Kite's ups and downs notation: Difference between revisions
Wikispaces>TallKite **Imported revision 588457424 - Original comment: ** |
Wikispaces>TallKite **Imported revision 588457914 - Original comment: ** |
||
| Line 1: | Line 1: | ||
<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 | : This revision was by author [[User:TallKite|TallKite]] and made on <tt>2016-08-01 04:46:20 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>588457914</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> | ||
| Line 340: | Line 340: | ||
C E G = C = "C" or "C major" (in perfect EDOs, "C" or "C perfect") | C E G = C = "C" or "C major" (in perfect EDOs, "C" or "C perfect") | ||
C Ev G = C.v = "C dot down" or "C downmajor" (in EDOs 10, 17, 24, 31, etc., C~ = "C | C Ev G = C.v = "C dot down" or "C downmajor" (in EDOs 10, 17, 24, 31, etc., C~ = "C mid") | ||
C Evv G = C.vv = "C dot double-down" or "C double-downmajor" (in EDOs 20, 27, 34, 41, etc., C | C Evv G = C.vv = "C dot double-down" or "C double-downmajor" (in EDOs 20, 27, 34, 41, etc., C~ = "C mid") | ||
C E^ G = C.^ = "C dot up" (not "C up", which would be C^ major = C^ E^ G^), or "C upmajor" | C E^ G = C.^ = "C dot up" (not "C up", which would be C^ major = C^ E^ G^), or "C upmajor" | ||
C E^^ G = C.^^ = "C dot double-up" or "C double-upmajor" | C E^^ G = C.^^ = "C dot double-up" or "C double-upmajor" | ||
| Line 349: | Line 349: | ||
C Fvv G = Csusvv4 = "C sus double-down four" | C Fvv G = Csusvv4 = "C sus double-down four" | ||
C D# G = Csus#2 = "C sus aug-two" | C D# G = Csus#2 = "C sus sharp-two" or "C sus aug-two" | ||
C Ebb G = C(bb3) = "C dim-three" | C Ebb G = C(bb3) = "C dim-three" | ||
C E# G = C(#3) = "C aug-three" | C E# G = C(#3) = "C sharp-three" or "C aug-three" | ||
C Fb G = Csusb4 = "C sus dim-four" | C Fb G = Csusb4 = "C sus flat-four" or "C sus dim-four" | ||
__**Altered fifths:**__ | __**Altered fifths:**__ | ||
| Line 358: | Line 358: | ||
C Eb Gbv = Cdim(v5) = "C dim down-five" | C Eb Gbv = Cdim(v5) = "C dim down-five" | ||
C Eb Gb^ = Cdim(^5) = "C dim up-five" | C Eb Gb^ = Cdim(^5) = "C dim up-five" | ||
C Eb^ Gb = Cdim(^3) = "C dim up-three" (in certain EDOs, C | C Eb^ Gb = Cdim(^3) = "C dim up-three" (in certain EDOs, C~(b5) = "C mid flat-five") | ||
(note that here "up-three" means upminor 3rd, not upmajor 3rd, because "dim" indicates a minor 3rd) | (note that here "up-three" means upminor 3rd, not upmajor 3rd, because "dim" indicates a minor 3rd) | ||
C Eb^ Gb^ = Cdim(^3,^5) = "C dim up-three up-five" (in certain EDOs, C | C Eb^ Gb^ = Cdim(^3,^5) = "C dim up-three up-five" (in certain EDOs, C~(^b5) = "C mid upflat-five") | ||
C Eb Gv = Cm(v5) = "C minor down-five" | C Eb Gv = Cm(v5) = "C minor down-five" | ||
| Line 367: | Line 367: | ||
C E G^ = C(^5) = "C up-five" | C E G^ = C(^5) = "C up-five" | ||
C E^ G^ = C.^(^5) = "C dot up, up-five" | C E^ G^ = C.^(^5) = "C dot up, up-five" | ||
C Ev Gv = C.v(v5) = "C dot down, down-five" (in certain EDOs, C | C Ev Gv = C.v(v5) = "C dot down, down-five" (in certain EDOs, C~(v5) = "C mid down-five") | ||
C E G# is 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") | ||
| Line 374: | Line 374: | ||
C E^ G# is 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" | ||
C E# G# is Caug(#3) | |||
C D# Gb = Csus#2(b5) = "C sus sharp-two, flat-five" | |||
C Ebb Gb = Cdim(bb3) = "C dim dim-three" | |||
C Eb G# is Cmin(#5) = "C minor sharp-five" | |||
C E# G# is Caug(#3) = "C aug sharp-three" | |||
C Fb G# is Caug,susb4 = "C aug sus flat-four" | |||
__**Seventh chords:**__ | __**Seventh chords:**__ | ||
| Line 380: | Line 385: | ||
C Ev G Bb = C7(v3) = "C seven down-three" (in certain EDOs, C7(~3) = "C seven mid-three") | C Ev G Bb = C7(v3) = "C seven down-three" (in certain EDOs, C7(~3) = "C seven mid-three") | ||
