~~

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

19edo: D * * E * F * * G * * A * * B * C * * D, ^/v 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

~~Note that~~ "dim chord" ~~means dim 3rd, perfect 5th,~~ and "aug chord" ~~means aug 3rd, perfect 5th:~~

The possibility of a dim 3rd or an aug 3rd changes the meaning of "dim chord" and "aug chord".

0-4-11 = d

0-4-11 = d (dim 3rd, perfect 5th, not a conventional dim chord)

0-4-10 = d,d5

0-5-11 = m

0-5-10 = m,d5 (conventional dim chord)

0-6-11 = M

0-7-11 = A

0-7-11 = A (aug 3rd, perfect 5th, not a conventional aug chord)

0-6-12 = M,A5 (conventional aug chord)

0-7-12 = A,A5

0-8-11 = sus4

24edo: D * * * E * F * * * G * * * A * * * B * C * * * D, 2 keys per #/b.

chord components: P1 vm2 m2 vM2 M2 vm3 m3 vM3 M3 ^M3/vP4 P4 ^P4 A4/d5 vP5 P5 vm6 m6 vM6 M6 ^M6/vm7 m7 vM7 M7 ^M7

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

0-5-14 = vm

0-6-14 = m

0-7-14 = vM

0-8-14 = M

0-9-14 = ^M

0-10-14 = sus4

31edo: D * * * * E * * F * * * * G * * * * A etc. 2 keys per #/b.

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0-10-18 = M

0-11-18 = ^M

0-12-18 = sus-v4</pre></div>

0-12-18 = sus-v4

==__EDOs with inaccurate 3/2__==

Such EDOs may be better notated with a notation not generated by the fifth.</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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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.

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.

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.

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 utonal 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.

~~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;.

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;.

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.

Sus chords: as usual, &quot;sus&quot; means the 3rd is replaced by the named note, a 2nd or 4th. &quot;Sus4&quot; implies a perfect 4th, and other 4ths are specified explicitly as sus^4 for an up-perfect 4th, etc. Some larger edos would have susv4, susvv4, etc. &quot;Sus2&quot; implies a major 2nd. In most edos, this M2 is always a perfect 4th below the perfect 5th, implying an approximate 8:9:12 chord. See 16edo below for an exception.

0-5-13 = m

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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:

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;

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

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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.

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. Enharmonic equivalents like ^I = bII are used in certain chord progressions like Im - ^IIIM - ^VIIM - ^IVm - ^Im.

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

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

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

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

15edo: ~~use 3/2 as a notation generator,~~ 3 keys per #/b, so ^/v is needed.

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

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

(the chain of ~~generators~~ is always centered on D)

(the chain of fifths is always centered on D)

chord components: P1 ^m2 vM2 M2/m3 ^m3 vM3 P4 ^P4 vP5 P5 ^m6 vM6 M6/m7 ^m7 vM7 P8

chord roots: I ^bII vII II/bIII ^bIII vIII IV ^IV vV V ^bVI vVI VI/bVII ^bVII vVII

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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

0-2-9 = ~~sus2~~

0-2-9 = susm2

0-3-9 = susM2

0-4-9 = m

0-5-9 = M

0-5-10 = M,A5 (aug chord)

0-5-10 = M,A5 (the conventional aug chord)

0-6-9 = A3

0-6-9 = A (aug 3rd, perfect 5th)

0-7-9 = sus4

0-4-8-12 = m,d5,d7 (dim tetrad)

0-4-8-12 = m,d5,d7 (the conventional dim tetrad)

17edo: D * * E F * * G * * A * * B C * * D, 2 keys per #/b.

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0-5-10-15 = vM7

0-6-10-16 = M7

~~Sure~~, we could replace downmajor with n = neutral~~, but that spoils the economy -- two new words up &amp; down, and we can name everything!~~

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

19edo: D * * E * F * * G * * A * * B * C * * D, ^/v 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

~~Note that~~ &quot;dim chord&quot; ~~means dim 3rd, perfect 5th,~~ and &quot;aug chord&quot; ~~means aug 3rd, perfect 5th:~~

The possibility of a dim 3rd or an aug 3rd changes the meaning of &quot;dim chord&quot; and &quot;aug chord&quot;.

