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Kite's ups and downs notation: Difference between revisions

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VisualWikitext
Wikispaces>TallKite
**Imported revision 588455520 - Original comment: **
Wikispaces>TallKite
**Imported revision 588456270 - Original comment: **
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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
<h2>IMPORTED REVISION FROM WIKISPACES</h2>
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
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>2016-08-01 01:28:25 UTC</tt>.<br>
: This revision was by author [[User:TallKite|TallKite]] and made on <tt>2016-08-01 02:19:22 UTC</tt>.<br>
: The original revision id was <tt>588455520</tt>.<br>
: The original revision id was <tt>588456270</tt>.<br>
: The revision comment was: <tt></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>
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
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C Ebv G = C.vm = "C downminor" or "C dot downminor" (in perfect EDOs, C.v = "C dot down")
C Ebv G = C.vm = "C downminor" or "C dot downminor" (in perfect EDOs, C.v = "C dot down")
C Ebvv G = C.vvm = "C double-downminor" or "C dot double-downminor"
C Ebvv G = C.vvm = "C double-downminor" or "C dot double-downminor"
C Eb^ G = C.^m = "C upminor" or "C dot upminor' (in EDOs 10, 17, 24, 31, etc., C.~ = "C dot mid")
C Eb^ G = C.^m = "C upminor" or "C dot upminor" (in EDOs 10, 17, 24, 31, etc., C.~ = "C mid" or "C dot mid")
C Eb^^ G = C.^^m = "C double-upminor" or "C dot double-upminor" (in EDOs 20, 27, 34, 41, etc., C.~ = "C dot mid")
C Eb^^ G = C.^^m = "C double-upminor" or "C dot double-upminor" (in EDOs 20, 27, 34, 41, etc., C.~ = "C dot mid")


Line 364: Line 364:
C Ev Gv = C.v(v5) = "C dot down, down-five" (in certain EDOs, C.~(v5) = "C dot mid, down five")
C Ev Gv = C.v(v5) = "C dot down, down-five" (in certain EDOs, C.~(v5) = "C dot mid, down five")


C E G# = Caug = "C aug" (in perfect EDOs, C = "C" or "C perfect")
C E G# is Caug = "C aug" (in perfect EDOs, C = "C" or "C perfect")
C E G#v = Caug(v5) = "C aug down-five"
C E G#v = Caug(v5) = "C aug down-five"
C E G#^ = Caug(^5) = "C aug up-five"
C E G#^ = Caug(^5) = "C aug up-five"
C E^ G# = Caug(^3) = "C aug up-three" (note that here "up-three" means upmajor 3rd, not upminor 3rd)
C E^ G# is Caug(^3) = "C aug up-three" (note that here "up-three" means upmajor 3rd, not upminor 3rd)
C E^ G#^ = Caug(^3,^5) = "C aug up-three up-five"
C E^ G#^ = Caug(^3,^5) = "C aug up-three up-five"


Line 473: Line 473:
0-5-9 = D F^ A^ = D.^(^5) ("D dot up, up-five")
0-5-9 = D F^ A^ = D.^(^5) ("D dot up, up-five")


0-4-8-12 = D F A C = D7 ("D seven")
0-4-8-11 = D F A Cv = D(v7) = "D down-seven", or D F A B^ = D(^6) = "D up-six"
0-4-8-11 = D F A Cv = D(v7) ("D down-seven"), or D F A B^ = D(^6) = "D up-six"
0-3-8-11 = D Fv A Cv = D.v7 = "D dot down-seven"
0-3-8-11 = D Fv A Cv = D.v7 ("D dot down-seven")
0-5-8-11 = D F^ A B^ = D.^6 = "D dot up-six"
0-3-8-13 = D Fv A C^ = D.v(^7) ("D dot down up-seven")
0-5-8-11 = D F^ A Cv = D.^(v7) ("D dot up down-seven"), or more likely D F^ A B^ = D.^6 = "D dot up-six"




Line 489: Line 487:
0-5-9 = D F#v A = D.v = "D dot down" or "D downmajor"
0-5-9 = D F#v A = D.v = "D dot down" or "D downmajor"
0-6-9 = D F# A = D (or possibly D G A = Dsus4)
0-6-9 = D F# A = D (or possibly D G A = Dsus4)
0-6-9-12 = D F# A C = D7, or D F# A B = D6
0-6-9-12 = D F# A C = D7 = "D seven", or D F# A B = D6 = "D six"


16edo: D * E * * F * G * A * B * * C * D, 1 key per #/b, ups and downs not needed.
16edo: D * E * * F * G * A * B * * C * D, 1 key per #/b, ups and downs not needed.
Line 520: Line 518:
chord components: P1 m2 ~2 M2 m3 ~3 M3 P4 ^P4/d5 A4/vP5 P5 m6 ~6 M6 m7 ~7 M7
chord components: P1 m2 ~2 M2 m3 ~3 M3 P4 ^P4/d5 A4/vP5 P5 m6 ~6 M6 m7 ~7 M7
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
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
0-4-10 = D F A = Dm = "D minor"
0-4-10 = D F A = Dm = "D minor"
0-5-10 = D F^ A = D.~ = "D dot mid"
0-5-10 = D F^ A = D.~ = "D dot mid"
0-6-10 = D F# A = D = "D" or "D major"
0-6-10 = D F# A = D = "D" or "D major"
 