C E G Bbv = C(v7) = "C down-seven" (not "C-down seven", which would be Cv.7 = Cv Ev Gv Bbv) | C E G Bbv = C(v7) = "C down-seven" (not "C-down seven", which would be Cv.7 = Cv Ev Gv Bbv) | ||
C Ev G Bbv = C.v7 = "C dot down-seven" | C Ev G Bbv = C.v7 = "C dot down-seven" (in certain EDOs, C~(v7) = "C mid down-seven") | ||
C E Gv Bb = C7(v5) = "C seven down-five" | C E Gv Bb = C7(v5) = "C seven down-five" | ||
C Ev Gv Bb = C7(v3,v5) = "C seven down-three down-five" | C Ev Gv Bb = C7(v3,v5) = "C seven down-three down-five" | ||
| Line 414: | Line 419: | ||
C Eb^ Gb^ Bb^ = C.^m7(^b5) = "C dot upminor seven upflat-five" or "C half-dim up-three up-five up-seven" | C Eb^ Gb^ Bb^ = C.^m7(^b5) = "C dot upminor seven upflat-five" or "C half-dim up-three up-five up-seven" | ||
C E G B# | C E G B# is C(#7) = "C sharp-seven" (not "C aug-seven", that sounds like "C aug seven" = Caug7) | ||
C | C E G Cb = C(b8) = "C dim-eight" or "C flat-eight" | ||
__**Sixth chords:**__ | __**Sixth chords:**__ | ||
| Line 429: | Line 434: | ||
C Eb^ G A = Cm6(^3) = "C minor six up-three" (in certain EDOs, C6(~3) = "C six mid-three") | C Eb^ G A = Cm6(^3) = "C minor six up-three" (in certain EDOs, C6(~3) = "C six mid-three") | ||
C | C E G Ab = C(b6) = "C flat-six" (not "C minor-six" because that sounds like "C minor six" = Cm6) | ||
C E G A# is C(#6) = "C sharp-six" | |||
C E G A# | |||
| Line 490: | Line 493: | ||
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" | 0-5-8-11 = D F^ A B^ = D.^6 = "D dot up-six" | ||
15edo: 3 keys per #/b, so ups and downs are needed. | 15edo: 3 keys per #/b, so ups and downs are needed. | ||
| Line 496: | Line 498: | ||
chord components: P1 ^m2 vM2 M2/m3 ^m3 vM3 M3/P4 ^P4 vP5 P5 ^m6 vM6 M6/m7 ^m7 vM7 | chord components: P1 ^m2 vM2 M2/m3 ^m3 vM3 M3/P4 ^P4 vP5 P5 ^m6 vM6 M6/m7 ^m7 vM7 | ||
chord roots: I ^bII vII II/bIII ^bIII vIII III/IV ^IV vV V ^bVI vVI VI/bVII ^bVII vVII | chord roots: I ^bII vII II/bIII ^bIII vIII III/IV ^IV vV V ^bVI vVI VI/bVII ^bVII vVII | ||
0-3-9 = D F A = Dm = "D minor" (or possibly D E A = Dsus2) | 0-3-9 = D F A = Dm = "D minor" (or possibly D E A = Dsus2) | ||
0-4-9 = D F^ A = D.^m = "D (dot) upminor" | 0-4-9 = D F^ A = D.^m = "D (dot) upminor" | ||
| Line 533: | Line 534: | ||
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 | 0-5-10 = D F^ A = D~ = "D 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) | 0-5-10-14 = D F^ A C = D7(~3) = "D seven mid-three" | ||
0-4-10-15 = D F A C^ = Dm(~7) | 0-4-10-15 = D F A C^ = Dm(~7) = "D minor mid-seven" | ||
0-5-10-15 = D F^ A C^ = D.~7 | 0-5-10-15 = D F^ A C^ = D.~7 = "D dot mid seven" | ||
0-6-10-15 = D F# A C^ = D(~7) | 0-6-10-15 = D F# A C^ = D(~7) = "D mid-seven" | ||
18edo: | 18edo: | ||
| Line 1,409: | Line 1,410: | ||
This is in addition to the trivial EDOs, 1, 2, 3, 4 and 6, which can be notated with standard notation as a subset of 12-EDO. The fifth is defined as the nearest approximation to 3/2. There is a little leeway to this in certain EDOs like 18 which have two possible fifths with nearly equal accuracy.<br /> | This is in addition to the trivial EDOs, 1, 2, 3, 4 and 6, which can be notated with standard notation as a subset of 12-EDO. The fifth is defined as the nearest approximation to 3/2. There is a little leeway to this in certain EDOs like 18 which have two possible fifths with nearly equal accuracy.<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextLocalImageRule: | <!-- ws:start:WikiTextLocalImageRule:4050:&lt;img src=&quot;/file/view/The%20fifth%20of%20EDOs%205-53.png/570450231/800x1035/The%20fifth%20of%20EDOs%205-53.png&quot; alt=&quot;&quot; title=&quot;&quot; style=&quot;height: 1035px; width: 800px;&quot; /&gt; --><img src="/file/view/The%20fifth%20of%20EDOs%205-53.png/570450231/800x1035/The%20fifth%20of%20EDOs%205-53.png" alt="The fifth of EDOs 5-53.png" title="The fifth of EDOs 5-53.png" style="height: 1035px; width: 800px;" /><!-- ws:end:WikiTextLocalImageRule:4050 --><br /> | ||