0-4-11 = d

0-4-11 = d (dim 3rd, perfect 5th, not a conventional dim chord)

0-4-10 = d,d5

0-5-11 = m

0-5-10 = m,d5 (conventional dim chord)

0-6-11 = M

0-7-11 = A

0-7-11 = A (aug 3rd, perfect 5th, not a conventional aug chord)

0-6-12 = M,A5 (conventional aug chord)

0-7-12 = A,A5

0-8-11 = sus4

24edo: D * * * E * F * * * G * * * A * * * B * C * * * D, 2 keys per #/b.

chord components: P1 vm2 m2 vM2 M2 vm3 m3 vM3 M3 ^M3/vP4 P4 ^P4 A4/d5 vP5 P5 vm6 m6 vM6 M6 ^M6/vm7 m7 vM7 M7 ^M7

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

0-5-14 = vm

0-6-14 = m

0-7-14 = vM

0-8-14 = M

0-9-14 = ^M

0-10-14 = sus4

31edo: D * * * * E * * F * * * * G * * * * A etc. 2 keys per #/b.

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0-10-18 = M

0-11-18 = ^M

0-12-18 = sus-v4</body></html></pre></div>

0-12-18 = sus-v4

<h2 id="toc4"><a name="Naming Chords-EDOs with inaccurate 3/2"></a>EDOs with inaccurate 3/2</h2>