0-5-10-14 = D F^ A C = D7(~3)
0-4-9 = D F Av = Dm(v5)
0-5-9 = D F^ Av = D.~(v5)
0-5-11 = D F^ A^ = D.~(^5)
0-6-11 = D F# A^ = D(v5)
 
0-4-10-14 = D F A C = Dm7
0-5-10-14 = D F^ A C = Dm7(~3), or D F#v A C = D7(~3)
0-4-10-15 = D F A C^ = Dm(~7)
0-4-10-15 = D F A C^ = Dm(~7)
0-5-10-15 = D F^ A C^ = D.~7
0-5-10-15 = D F^ A C^ = D.~7
0-6-10-15 = D F# A C^ = D(~7)
0-6-10-15 = D F# A C^ = D(~7)
0-6-10-16 = D F# A C# = DM7


19edo: D * * E * F * * G * * A * * B * C * * D, ups and downs 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 A5 m6 M6 d7 m7 M7 A7
chord components: P1 d2 m2 M2 d3 m3 M3 A3 P4 A4 d5 P5 A5 m6 M6 d7 m7 M7 A7
chord roots: I #I/bbII bII II #II/bbIII bIII III #III/bIV IV #IV bV V #V/bbVI bVI VI bbVII bVII VII #VII/bI
chord roots: I #I/bbII bII II #II/bbIII bIII III #III/bIV IV #IV bV V #V/bbVI bVI VI bbVII bVII VII #VII/bI
0-4-11 = D Fb A = D(d3) = "D dim-three" (dim 3rd, perfect 5th)
0-4-11 = D Fb A = D(bb3) = "D dim-three" (dim 3rd, perfect 5th = approx. 6:7:9)
0-4-10 = D Fb Ab = Ddim(d3) = "D dim dim-three"
0-4-10 = D Fb Ab = Ddim(bb3) = "D dim dim-three"
0-5-11 = D F A = Dm = "D minor"
0-7-11 = D F## A = D(#3) = "D aug-three" (aug 3rd, perfect 5th)
0-5-10 = D F Ab = Ddim (conventional dim chord)
0-7-12 = D F## A# = Daug(#3) = "D aug aug-three"
0-6-11 = D F# A = D (major)
0-5-10-15 = D F Ab Cb = Ddim7 = "D dim-seven"
0-7-11 = D F## A = D(A3) (aug 3rd, perfect 5th)
0-6-11-15 = D F# A Cb = D(bb7) = "D add dim-seven"? (approx. 4:5:6:7)
0-6-12 = D F# A# = Daug (conventional aug chord)
0-7-12 = D F## A# = Daug(A3)
0-8-11 = D G A = Dsus4


21edo: D * * E * * F * * G * * A * * B * * C * * D, zero keys per #/b.
21edo: D * * E * * F * * G * * A * * B * * C * * D, zero keys per #/b.
Line 554: Line 540:
chord components: 1 ^1/vv2 v2 2 ^2 v3 3 ^3 v4 4 ^4 v5 5 ^5 v6 6 ^6 v7 7 ^7 ^^7/v8
chord components: 1 ^1/vv2 v2 2 ^2 v3 3 ^3 v4 4 ^4 v5 5 ^5 v6 6 ^6 v7 7 ^7 ^^7/v8
chord roots: I ^I vII II ^II vIII III vIII vIV IV ^IV vV V ^V vVI VI ^VI vVII VII ^VII vI
chord roots: I ^I vII II ^II vIII III vIII vIV IV ^IV vV V ^V vVI VI ^VI vVII VII ^VII vI
 
0-4-12 = D Fvv A = D.vv = "D dot double-down", or D E^ A = Dsus^2 = "D sus up-two"
0-3-12 = D E A = Dsus2
0-5-12 = D Fv A = D.v = "D dot down"
0-4-12 = D Fvv A = D.vv, or D E^ A = Dsus^2
0-6-12 = D F A = D = "D" or "D perfect"
0-5-12 = D Fv A = D.v ("D dot down")
0-7-12 = D F^ A = D.^ = "D dot up" (approx. 4:5:6)
0-6-12 = D F A = D ("D" or "D perfect")
0-8-12 = D F^^ A = D.^^ = "D dot double-up", or D Gv A = Dsusv4 = "D sus down-four"
0-7-12 = D F^ A = D.^ ("D dot up")
0-7-12-17 = D F^ A Cv = D.^(v7) = "D dot up down-seven" (approx. 4:5:6:7)
0-8-12 = D F^^ A = D.^^, or D Gv A = Dsusv4
0-9-12 = D G A = Dsus4
 