The above diagram is actually a section of the Stern-Brocot tree. The tree usually has ratios, not octave fractions (i.e. 4/7, not 4\7 as above). Also it's usually arranged vertically with nodes of the same &quot;generation&quot; occurring at the same height. For example, 5\9 and 7\12 are both children of 4\7, and would usually be level with each other. Here the nodes are arranged vertically by denominator, i.e., the EDO itself. The colored regions of the tree are what I call <strong>kites</strong>, and this version of the Stern-Brocot tree I call the <strong>Tree of Kites</strong>. The heptatonic kite is blue and the pentatonic kite is orange. Every kite has a head (4\7 for the blue kite), a central spine (8\14, 12\21, etc.), a fifthward side on the right (7\12, 11\19, etc.) and a fourthward side on the left (5\9, 9\16, etc.). Every node on a spine is a <strong>spinal</strong> node. Every non-spinal node is part of three kites. It's the head of one kite and on the side of two others.<br /> | The above diagram is actually a section of the Stern-Brocot tree. The tree usually has ratios, not octave fractions (i.e. 4/7, not 4\7 as above). Also it's usually arranged vertically with nodes of the same &quot;generation&quot; occurring at the same height. For example, 5\9 and 7\12 are both children of 4\7, and would usually be level with each other. Here the nodes are arranged vertically by denominator, i.e., the EDO itself. The colored regions of the tree are what I call <strong>kites</strong>, and this version of the Stern-Brocot tree I call the <strong>Tree of Kites</strong>. The heptatonic kite is blue and the pentatonic kite is orange. Every kite has a head (4\7 for the blue kite), a central spine (8\14, 12\21, etc.), a fifthward side on the right (7\12, 11\19, etc.) and a fourthward side on the left (5\9, 9\16, etc.). Every node on a spine is a <strong>spinal</strong> node. Every non-spinal node is part of three kites. It's the head of one kite and on the side of two others.<br /> | ||
<br /> | <br /> | ||
| Line 1,625: | Line 1,626: | ||
<br /> | <br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextLocalImageRule: | <!-- ws:start:WikiTextLocalImageRule:4051:&lt;img src=&quot;/file/view/Tibia%20in%20G%20with%20%5Ev%2C%20rygb%201.jpg/570451171/800x1035/Tibia%20in%20G%20with%20%5Ev%2C%20rygb%201.jpg&quot; alt=&quot;&quot; title=&quot;&quot; style=&quot;height: 1035px; width: 800px;&quot; /&gt; --><img src="/file/view/Tibia%20in%20G%20with%20%5Ev%2C%20rygb%201.jpg/570451171/800x1035/Tibia%20in%20G%20with%20%5Ev%2C%20rygb%201.jpg" alt="Tibia in G with ^v, rygb 1.jpg" title="Tibia in G with ^v, rygb 1.jpg" style="height: 1035px; width: 800px;" /><!-- ws:end:WikiTextLocalImageRule:4051 --><br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:8:&lt;h2&gt; --><h2 id="toc4"><!-- ws:end:WikiTextHeadingRule:8 --><!-- ws:start:WikiTextLocalImageRule: | <!-- ws:start:WikiTextHeadingRule:8:&lt;h2&gt; --><h2 id="toc4"><!-- ws:end:WikiTextHeadingRule:8 --><!-- ws:start:WikiTextLocalImageRule:4052:&lt;img src=&quot;/file/view/Tibia%20in%20G%20with%20%5Ev%2C%20rygb%202.jpg/570451199/800x957/Tibia%20in%20G%20with%20%5Ev%2C%20rygb%202.jpg&quot; alt=&quot;&quot; title=&quot;&quot; style=&quot;height: 957px; width: 800px;&quot; /&gt; --><img src="/file/view/Tibia%20in%20G%20with%20%5Ev%2C%20rygb%202.jpg/570451199/800x957/Tibia%20in%20G%20with%20%5Ev%2C%20rygb%202.jpg" alt="Tibia in G with ^v, rygb 2.jpg" title="Tibia in G with ^v, rygb 2.jpg" style="height: 957px; width: 800px;" /><!-- ws:end:WikiTextLocalImageRule:4052 --></h2> | ||