Such EDOs may be better notated with a notation not generated by the fifth.</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>2015-08-31 20:01:05 UTC</tt>.<br>
+: This revision was by author [[User:TallKite|TallKite]] and made on <tt>2015-08-31 20:44:07 UTC</tt>.<br>
-: The original revision id was <tt>557847993</tt>.<br>
+: The original revision id was <tt>557851235</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 164: / Line 164: @@
 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.
+-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.
-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.
+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 utonal 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.
-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".
+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.
-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.
+Sus chords: as usual, "sus" means the 3rd is replaced by the named note, a 2nd or 4th. "Sus4" implies a perfect 4th, and other 4ths are specified explicitly as sus^4 for an up-perfect 4th, etc. Some larger edos would have susv4, susvv4, etc. "Sus2" implies a major 2nd. In most edos, this M2 is always a perfect 4th below the perfect 5th, implying an approximate 8:9:12 chord. See 16edo below for an exception.
 -5-13 = m
@@ Line 201: / Line 201: @@
 -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:
+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""
 Eb^ vM,M9 = "E flat up, downmajor, major nine"
@@ Line 207: / Line 207: @@
 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.
+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. Enharmonic equivalents like ^I = bII are used in certain chord progressions like Im - ^IIIM - ^VIIM - ^IVm - ^Im.
 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
+V ^V/bVI v#V/^bVI #V/vVI VI ^VI/bVII v#VI/^bVII #VI/vVII VII/vI
 These are pronounced "down-two", "up-flat-three", "down-sharp-four", etc.
@@ Line 220: / Line 220: @@
 ==__Chord names in other EDOs__==
-edo: use 3/2 as a notation generator, 3 keys per #/b, so ^/v is needed.
+edo: 3 keys per #/b, so ^/v is needed.
 keyboard/fretboard: D * * E/F * * G * * A * * B/C * * D
-(the chain of generators is always centered on D)
+(the chain of fifths is always centered on D)
 chord components: P1 ^m2 vM2 M2/m3 ^m3 vM3 P4 ^P4 vP5 P5 ^m6 vM6 M6/m7 ^m7 vM7 P8
 chord roots: I ^bII vII II/bIII ^bIII vIII IV ^IV vV V ^bVI vVI VI/bVII ^bVII vVII
@@ Line 234: / Line 234: @@
 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
--2-9 = sus2
+-2-9 = susm2
 -3-9 = susM2
 -4-9 = m
 -5-9 = M
--5-10 = M,A5 (aug chord)
+-5-10 = M,A5 (the conventional aug chord)
--6-9 = A3
+-6-9 = A (aug 3rd, perfect 5th)
 -7-9 = sus4
--4-8-12 = m,d5,d7 (dim tetrad)
+-4-8-12 = m,d5,d7 (the conventional dim tetrad)
 edo: D * * E F * * G * * A * * B C * * D, 2 keys per #/b.
@@ Line 253: / Line 253: @@
 -5-10-15 = vM7
 -6-10-16 = M7
-Sure, we could replace downmajor with n = neutral, but that spoils the economy -- two new words up &amp; down, and we can name everything!
+Alternatively, one could replace downmajor with n = neutral or somesuch.
 edo: D * * E * F * * G * * A * * B * C * * D, ^/v 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
-Note that "dim chord" means dim 3rd, perfect 5th, and "aug chord" means aug 3rd, perfect 5th:
+The possibility of a dim 3rd or an aug 3rd changes the meaning of "dim chord" and "aug chord".
--4-11 = d
+-4-11 = d (dim 3rd, perfect 5th, not a conventional dim chord)
 -4-10 = d,d5
 -5-11 = m
+-5-10 = m,d5 (conventional dim chord)
 -6-11 = M
--7-11 = A
+-7-11 = A (aug 3rd, perfect 5th, not a conventional aug chord)
+-6-12 = M,A5 (conventional aug chord)
 -7-12 = A,A5
 -8-11 = sus4
+edo: D * * * E * F * * * G * * * A * * * B * C * * * D, 2 keys per #/b.
+chord components: P1 vm2 m2 vM2 M2 vm3 m3 vM3 M3 ^M3/vP4 P4 ^P4 A4/d5 vP5 P5 vm6 m6 vM6 M6 ^M6/vm7 m7 vM7 M7 ^M7
+chord roots: I v#I/vbII #I/bII vII II vbIII bIII vIII III ^III/vIV IV ^IV #IV/bV vV V ^#V/vbVI bVI vVI VI ^VI/vbVII bVII vVII VII ^VII/vI
+-5-14 = vm
+-6-14 = m
+-7-14 = vM
+-8-14 = M
+-9-14 = ^M
+-10-14 = sus4
 edo: D * * * * E * * F * * * * G * * * * A etc. 2 keys per #/b.
@@ Line 275: / Line 287: @@
 -10-18 = M
 -11-18 = ^M
--12-18 = sus-v4</pre></div>
+-12-18 = sus-v4
+==__EDOs with inaccurate 3/2__==
+Such EDOs may be better notated with a notation not generated by the fifth.</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">&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;
@@ Line 435: / Line 451: @@
 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;
+-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;
 &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;
+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 utonal 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;