0-5-11 = D Fv Av = D.v(v5)
0-6-11 = D F Av = D(v5)
0-6-13 = D F A^ = D(^5)
0-7-13 = D F^ A^ = D.^(^5)
 
0-6-12-18 = D F A C = D7
0-7-12-18 = D F^ A C = D7(^3)
0-6-12-19 = D F A C^ = D7(^7)
0-7-12-19 = D F^ A C^ = D.^7
0-7-12-17 = D F^ A Cv = D.^(v7)
0-5-12-19 = D Fv A C^ = D.v(^7)
 
0-6-12-15 = D F A B = D6
0-7-12-15 = D F^ A B = D6(^3)
0-7-12-16 = D F^ A B^ = D.^6
0-7-12-14 = D F^ A Bv = D.^(v6)


24edo: D * * * E * F * * * G * * * A * * * B * C * * * D, 2 keys per #/b.
24edo: D * * * E * F * * * G * * * A * * * B * C * * * D, 2 keys per #/b.
chord components: P1 vm2 m2 ~2 M2 vm3 m3 ~3 M3 ^M3/vP4 P4 ^P4 A4/d5 vP5 P5 vm6 m6 ~6 M6 ^M6/vm7 m7 ~7 M7 ^M7
chord components: P1 vm2 m2 ~2 M2 vm3 m3 ~3 M3 ^M3/vP4 P4 ^P4 A4/d5 vP5 P5 vm6 m6 ~6 M6 ^M6/vm7 m7 ~7 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
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 = D Fv A = D.vm
0-5-14 = D Fv A = D.vm = "D downminor"
0-6-14 = D F A = Dm
0-6-14 = D F A = Dm = "D minor"
0-7-14 = D F^ A = D~
0-7-14 = D F^ A = D.~ = "D dot mid"
0-8-14 = D F# A = D (major)
0-8-14 = D F# A = D = "D" or "D major"
0-9-14 = D F#^ A = D.^
0-9-14 = D F#^ A = D.^ = "D dot up" or "D upmajor"
0-10-14 = D G A = Dsus4


31edo: D * * * * E * * F * * * * G * * * * A etc. 2 keys per #/b.
31edo: D * * * * E * * F * * * * G * * * * A etc. 2 keys per #/b.
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P1 ^P1 vm2 m2 ^m2 ~2 vM2 M2 ^M2 vm3 m3 ^m3 ~3 vM3 M3 ^M3 vP4 P4 ^P4 vd5 d5 A4/^d5 ^A4/vvP5 vP5 P5 etc.
P1 ^P1 vm2 m2 ^m2 ~2 vM2 M2 ^M2 vm3 m3 ^m3 ~3 vM3 M3 ^M3 vP4 P4 ^P4 vd5 d5 A4/^d5 ^A4/vvP5 vP5 P5 etc.
I ^I vbII bII ^bII vvII vII II ^II vbIII bIII ^bIII vvIII vIII III ^III vIV IV ^IV vbV bV #IV ^#IV vV V etc.
I ^I vbII bII ^bII vvII vII II ^II vbIII bIII ^bIII vvIII vIII III ^III vIV IV ^IV vbV bV #IV ^#IV vV V etc.
0-7-24 = D E A = Dsus2
0-10-20 = D F Ab = Ddim = "D dim"
0-8-24 = D E^ A = Dsus^2
0-10-21 = D F Ab^ = Ddim(^5) = "D dim up-five"
0-9-24 = D Fv A = D.vm
0-10-22 = D F Avv = Dm(vv5) = "D minor double-down five"
0-10-24 = D F A = Dm
0-10-23 = D F Av = Dm(v5) = "D minor down-five"
0-11-24 = D F^ A = D.^m
0-14-25 = D F# A^ = D(^5) = "D up-five"
0-12-24 = D F^^ A = D.~
0-14-26 = D F# A^^ = D(^^5) = "D double-up-five"
0-13-24 = D F#v A = D.v
0-14-27 = D F# A#v = Daug(v5) = "D aug down-five"
0-14-24 = D F# A = D (major)
0-14-28 = D F# A# = Daug = "D aug"
0-15-24 = D F#^ A = D.^
0-16-24 = D Gv A = Dsusv4
0-17-24 = D G A = Dsus4
 
0-10-20 = D F Ab = Ddim
0-10-21 = D F Ab^ = Ddim(^5) or Dm(^b5)
0-10-22 = D F Avv = Dm(vv5)
0-10-23 = D F Av = Dm(v5)
0-14-25 = D F# A^ = D(^5) ("D up-five")
0-14-26 = D F# A^^ = D(^^5) ("D double-up-five")
0-14-27 = D F# A#v = Daug(v5) or D(v#5)
0-14-28 = D F# A# = Daug