<!-- ws:start:WikiTextHeadingRule:10:&lt;h2&gt; --><h2 id="toc5"><!-- ws:end:WikiTextHeadingRule:10 --> </h2> | <!-- ws:start:WikiTextHeadingRule:10:&lt;h2&gt; --><h2 id="toc5"><!-- ws:end:WikiTextHeadingRule:10 --> </h2> | ||
<!-- ws:start:WikiTextHeadingRule:12:&lt;h2&gt; --><h2 id="toc6"><!-- ws:end:WikiTextHeadingRule:12 --> </h2> | <!-- ws:start:WikiTextHeadingRule:12:&lt;h2&gt; --><h2 id="toc6"><!-- ws:end:WikiTextHeadingRule:12 --> </h2> | ||
| Line 1,652: | Line 1,653: | ||
<br /> | <br /> | ||
C E G = C = &quot;C&quot; or &quot;C major&quot; (in perfect EDOs, &quot;C&quot; or &quot;C perfect&quot;)<br /> | C E G = C = &quot;C&quot; or &quot;C major&quot; (in perfect EDOs, &quot;C&quot; or &quot;C perfect&quot;)<br /> | ||
C Ev G = C.v = &quot;C dot down&quot; or &quot;C downmajor&quot; (in EDOs 10, 17, 24, 31, etc., C~ = &quot;C | C Ev G = C.v = &quot;C dot down&quot; or &quot;C downmajor&quot; (in EDOs 10, 17, 24, 31, etc., C~ = &quot;C mid&quot;)<br /> | ||
C Evv G = C.vv = &quot;C dot double-down&quot; or &quot;C double-downmajor&quot; (in EDOs 20, 27, 34, 41, etc., C | C Evv G = C.vv = &quot;C dot double-down&quot; or &quot;C double-downmajor&quot; (in EDOs 20, 27, 34, 41, etc., C~ = &quot;C mid&quot;)<br /> | ||
C E^ G = C.^ = &quot;C dot up&quot; (not &quot;C up&quot;, which would be C^ major = C^ E^ G^), or &quot;C upmajor&quot;<br /> | C E^ G = C.^ = &quot;C dot up&quot; (not &quot;C up&quot;, which would be C^ major = C^ E^ G^), or &quot;C upmajor&quot;<br /> | ||
C E^^ G = C.^^ = &quot;C dot double-up&quot; or &quot;C double-upmajor&quot;<br /> | C E^^ G = C.^^ = &quot;C dot double-up&quot; or &quot;C double-upmajor&quot;<br /> | ||
| Line 1,661: | Line 1,662: | ||
C Fvv G = Csusvv4 = &quot;C sus double-down four&quot;<br /> | C Fvv G = Csusvv4 = &quot;C sus double-down four&quot;<br /> | ||
<br /> | <br /> | ||
C D# G = Csus#2 = &quot;C sus aug-two&quot;<br /> | C D# G = Csus#2 = &quot;C sus sharp-two&quot; or &quot;C sus aug-two&quot;<br /> | ||
C Ebb G = C(bb3) = &quot;C dim-three&quot;<br /> | C Ebb G = C(bb3) = &quot;C dim-three&quot;<br /> | ||
C E# G = C(#3) = &quot;C aug-three&quot;<br /> | C E# G = C(#3) = &quot;C sharp-three&quot; or &quot;C aug-three&quot;<br /> | ||
C Fb G = Csusb4 = &quot;C sus dim-four&quot;<br /> | C Fb G = Csusb4 = &quot;C sus flat-four&quot; or &quot;C sus dim-four&quot;<br /> | ||
<br /> | <br /> | ||
<u><strong>Altered fifths:</strong></u><br /> | <u><strong>Altered fifths:</strong></u><br /> | ||
| Line 1,670: | Line 1,671: | ||
C Eb Gbv = Cdim(v5) = &quot;C dim down-five&quot;<br /> | C Eb Gbv = Cdim(v5) = &quot;C dim down-five&quot;<br /> | ||
C Eb Gb^ = Cdim(^5) = &quot;C dim up-five&quot;<br /> | C Eb Gb^ = Cdim(^5) = &quot;C dim up-five&quot;<br /> | ||
C Eb^ Gb = Cdim(^3) = &quot;C dim up-three&quot; (in certain EDOs, C | C Eb^ Gb = Cdim(^3) = &quot;C dim up-three&quot; (in certain EDOs, C~(b5) = &quot;C mid flat-five&quot;)<br /> | ||
(note that here &quot;up-three&quot; means upminor 3rd, not upmajor 3rd, because &quot;dim&quot; indicates a minor 3rd)<br /> | (note that here &quot;up-three&quot; means upminor 3rd, not upmajor 3rd, because &quot;dim&quot; indicates a minor 3rd)<br /> | ||
C Eb^ Gb^ = Cdim(^3,^5) = &quot;C dim up-three up-five&quot; (in certain EDOs, C | C Eb^ Gb^ = Cdim(^3,^5) = &quot;C dim up-three up-five&quot; (in certain EDOs, C~(^b5) = &quot;C mid upflat-five&quot;)<br /> | ||
<br /> | <br /> | ||