-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;
+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;
 &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;
+Sus chords: as usual, &amp;quot;sus&amp;quot; means the 3rd is replaced by the named note, a 2nd or 4th. &amp;quot;Sus4&amp;quot; implies a perfect 4th, and other 4ths are specified explicitly as sus^4 for an up-perfect 4th, etc. Some larger edos would have susv4, susvv4, etc. &amp;quot;Sus2&amp;quot; implies a major 2nd. In most edos, this M2 is always a perfect 4th below the perfect 5th, implying an approximate 8:9:12 chord. See 16edo below for an exception.&lt;br /&gt;
 &lt;br /&gt;
 -5-13 = m&lt;br /&gt;
@@ Line 472: / Line 488: @@
 -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;
+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;
 Eb^ vM,M9 = &amp;quot;E flat up, downmajor, major nine&amp;quot;&lt;br /&gt;
@@ Line 478: / Line 494: @@
 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;
+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. Enharmonic equivalents like ^I = bII are used in certain chord progressions like Im - ^IIIM - ^VIIM - ^IVm - ^Im.&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;
+V ^V/bVI v#V/^bVI #V/vVI VI ^VI/bVII v#VI/^bVII #VI/vVII VII/vI&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;
@@ Line 491: / Line 507: @@
 &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: use 3/2 as a notation generator, 3 keys per #/b, so ^/v is needed.&lt;br /&gt;
+edo: 3 keys per #/b, so ^/v is needed.&lt;br /&gt;
 keyboard/fretboard: D * * E/F * * G * * A * * B/C * * D&lt;br /&gt;
-(the chain of generators is always centered on D)&lt;br /&gt;
+(the chain of fifths is always centered on D)&lt;br /&gt;
 chord components: P1 ^m2 vM2 M2/m3 ^m3 vM3 P4 ^P4 vP5 P5 ^m6 vM6 M6/m7 ^m7 vM7 P8&lt;br /&gt;
 chord roots: I ^bII vII II/bIII ^bIII vIII IV ^IV vV V ^bVI vVI VI/bVII ^bVII vVII&lt;br /&gt;
@@ Line 505: / Line 521: @@
 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;
--2-9 = sus2&lt;br /&gt;
+-2-9 = susm2&lt;br /&gt;
 -3-9 = susM2&lt;br /&gt;
 -4-9 = m&lt;br /&gt;
 -5-9 = M&lt;br /&gt;
--5-10 = M,A5 (aug chord)&lt;br /&gt;
+-5-10 = M,A5 (the conventional aug chord)&lt;br /&gt;
--6-9 = A3&lt;br /&gt;
+-6-9 = A (aug 3rd, perfect 5th)&lt;br /&gt;
 -7-9 = sus4&lt;br /&gt;
--4-8-12 = m,d5,d7 (dim tetrad)&lt;br /&gt;
+-4-8-12 = m,d5,d7 (the conventional dim tetrad)&lt;br /&gt;
 &lt;br /&gt;
 edo: D * * E F * * G * * A * * B C * * D, 2 keys per #/b.&lt;br /&gt;
@@ Line 524: / Line 540: @@
 -5-10-15 = vM7&lt;br /&gt;
 -6-10-16 = M7&lt;br /&gt;
-Sure, we could replace downmajor with n = neutral, but that spoils the economy -- two new words up &amp;amp; down, and we can name everything!&lt;br /&gt;
+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;
 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;
-Note that &amp;quot;dim chord&amp;quot; means dim 3rd, perfect 5th, and &amp;quot;aug chord&amp;quot; means aug 3rd, perfect 5th:&lt;br /&gt;
+The possibility of a dim 3rd or an aug 3rd changes the meaning of &amp;quot;dim chord&amp;quot; and &amp;quot;aug chord&amp;quot;.&lt;br /&gt;
--4-11 = d&lt;br /&gt;
+-4-11 = d (dim 3rd, perfect 5th, not a conventional dim chord)&lt;br /&gt;
 -4-10 = d,d5&lt;br /&gt;
 -5-11 = m&lt;br /&gt;
+-5-10 = m,d5 (conventional dim chord)&lt;br /&gt;
 -6-11 = M&lt;br /&gt;
--7-11 = A&lt;br /&gt;
+-7-11 = A (aug 3rd, perfect 5th, not a conventional aug chord)&lt;br /&gt;
+-6-12 = M,A5 (conventional aug chord)&lt;br /&gt;
 -7-12 = A,A5&lt;br /&gt;
 -8-11 = sus4&lt;br /&gt;
+&lt;br /&gt;
+edo: D * * * E * F * * * G * * * A * * * B * C * * * D, 2 keys per #/b.&lt;br /&gt;
+chord components: P1 vm2 m2 vM2 M2 vm3 m3 vM3 M3 ^M3/vP4 P4 ^P4 A4/d5 vP5 P5 vm6 m6 vM6 M6 ^M6/vm7 m7 vM7 M7 ^M7&lt;br /&gt;
+chord roots: I v#I/vbII #I/bII vII II vbIII bIII vIII III ^III/vIV IV ^IV #IV/bV vV V ^#V/vbVI bVI vVI VI ^VI/vbVII bVII vVII VII ^VII/vI&lt;br /&gt;
+-5-14 = vm&lt;br /&gt;
+-6-14 = m&lt;br /&gt;
+-7-14 = vM&lt;br /&gt;
+-8-14 = M&lt;br /&gt;
+-9-14 = ^M&lt;br /&gt;
+-10-14 = sus4&lt;br /&gt;
 &lt;br /&gt;
 edo: D * * * * E * * F * * * * G * * * * A etc. 2 keys per #/b.&lt;br /&gt;
@@ Line 546: / Line 574: @@
 -10-18 = M&lt;br /&gt;
 -11-18 = ^M&lt;br /&gt;
--12-18 = sus-v4&lt;/body&gt;&lt;/html&gt;</pre></div>
+-12-18 = sus-v4&lt;br /&gt;
+&lt;br /&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:8:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc4"&gt;&lt;a name="Naming Chords-EDOs with inaccurate 3/2"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;&lt;u&gt;EDOs with inaccurate 3/2&lt;/u&gt;&lt;/h2&gt;
+ &lt;br /&gt;
+Such EDOs may be better notated with a notation not generated by the fifth.&lt;/body&gt;&lt;/html&gt;</pre></div>