Line 1,655: Line 1,609:
C Ebv G = C.vm = &amp;quot;C downminor&amp;quot; or &amp;quot;C dot downminor&amp;quot; (in perfect EDOs, C.v = &amp;quot;C dot down&amp;quot;)&lt;br /&gt;
C Ebv G = C.vm = &amp;quot;C downminor&amp;quot; or &amp;quot;C dot downminor&amp;quot; (in perfect EDOs, C.v = &amp;quot;C dot down&amp;quot;)&lt;br /&gt;
C Ebvv G = C.vvm = &amp;quot;C double-downminor&amp;quot; or &amp;quot;C dot double-downminor&amp;quot;&lt;br /&gt;
C Ebvv G = C.vvm = &amp;quot;C double-downminor&amp;quot; or &amp;quot;C dot double-downminor&amp;quot;&lt;br /&gt;
C Eb^ G = C.^m = &amp;quot;C upminor&amp;quot; or &amp;quot;C dot upminor' (in EDOs 10, 17, 24, 31, etc., C.~ = &amp;quot;C dot mid&amp;quot;)&lt;br /&gt;
C Eb^ G = C.^m = &amp;quot;C upminor&amp;quot; or &amp;quot;C dot upminor&amp;quot; (in EDOs 10, 17, 24, 31, etc., C.~ = &amp;quot;C mid&amp;quot; or &amp;quot;C dot mid&amp;quot;)&lt;br /&gt;
C Eb^^ G = C.^^m = &amp;quot;C double-upminor&amp;quot; or &amp;quot;C dot double-upminor&amp;quot; (in EDOs 20, 27, 34, 41, etc., C.~ = &amp;quot;C dot mid&amp;quot;)&lt;br /&gt;
C Eb^^ G = C.^^m = &amp;quot;C double-upminor&amp;quot; or &amp;quot;C dot double-upminor&amp;quot; (in EDOs 20, 27, 34, 41, etc., C.~ = &amp;quot;C dot mid&amp;quot;)&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Line 1,683: Line 1,637:
C Ev Gv = C.v(v5) = &amp;quot;C dot down, down-five&amp;quot; (in certain EDOs, C.~(v5) = &amp;quot;C dot mid, down five&amp;quot;)&lt;br /&gt;
C Ev Gv = C.v(v5) = &amp;quot;C dot down, down-five&amp;quot; (in certain EDOs, C.~(v5) = &amp;quot;C dot mid, down five&amp;quot;)&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
C E G# &lt;!-- ws:start:WikiTextHeadingRule:16:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc8"&gt;&lt;a name="Caug"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:16 --&gt; Caug &lt;/h1&gt;
C E G# is Caug = &amp;quot;C aug&amp;quot; (in perfect EDOs, C = &amp;quot;C&amp;quot; or &amp;quot;C perfect&amp;quot;)&lt;br /&gt;
&amp;quot;C aug&amp;quot; (in perfect EDOs, C = &amp;quot;C&amp;quot; or &amp;quot;C perfect&amp;quot;)&lt;br /&gt;
C E G#v = Caug(v5) = &amp;quot;C aug down-five&amp;quot;&lt;br /&gt;
C E G#v = Caug(v5) = &amp;quot;C aug down-five&amp;quot;&lt;br /&gt;
C E G#^ = Caug(^5) = &amp;quot;C aug up-five&amp;quot;&lt;br /&gt;
C E G#^ = Caug(^5) = &amp;quot;C aug up-five&amp;quot;&lt;br /&gt;
C E^ G# &lt;!-- ws:start:WikiTextHeadingRule:18:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc9"&gt;&lt;a name="Caug(^3)"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:18 --&gt; Caug(^3) &lt;/h1&gt;
C E^ G# is Caug(^3) = &amp;quot;C aug up-three&amp;quot; (note that here &amp;quot;up-three&amp;quot; means upmajor 3rd, not upminor 3rd)&lt;br /&gt;
&amp;quot;C aug up-three&amp;quot; (note that here &amp;quot;up-three&amp;quot; means upmajor 3rd, not upminor 3rd)&lt;br /&gt;
C E^ G#^ = Caug(^3,^5) = &amp;quot;C aug up-three up-five&amp;quot;&lt;br /&gt;
C E^ G#^ = Caug(^3,^5) = &amp;quot;C aug up-three up-five&amp;quot;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Line 1,794: Line 1,746:
0-5-9 = D F^ A^ = D.^(^5) (&amp;quot;D dot up, up-five&amp;quot;)&lt;br /&gt;
0-5-9 = D F^ A^ = D.^(^5) (&amp;quot;D dot up, up-five&amp;quot;)&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
0-4-8-12 = D F A C = D7 (&amp;quot;D seven&amp;quot;)&lt;br /&gt;