C Eb Gv = Cm(v5) = &quot;C minor down-five&quot;<br /> | C Eb Gv = Cm(v5) = &quot;C minor down-five&quot;<br /> | ||
| Line 1,679: | Line 1,680: | ||
C E G^ = C(^5) = &quot;C up-five&quot;<br /> | C E G^ = C(^5) = &quot;C up-five&quot;<br /> | ||
C E^ G^ = C.^(^5) = &quot;C dot up, up-five&quot;<br /> | C E^ G^ = C.^(^5) = &quot;C dot up, up-five&quot;<br /> | ||
C Ev Gv = C.v(v5) = &quot;C dot down, down-five&quot; (in certain EDOs, C | C Ev Gv = C.v(v5) = &quot;C dot down, down-five&quot; (in certain EDOs, C~(v5) = &quot;C mid down-five&quot;)<br /> | ||
<br /> | <br /> | ||
C E G# is Caug = &quot;C aug&quot; (in perfect EDOs, C = &quot;C&quot; or &quot;C perfect&quot;)<br /> | C E G# is Caug = &quot;C aug&quot; (in perfect EDOs, C = &quot;C&quot; or &quot;C perfect&quot;)<br /> | ||
| Line 1,686: | Line 1,687: | ||
C E^ G# is Caug(^3) = &quot;C aug up-three&quot; (note that here &quot;up-three&quot; means upmajor 3rd, not upminor 3rd)<br /> | C E^ G# is Caug(^3) = &quot;C aug up-three&quot; (note that here &quot;up-three&quot; means upmajor 3rd, not upminor 3rd)<br /> | ||
C E^ G#^ = Caug(^3,^5) = &quot;C aug up-three up-five&quot;<br /> | C E^ G#^ = Caug(^3,^5) = &quot;C aug up-three up-five&quot;<br /> | ||
C E# G# is Caug(#3)<br /> | <br /> | ||
C D# Gb = Csus#2(b5) = &quot;C sus sharp-two, flat-five&quot;<br /> | |||
C Ebb Gb = Cdim(bb3) = &quot;C dim dim-three&quot;<br /> | |||
C Eb G# is Cmin(#5) = &quot;C minor sharp-five&quot;<br /> | |||
C E# G# is Caug(#3) = &quot;C aug sharp-three&quot;<br /> | |||
C Fb G# is Caug,susb4 = &quot;C aug sus flat-four&quot;<br /> | |||
<br /> | <br /> | ||
<u><strong>Seventh chords:</strong></u><br /> | <u><strong>Seventh chords:</strong></u><br /> | ||
| Line 1,692: | Line 1,698: | ||
C Ev G Bb = C7(v3) = &quot;C seven down-three&quot; (in certain EDOs, C7(~3) = &quot;C seven mid-three&quot;)<br /> | C Ev G Bb = C7(v3) = &quot;C seven down-three&quot; (in certain EDOs, C7(~3) = &quot;C seven mid-three&quot;)<br /> | ||
C E G Bbv = C(v7) = &quot;C down-seven&quot; (not &quot;C-down seven&quot;, which would be Cv.7 = Cv Ev Gv Bbv)<br /> | C E G Bbv = C(v7) = &quot;C down-seven&quot; (not &quot;C-down seven&quot;, which would be Cv.7 = Cv Ev Gv Bbv)<br /> | ||
C Ev G Bbv = C.v7 = &quot;C dot down-seven&quot;<br /> | C Ev G Bbv = C.v7 = &quot;C dot down-seven&quot; (in certain EDOs, C~(v7) = &quot;C mid down-seven&quot;)<br /> | ||
C E Gv Bb = C7(v5) = &quot;C seven down-five&quot;<br /> | C E Gv Bb = C7(v5) = &quot;C seven down-five&quot;<br /> | ||
C Ev Gv Bb = C7(v3,v5) = &quot;C seven down-three down-five&quot;<br /> | C Ev Gv Bb = C7(v3,v5) = &quot;C seven down-three down-five&quot;<br /> | ||
| Line 1,726: | Line 1,732: | ||
C Eb^ Gb^ Bb^ = C.^m7(^b5) = &quot;C dot upminor seven upflat-five&quot; or &quot;C half-dim up-three up-five up-seven&quot;<br /> | C Eb^ Gb^ Bb^ = C.^m7(^b5) = &quot;C dot upminor seven upflat-five&quot; or &quot;C half-dim up-three up-five up-seven&quot;<br /> | ||
<br /> | <br /> | ||
C E G B# | C E G B# is C(#7) = &quot;C sharp-seven&quot; (not &quot;C aug-seven&quot;, that sounds like &quot;C aug seven&quot; = Caug7) <br /> | ||
C E G Cb = C(b8) = &quot;C dim-eight&quot; or &quot;C flat-eight&quot;<br /> | |||
C | |||
<br /> | <br /> | ||
<u><strong>Sixth chords:</strong></u><br /> | <u><strong>Sixth chords:</strong></u><br /> | ||
| Line 1,743: | Line 1,747: | ||
C Eb^ G A = Cm6(^3) = &quot;C minor six up-three&quot; (in certain EDOs, C6(~3) = &quot;C six mid-three&quot;)<br /> | C Eb^ G A = Cm6(^3) = &quot;C minor six up-three&quot; (in certain EDOs, C6(~3) = &quot;C six mid-three&quot;)<br /> | ||
<br /> | <br /> | ||
C | C E G Ab = C(b6) = &quot;C flat-six&quot; (not &quot;C minor-six&quot; because that sounds like &quot;C minor six&quot; = Cm6)<br /> | ||