0-4-8-11 = D F A Cv = D(v7) = &amp;quot;D down-seven&amp;quot;, or D F A B^ = D(^6) = &amp;quot;D up-six&amp;quot;&lt;br /&gt;
0-4-8-11 = D F A Cv = D(v7) (&amp;quot;D down-seven&amp;quot;), or D F A B^ = D(^6) = &amp;quot;D up-six&amp;quot;&lt;br /&gt;
0-3-8-11 = D Fv A Cv = D.v7 = &amp;quot;D dot down-seven&amp;quot;&lt;br /&gt;
0-3-8-11 = D Fv A Cv = D.v7 (&amp;quot;D dot down-seven&amp;quot;)&lt;br /&gt;
0-5-8-11 = D F^ A B^ = D.^6 = &amp;quot;D dot up-six&amp;quot;&lt;br /&gt;
0-3-8-13 = D Fv A C^ = D.v(^7) (&amp;quot;D dot down up-seven&amp;quot;)&lt;br /&gt;
0-5-8-11 = D F^ A Cv = D.^(v7) (&amp;quot;D dot up down-seven&amp;quot;), or more likely D F^ A B^ = D.^6 = &amp;quot;D dot up-six&amp;quot;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Line 1,810: Line 1,760:
0-5-9 = D F#v A = D.v = &amp;quot;D dot down&amp;quot; or &amp;quot;D downmajor&amp;quot;&lt;br /&gt;
0-5-9 = D F#v A = D.v = &amp;quot;D dot down&amp;quot; or &amp;quot;D downmajor&amp;quot;&lt;br /&gt;
0-6-9 = D F# A = D (or possibly D G A = Dsus4)&lt;br /&gt;
0-6-9 = D F# A = D (or possibly D G A = Dsus4)&lt;br /&gt;
0-6-9-12 = D F# A C = D7, or D F# A B = D6&lt;br /&gt;
0-6-9-12 = D F# A C = D7 = &amp;quot;D seven&amp;quot;, or D F# A B = D6 = &amp;quot;D six&amp;quot;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
16edo: D * E * * F * G * A * B * * C * D, 1 key per #/b, ups and downs not needed.&lt;br /&gt;
16edo: D * E * * F * G * A * B * * C * D, 1 key per #/b, ups and downs not needed.&lt;br /&gt;
Line 1,841: Line 1,791:
chord components: P1 m2 ~2 M2 m3 ~3 M3 P4 ^P4/d5 A4/vP5 P5 m6 ~6 M6 m7 ~7 M7&lt;br /&gt;
chord components: P1 m2 ~2 M2 m3 ~3 M3 P4 ^P4/d5 A4/vP5 P5 m6 ~6 M6 m7 ~7 M7&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;
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;
&lt;br /&gt;
0-4-10 = D F A = Dm = &amp;quot;D minor&amp;quot;&lt;br /&gt;
0-4-10 = D F A = Dm = &amp;quot;D minor&amp;quot;&lt;br /&gt;
0-5-10 = D F^ A = D.~ = &amp;quot;D dot mid&amp;quot;&lt;br /&gt;
0-5-10 = D F^ A = D.~ = &amp;quot;D dot mid&amp;quot;&lt;br /&gt;
0-6-10 = D F# A = D = &amp;quot;D&amp;quot; or &amp;quot;D major&amp;quot;&lt;br /&gt;
0-6-10 = D F# A = D = &amp;quot;D&amp;quot; or &amp;quot;D major&amp;quot;&lt;br /&gt;
&lt;br /&gt;
0-5-10-14 = D F^ A C = D7(~3)&lt;br /&gt;
0-4-9 = D F Av = Dm(v5)&lt;br /&gt;
0-5-9 = D F^ Av = D.~(v5)&lt;br /&gt;
0-5-11 = D F^ A^ = D.~(^5)&lt;br /&gt;
0-6-11 = D F# A^ = D(v5)&lt;br /&gt;
&lt;br /&gt;
0-4-10-14 = D F A C = Dm7&lt;br /&gt;
0-5-10-14 = D F^ A C = Dm7(~3), or D F#v A C = D7(~3)&lt;br /&gt;
0-4-10-15 = D F A C^ = Dm(~7)&lt;br /&gt;
0-4-10-15 = D F A C^ = Dm(~7)&lt;br /&gt;
0-5-10-15 = D F^ A C^ = D.~7&lt;br /&gt;
0-5-10-15 = D F^ A C^ = D.~7&lt;br /&gt;
0-6-10-15 = D F# A C^ = D(~7)&lt;br /&gt;
0-6-10-15 = D F# A C^ = D(~7)&lt;br /&gt;
0-6-10-16 = D F# A C# = DM7&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
19edo: D * * E * F * * G * * A * * B * C * * D, ups and downs not needed.&lt;br /&gt;
19edo: 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 A5 m6 M6 d7 m7 M7 A7&lt;br /&gt;
chord components: P1 d2 m2 M2 d3 m3 M3 A3 P4 A4 d5 P5 A5 m6 M6 d7 m7 M7 A7&lt;br /&gt;
chord roots: I #I/bbII bII II #II/bbIII bIII III #III/bIV IV #IV bV V #V/bbVI bVI VI bbVII bVII VII #VII/bI&lt;br /&gt;
chord roots: I #I/bbII bII II #II/bbIII bIII III #III/bIV IV #IV bV V #V/bbVI bVI VI bbVII bVII VII #VII/bI&lt;br /&gt;
0-4-11 = D Fb A = D(d3) = &amp;quot;D dim-three&amp;quot; (dim 3rd, perfect 5th)&lt;br /&gt;
0-4-11 = D Fb A = D(bb3) = &amp;quot;D dim-three&amp;quot; (dim 3rd, perfect 5th = approx. 6:7:9)&lt;br /&gt;
0-4-10 = D Fb Ab = Ddim(d3) = &amp;quot;D dim dim-three&amp;quot;&lt;br /&gt;
0-4-10 = D Fb Ab = Ddim(bb3) = &amp;quot;D dim dim-three&amp;quot;&lt;br /&gt;
0-5-11 = D F A = Dm = &amp;quot;D minor&amp;quot;&lt;br /&gt;
0-7-11 = D F## A = D(#3) = &amp;quot;D aug-three&amp;quot; (aug 3rd, perfect 5th)&lt;br /&gt;
0-5-10 = D F Ab = Ddim (conventional dim chord)&lt;br /&gt;
0-7-12 = D F## A#  &lt;!-- ws:start:WikiTextHeadingRule:16:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc8"&gt;&lt;a name="Daug(#3)"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:16 --&gt; Daug(#3) &lt;/h1&gt;
0-6-11 = D F# A = D (major)&lt;br /&gt;
&amp;quot;D aug aug-three&amp;quot;&lt;br /&gt;
0-7-11 = D F## A = D(A3) (aug 3rd, perfect 5th)&lt;br /&gt;
0-5-10-15 = D F Ab Cb = Ddim7 = &amp;quot;D dim-seven&amp;quot;&lt;br /&gt;
0-6-12 = D F# A# = Daug (conventional aug chord)&lt;br /&gt;
0-6-11-15 = D F# A Cb = D(bb7) = &amp;quot;D add dim-seven&amp;quot;? (approx. 4:5:6:7)&lt;br /&gt;
0-7-12 = D F## A# = Daug(A3)&lt;br /&gt;
0-8-11 = D G A = Dsus4&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
21edo: D * * E * * F * * G * * A * * B * * C * * D, zero keys per #/b.&lt;br /&gt;
21edo: D * * E * * F * * G * * A * * B * * C * * D, zero keys per #/b.&lt;br /&gt;
Line 1,875: Line 1,814:
chord components: 1 ^1/vv2 v2 2 ^2 v3 3 ^3 v4 4 ^4 v5 5 ^5 v6 6 ^6 v7 7 ^7 ^^7/v8&lt;br /&gt;
chord components: 1 ^1/vv2 v2 2 ^2 v3 3 ^3 v4 4 ^4 v5 5 ^5 v6 6 ^6 v7 7 ^7 ^^7/v8&lt;br /&gt;
chord roots: I ^I vII II ^II vIII III vIII vIV IV ^IV vV V ^V vVI VI ^VI vVII VII ^VII vI&lt;br /&gt;
chord roots: I ^I vII II ^II vIII III vIII vIV IV ^IV vV V ^V vVI VI ^VI vVII VII ^VII vI&lt;br /&gt;
&lt;br /&gt;
0-4-12 = D Fvv A = D.vv = &amp;quot;D dot double-down&amp;quot;, or D E^ A = Dsus^2 = &amp;quot;D sus up-two&amp;quot;&lt;br /&gt;
0-3-12 = D E A = Dsus2&lt;br /&gt;
0-5-12 = D Fv A = D.v = &amp;quot;D dot down&amp;quot;&lt;br /&gt;
0-4-12 = D Fvv A = D.vv, or D E^ A = Dsus^2&lt;br /&gt;
0-6-12 = D F A = D = &amp;quot;D&amp;quot; or &amp;quot;D perfect&amp;quot;&lt;br /&gt;
0-5-12 = D Fv A = D.v (&amp;quot;D dot down&amp;quot;)&lt;br /&gt;
0-7-12 = D F^ A = D.^ = &amp;quot;D dot up&amp;quot; (approx. 4:5:6)&lt;br /&gt;
0-6-12 = D F A = D (&amp;quot;D&amp;quot; or &amp;quot;D perfect&amp;quot;)&lt;br /&gt;
0-8-12 = D F^^ A = D.^^ = &amp;quot;D dot double-up&amp;quot;, or D Gv A = Dsusv4 = &amp;quot;D sus down-four&amp;quot;&lt;br /&gt;
0-7-12 = D F^ A = D.^ (&amp;quot;D dot up&amp;quot;)&lt;br /&gt;
0-7-12-17 = D F^ A Cv = D.^(v7) = &amp;quot;D dot up down-seven&amp;quot; (approx. 4:5:6:7)&lt;br /&gt;
0-8-12 = D F^^ A = D.^^, or D Gv A = Dsusv4&lt;br /&gt;
0-9-12 = D G A = Dsus4&lt;br /&gt;
&lt;br /&gt;
0-5-11 = D Fv Av = D.v(v5)&lt;br /&gt;
0-6-11 = D F Av = D(v5)&lt;br /&gt;
0-6-13 = D F A^ = D(^5)&lt;br /&gt;
0-7-13 = D F^ A^ = D.^(^5)&lt;br /&gt;
&lt;br /&gt;
0-6-12-18 = D F A C = D7&lt;br /&gt;
0-7-12-18 = D F^ A C = D7(^3)&lt;br /&gt;
0-6-12-19 = D F A C^ = D7(^7)&lt;br /&gt;
0-7-12-19 = D F^ A C^ = D.^7&lt;br /&gt;
0-7-12-17 = D F^ A Cv = D.^(v7)&lt;br /&gt;