C E G A# is C(#6) = &quot;C sharp-six&quot;<br /> | |||
C E G A# | |||
<br /> | <br /> | ||
<br /> | <br /> | ||
| Line 1,785: | Line 1,785: | ||
C Dbv Ev G Bbv = C.v7(vb9) = &quot;C dot down seven downflat-nine&quot;<br /> | C Dbv Ev G Bbv = C.v7(vb9) = &quot;C dot down seven downflat-nine&quot;<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:16:&lt;h4&gt; --><h4 id="toc8"><a name="Naming Chords-Chord names in other EDOs--Example EDOs:"></a><!-- ws:end:WikiTextHeadingRule:16 --><u><strong>Example EDOs:</strong></u></h4> | ||
<br /> | <br /> | ||
14edo: D * E * F * G * A * B * C * D, zero keys per #/b.<br /> | 14edo: D * E * F * G * A * B * C * D, zero keys per #/b.<br /> | ||
| Line 1,806: | Line 1,806: | ||
0-3-8-11 = D Fv A Cv = D.v7 = &quot;D dot down-seven&quot;<br /> | 0-3-8-11 = D Fv A Cv = D.v7 = &quot;D dot down-seven&quot;<br /> | ||
0-5-8-11 = D F^ A B^ = D.^6 = &quot;D dot up-six&quot;<br /> | 0-5-8-11 = D F^ A B^ = D.^6 = &quot;D dot up-six&quot;<br /> | ||
<br /> | <br /> | ||
15edo: 3 keys per #/b, so ups and downs are needed.<br /> | 15edo: 3 keys per #/b, so ups and downs are needed.<br /> | ||
| Line 1,812: | Line 1,811: | ||
chord components: P1 ^m2 vM2 M2/m3 ^m3 vM3 M3/P4 ^P4 vP5 P5 ^m6 vM6 M6/m7 ^m7 vM7<br /> | chord components: P1 ^m2 vM2 M2/m3 ^m3 vM3 M3/P4 ^P4 vP5 P5 ^m6 vM6 M6/m7 ^m7 vM7<br /> | ||
chord roots: I ^bII vII II/bIII ^bIII vIII III/IV ^IV vV V ^bVI vVI VI/bVII ^bVII vVII<br /> | chord roots: I ^bII vII II/bIII ^bIII vIII III/IV ^IV vV V ^bVI vVI VI/bVII ^bVII vVII<br /> | ||
0-3-9 = D F A = Dm = &quot;D minor&quot; (or possibly D E A = Dsus2)<br /> | 0-3-9 = D F A = Dm = &quot;D minor&quot; (or possibly D E A = Dsus2)<br /> | ||
0-4-9 = D F^ A = D.^m = &quot;D (dot) upminor&quot;<br /> | 0-4-9 = D F^ A = D.^m = &quot;D (dot) upminor&quot;<br /> | ||
| Line 1,842: | Line 1,840: | ||
0-6-10 = D Fb Ab = Ddim(bb3) = &quot;D dim dim-three&quot;<br /> | 0-6-10 = D Fb Ab = Ddim(bb3) = &quot;D dim dim-three&quot;<br /> | ||
0-7-9 = D G A = Dsus4 = &quot;D sus four&quot;<br /> | 0-7-9 = D G A = Dsus4 = &quot;D sus four&quot;<br /> | ||
0-5-9-13 = D F A C# <!-- ws:start:WikiTextHeadingRule: | 0-5-9-13 = D F A C# <!-- ws:start:WikiTextHeadingRule:18:&lt;h1&gt; --><h1 id="toc9"><a name="DmM7"></a><!-- ws:end:WikiTextHeadingRule:18 --> DmM7 </h1> | ||
&quot; D minor major seven&quot;<br /> | &quot; D minor major seven&quot;<br /> | ||
0-4-8-12 = D F# A# C## <!-- ws:start:WikiTextHeadingRule: | 0-4-8-12 = D F# A# C## <!-- ws:start:WikiTextHeadingRule:20:&lt;h1&gt; --><h1 id="toc10"><a name="Daug(#7)"></a><!-- ws:end:WikiTextHeadingRule:20 --> Daug(#7) </h1> | ||
&quot;D aug aug-seven&quot;<br /> | &quot;D aug aug-seven&quot;<br /> | ||
<br /> | <br /> | ||
| Line 1,851: | Line 1,849: | ||
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<br /> | 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<br /> | ||
0-4-10 = D F A = Dm = &quot;D minor&quot;<br /> | 0-4-10 = D F A = Dm = &quot;D minor&quot;<br /> | ||
0-5-10 = D F^ A = D | 0-5-10 = D F^ A = D~ = &quot;D mid&quot;<br /> | ||
0-6-10 = D F# A = D = &quot;D&quot; or &quot;D major&quot;<br /> | 0-6-10 = D F# A = D = &quot;D&quot; or &quot;D major&quot;<br /> | ||
0-5-10-14 = D F^ A C = D7(~3)<br /> | 0-5-10-14 = D F^ A C = D7(~3) = &quot;D seven mid-three&quot;<br /> | ||
0-4-10-15 = D F A C^ = Dm(~7)<br /> | 0-4-10-15 = D F A C^ = Dm(~7) = &quot;D minor mid-seven&quot;<br /> | ||
0-5-10-15 = D F^ A C^ = D.~7<br /> | 0-5-10-15 = D F^ A C^ = D.~7 = &quot;D dot mid seven&quot;<br /> | ||
0-6-10-15 = D F# A C^ = D(~7)<br /> | 0-6-10-15 = D F# A C^ = D(~7) = &quot;D mid-seven&quot;<br /> | ||
<br /> | <br /> | ||