0-5-12-19 = D Fv A C^ = D.v(^7)&lt;br /&gt;
&lt;br /&gt;
0-6-12-15 = D F A B = D6&lt;br /&gt;
0-7-12-15 = D F^ A B = D6(^3)&lt;br /&gt;
0-7-12-16 = D F^ A B^ = D.^6&lt;br /&gt;
0-7-12-14 = D F^ A Bv = D.^(v6)&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
24edo: D * * * E * F * * * G * * * A * * * B * C * * * D, 2 keys per #/b.&lt;br /&gt;
24edo: D * * * E * F * * * G * * * A * * * B * C * * * D, 2 keys per #/b.&lt;br /&gt;
chord components: P1 vm2 m2 ~2 M2 vm3 m3 ~3 M3 ^M3/vP4 P4 ^P4 A4/d5 vP5 P5 vm6 m6 ~6 M6 ^M6/vm7 m7 ~7 M7 ^M7&lt;br /&gt;
chord components: P1 vm2 m2 ~2 M2 vm3 m3 ~3 M3 ^M3/vP4 P4 ^P4 A4/d5 vP5 P5 vm6 m6 ~6 M6 ^M6/vm7 m7 ~7 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;
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;
0-5-14 = D Fv A = D.vm&lt;br /&gt;
0-5-14 = D Fv A = D.vm = &amp;quot;D downminor&amp;quot;&lt;br /&gt;
0-6-14 = D F A = Dm&lt;br /&gt;
0-6-14 = D F A = Dm = &amp;quot;D minor&amp;quot;&lt;br /&gt;
0-7-14 = D F^ A = D~&lt;br /&gt;
0-7-14 = D F^ A = D.~ = &amp;quot;D dot mid&amp;quot;&lt;br /&gt;
0-8-14 = D F# A = D (major)&lt;br /&gt;
0-8-14 = D F# A = D = &amp;quot;D&amp;quot; or &amp;quot;D major&amp;quot;&lt;br /&gt;
0-9-14 = D F#^ A = D.^&lt;br /&gt;
0-9-14 = D F#^ A = D.^ = &amp;quot;D dot up&amp;quot; or &amp;quot;D upmajor&amp;quot;&lt;br /&gt;
0-10-14 = D G A = Dsus4&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
31edo: D * * * * E * * F * * * * G * * * * A etc. 2 keys per #/b.&lt;br /&gt;
31edo: D * * * * E * * F * * * * G * * * * A etc. 2 keys per #/b.&lt;br /&gt;
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P1 ^P1 vm2 m2 ^m2 ~2 vM2 M2 ^M2 vm3 m3 ^m3 ~3 vM3 M3 ^M3 vP4 P4 ^P4 vd5 d5 A4/^d5 ^A4/vvP5 vP5 P5 etc.&lt;br /&gt;
P1 ^P1 vm2 m2 ^m2 ~2 vM2 M2 ^M2 vm3 m3 ^m3 ~3 vM3 M3 ^M3 vP4 P4 ^P4 vd5 d5 A4/^d5 ^A4/vvP5 vP5 P5 etc.&lt;br /&gt;
I ^I vbII bII ^bII vvII vII II ^II vbIII bIII ^bIII vvIII vIII III ^III vIV IV ^IV vbV bV #IV ^#IV vV V etc.&lt;br /&gt;
I ^I vbII bII ^bII vvII vII II ^II vbIII bIII ^bIII vvIII vIII III ^III vIV IV ^IV vbV bV #IV ^#IV vV V etc.&lt;br /&gt;
0-7-24 = D E A = Dsus2&lt;br /&gt;
0-10-20 = D F Ab = Ddim = &amp;quot;D dim&amp;quot;&lt;br /&gt;
0-8-24 = D E^ A = Dsus^2&lt;br /&gt;
0-10-21 = D F Ab^ = Ddim(^5) = &amp;quot;D dim up-five&amp;quot;&lt;br /&gt;
0-9-24 = D Fv A = D.vm&lt;br /&gt;
0-10-22 = D F Avv = Dm(vv5) = &amp;quot;D minor double-down five&amp;quot;&lt;br /&gt;
0-10-24 = D F A = Dm&lt;br /&gt;
0-10-23 = D F Av = Dm(v5) = &amp;quot;D minor down-five&amp;quot;&lt;br /&gt;
0-11-24 = D F^ A = D.^m&lt;br /&gt;
0-14-25 = D F# A^ = D(^5) = &amp;quot;D up-five&amp;quot;&lt;br /&gt;
0-12-24 = D F^^ A = D.~&lt;br /&gt;
0-14-26 = D F# A^^ = D(^^5) = &amp;quot;D double-up-five&amp;quot;&lt;br /&gt;
0-13-24 = D F#v A = D.v&lt;br /&gt;
0-14-27 = D F# A#v = Daug(v5) = &amp;quot;D aug down-five&amp;quot;&lt;br /&gt;
0-14-24 = D F# A = D (major)&lt;br /&gt;
0-14-28 = D F# A# &lt;!-- ws:start:WikiTextHeadingRule:18:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc9"&gt;&lt;a name="Daug"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:18 --&gt; Daug &lt;/h1&gt;
0-15-24 = D F#^ A = D.^&lt;br /&gt;
&amp;quot;D aug&amp;quot;&lt;br /&gt;
0-16-24 = D Gv A = Dsusv4&lt;br /&gt;
0-17-24 = D G A = Dsus4&lt;br /&gt;
&lt;br /&gt;
0-10-20 = D F Ab = Ddim&lt;br /&gt;
0-10-21 = D F Ab^ = Ddim(^5) or Dm(^b5)&lt;br /&gt;
0-10-22 = D F Avv = Dm(vv5)&lt;br /&gt;
0-10-23 = D F Av = Dm(v5)&lt;br /&gt;
0-14-25 = D F# A^ = D(^5) (&amp;quot;D up-five&amp;quot;)&lt;br /&gt;
0-14-26 = D F# A^^ = D(^^5) (&amp;quot;D double-up-five&amp;quot;)&lt;br /&gt;
0-14-27 = D F# A#v = Daug(v5) or D(v#5)&lt;br /&gt;
0-14-28 = D F# A# = Daug&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:20:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc10"&gt;&lt;a name="Caug(^3)-Cross-EDO considerations"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:20 --&gt;&lt;strong&gt;&lt;u&gt;Cross-EDO considerations&lt;/u&gt;&lt;/strong&gt;&lt;/h2&gt;
&lt;!-- ws:start:WikiTextHeadingRule:20:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc10"&gt;&lt;a name="Daug-Cross-EDO considerations"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:20 --&gt;&lt;strong&gt;&lt;u&gt;Cross-EDO considerations&lt;/u&gt;&lt;/strong&gt;&lt;/h2&gt;
  &lt;br /&gt;
  &lt;br /&gt;
In 22edo, the major chord is 0-8-13 = 0¢-436¢-709¢. In 19edo, it's 0-6-11 = 0¢-379¢-695¢. The two chords sound quite different, because &amp;quot;major 3rd&amp;quot; is defined only in terms of the fifth, not in terms of what JI ratios it approximates. To describe the sound of the chord, color notation can be used. 22edo major chords sound red and 19edo major chords sound yellow.&lt;br /&gt;
In 22edo, the major chord is 0-8-13 = 0¢-436¢-709¢. In 19edo, it's 0-6-11 = 0¢-379¢-695¢. The two chords sound quite different, because &amp;quot;major 3rd&amp;quot; is defined only in terms of the fifth, not in terms of what JI ratios it approximates. To describe the sound of the chord, color notation can be used. 22edo major chords sound red and 19edo major chords sound yellow.&lt;br /&gt;
Line 1,958: Line 1,866:
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:22:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc11"&gt;&lt;a name="Caug(^3)-EDOs with an inaccurate 3/2"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:22 --&gt;&lt;u&gt;EDOs with an inaccurate 3/2&lt;/u&gt;&lt;/h2&gt;
&lt;!-- ws:start:WikiTextHeadingRule:22:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc11"&gt;&lt;a name="Daug-EDOs with an inaccurate 3/2"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:22 --&gt;&lt;u&gt;EDOs with an inaccurate 3/2&lt;/u&gt;&lt;/h2&gt;
  &lt;br /&gt;
  &lt;br /&gt;
Not counting the trivial edos 2, 3, 4 and 6, there are only seven such edos. As seen in the above diagram, they are the ones to the left of the heptatonic kite's spine, plus the ones to the right of the pentatonic kite's spine. The ones on the left edge of the heptatonic kite are the fourthward ones like 16edo, and have been dealt with already. 23edo can be notated similarly to 16edo by using a fifth of 13\23 instead of 14\23. That leaves only four edos: 8, 11, 13, and 18.&lt;br /&gt;
Not counting the trivial edos 2, 3, 4 and 6, there are only seven such edos. As seen in the above diagram, they are the ones to the left of the heptatonic kite's spine, plus the ones to the right of the pentatonic kite's spine. The ones on the left edge of the heptatonic kite are the fourthward ones like 16edo, and have been dealt with already. 23edo can be notated similarly to 16edo by using a fifth of 13\23 instead of 14\23. That leaves only four edos: 8, 11, 13, and 18.&lt;br /&gt;
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