18edo:<br /> | 18edo:<br /> | ||
| Line 1,866: | Line 1,864: | ||
0-4-10 = D Fb Ab = Ddim(bb3) = &quot;D dim dim-three&quot;<br /> | 0-4-10 = D Fb Ab = Ddim(bb3) = &quot;D dim dim-three&quot;<br /> | ||
0-7-11 = D F## A = D(#3) = &quot;D aug-three&quot; (aug 3rd, perfect 5th)<br /> | 0-7-11 = D F## A = D(#3) = &quot;D aug-three&quot; (aug 3rd, perfect 5th)<br /> | ||
0-7-12 = D F## A# <!-- ws:start:WikiTextHeadingRule: | 0-7-12 = D F## A# <!-- ws:start:WikiTextHeadingRule:22:&lt;h1&gt; --><h1 id="toc11"><a name="Daug(#3)"></a><!-- ws:end:WikiTextHeadingRule:22 --> Daug(#3) </h1> | ||
&quot;D aug aug-three&quot;<br /> | &quot;D aug aug-three&quot;<br /> | ||
0-5-10-15 = D F Ab Cb = Ddim7 = &quot;D dim-seven&quot;<br /> | 0-5-10-15 = D F Ab Cb = Ddim7 = &quot;D dim-seven&quot;<br /> | ||
| Line 1,912: | Line 1,910: | ||
0-14-26 = D F# A^^ = D(^^5) = &quot;D double-up-five&quot;<br /> | 0-14-26 = D F# A^^ = D(^^5) = &quot;D double-up-five&quot;<br /> | ||
0-14-27 = D F# A#v = Daug(v5) = &quot;D aug down-five&quot;<br /> | 0-14-27 = D F# A#v = Daug(v5) = &quot;D aug down-five&quot;<br /> | ||
0-14-28 = D F# A# <!-- ws:start:WikiTextHeadingRule: | 0-14-28 = D F# A# <!-- ws:start:WikiTextHeadingRule:24:&lt;h1&gt; --><h1 id="toc12"><a name="Daug"></a><!-- ws:end:WikiTextHeadingRule:24 --> Daug </h1> | ||
&quot;D aug&quot;<br /> | &quot;D aug&quot;<br /> | ||
<br /> | <br /> | ||
| Line 1,935: | Line 1,933: | ||
0-3-6-7 = D Fv A B = D6(~3)<br /> | 0-3-6-7 = D Fv A B = D6(~3)<br /> | ||
0-4-6-7 = D F A B = Dm6<br /> | 0-4-6-7 = D F A B = Dm6<br /> | ||
0-2-6-8 = D F# A C# <!-- ws:start:WikiTextHeadingRule: | 0-2-6-8 = D F# A C# <!-- ws:start:WikiTextHeadingRule:26:&lt;h1&gt; --><h1 id="toc13"><a name="DM7, or D F# A B^"></a><!-- ws:end:WikiTextHeadingRule:26 --> DM7, or D F# A B^ </h1> | ||
D(~6) = &quot;D mid-six&quot;<br /> | D(~6) = &quot;D mid-six&quot;<br /> | ||
0-3-6-8 = D F#^ A C# <!-- ws:start:WikiTextHeadingRule: | 0-3-6-8 = D F#^ A C# <!-- ws:start:WikiTextHeadingRule:28:&lt;h1&gt; --><h1 id="toc14"><a name="DM7(^3), or D F#^ A B^"></a><!-- ws:end:WikiTextHeadingRule:28 --> DM7(^3), or D F#^ A B^ </h1> | ||
D.^6 = &quot;D dot up-six&quot;<br /> | D.^6 = &quot;D dot up-six&quot;<br /> | ||
0-3-6-9 = D Fv A Cv = D.~7 = &quot;D dot mid seven&quot;, or D Fv A Bb = D.~(b6) = &quot;D mid flat-six&quot;<br /> | 0-3-6-9 = D Fv A Cv = D.~7 = &quot;D dot mid seven&quot;, or D Fv A Bb = D.~(b6) = &quot;D mid flat-six&quot;<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:30:&lt;h2&gt; --><h2 id="toc15"><a name="DM7(^3), or D F#^ A B^-Cross-EDO considerations"></a><!-- ws:end:WikiTextHeadingRule:30 --><strong><u>Cross-EDO considerations</u></strong></h2> | ||
<br /> | <br /> | ||
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 &quot;major 3rd&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.<br /> | 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 &quot;major 3rd&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.<br /> | ||
| Line 1,952: | Line 1,950: | ||
<br /> | <br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:32:&lt;h2&gt; --><h2 id="toc16"><a name="DM7(^3), or D F#^ A B^-EDOs with an inaccurate 3/2"></a><!-- ws:end:WikiTextHeadingRule:32 --><u>EDOs with an inaccurate 3/2</u></h2> | ||
<br /> | <br /> | ||
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.<br /> | 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.<br /> | ||
| Line 2,026: | Line 2,024: | ||
<br /> | <br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:34:&lt;h1&gt; --><h1 id="toc17"><a name="Summary of EDO notation"></a><!-- ws:end:WikiTextHeadingRule:34 --><u><strong>Summary of EDO notation</strong></u></h1> | ||
<br /> | <br /> | ||
Besides the trivial EDOs, 1, 2, 3, 4 and 6, which can be notated with standard notation as a subset of 12-EDO, there are five EDO categories, based on the size of the fifth:<br /> | Besides the trivial EDOs, 1, 2, 3, 4 and 6, which can be notated with standard notation as a subset of 12-EDO, there are five EDO categories, based on the size of the fifth:<br /> | ||
| Line 3,398: | Line 3,396: | ||
<br /> | <br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:36:&lt;h3&gt; --><h3 id="toc18"><a name="Summary of EDO notation--&quot;Fifth-less&quot; EDOs (8, 11, 13 and 18)"></a><!-- ws:end:WikiTextHeadingRule:36 --><u><strong>&quot;Fifth-less&quot; EDOs (8, 11, 13 and 18)</strong></u></h3> | ||
<br /> | <br /> | ||
<strong><u>8edo</u>:</strong> (generator = 1\8 = perfect 2nd = 150¢)<br /> | <strong><u>8edo</u>:</strong> (generator = 1\8 = perfect 2nd = 150¢)<br /> | ||
| Line 3,428: | Line 3,426: | ||
E# - G# - B# - D# - F# - A# - C# - E - G - B - D - F - A - C - Eb - Gb - Bb - Db - Fb - Ab - Cb<br /> | E# - G# - B# - D# - F# - A# - C# - E - G - B - D - F - A - C - Eb - Gb - Bb - Db - Fb - Ab - Cb<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:38:&lt;h3&gt; --><h3 id="toc19"><a name="Summary of EDO notation--Alternate pentatonic notation for EDOs 8, 13 and 18"></a><!-- ws:end:WikiTextHeadingRule:38 --><u><strong>Alternate pentatonic notation for EDOs 8, 13 and 18</strong></u></h3> | ||
<br /> | <br /> | ||
All three EDOs use the same pentatonic fifthwards chain of fifths: ms3 - ms7 - P4d - P1 - P5d - Ms3 - Ms7 - A4d etc.<br /> | All three EDOs use the same pentatonic fifthwards chain of fifths: ms3 - ms7 - P4d - P1 - P5d - Ms3 - Ms7 - A4d etc.<br /> | ||
| Line 3,449: | Line 3,447: | ||
<br /> | <br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:40:&lt;h3&gt; --><h3 id="toc20"><a name="Summary of EDO notation--Fourthward EDOs (9, 16 and 23)"></a><!-- ws:end:WikiTextHeadingRule:40 --><u>Fourthward EDOs (9, 16 and 23)</u></h3> | ||
<br /> | <br /> | ||
All fourthwards EDOs use the same chain of fifths: M2 - M6 - M3 - M7 - P4 - P1 - P5 - m2 - m6 - m3 - m7 - A4 etc.<br /> | All fourthwards EDOs use the same chain of fifths: M2 - M6 - M3 - M7 - P4 - P1 - P5 - m2 - m6 - m3 - m7 - A4 etc.<br /> | ||
| Line 3,470: | Line 3,468: | ||
<br /> | <br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:42:&lt;h3&gt; --><h3 id="toc21"><a name="Summary of EDO notation--&quot;Perfect&quot; EDOs (7, 14, 21, 28 and 35)"></a><!-- ws:end:WikiTextHeadingRule:42 --><u>&quot;Perfect&quot; EDOs (7, 14, 21, 28 and 35)</u></h3> | ||
<br /> | <br /> | ||
All perfect EDOs use the same chain of fifths: P2 - P6 - P3 - P7 - P4 - P1 - P5 - P2 - P6 - P3 - P7 etc.<br /> | All perfect EDOs use the same chain of fifths: P2 - P6 - P3 - P7 - P4 - P1 - P5 - P2 - P6 - P3 - P7 etc.<br /> | ||
| Line 3,501: | Line 3,499: | ||
<br /> | <br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:44:&lt;h3&gt; --><h3 id="toc22"><a name="Summary of EDO notation--Pentatonic EDOs (5, 10, 15, 20, 25 and 30)"></a><!-- ws:end:WikiTextHeadingRule:44 --><u>Pentatonic EDOs (5, 10, 15, 20, 25 and 30)</u></h3> | ||
<br /> | <br /> | ||
All pentatonic EDOs use the usual chain of fifths: m2 - m6 - m3 - m7 - P4 - P1 - P5 - M2 - M6 - M3 - M7 etc.<br /> | All pentatonic EDOs use the usual chain of fifths: m2 - m6 - m3 - m7 - P4 - P1 - P5 - M2 - M6 - M3 - M7 etc.<br /> | ||
| Line 3,536: | Line 3,534: | ||
P1/m2 - ^m2 - ^^m2 - vvM2 - vM2 - M2/m3 - ^m3 - ^^m3 - vvM3 - vM3 - M3/P4 - ^P4 - ^^P4 - vvP5 - vP5 - P5/m6 - ^m6 - ^^m6 - vvM6 - vM6 - M6/m7 - ^m7 - ^^m7 - vvM7 - vM7 - P8<br /> | P1/m2 - ^m2 - ^^m2 - vvM2 - vM2 - M2/m3 - ^m3 - ^^m3 - vvM3 - vM3 - M3/P4 - ^P4 - ^^P4 - vvP5 - vP5 - P5/m6 - ^m6 - ^^m6 - vvM6 - vM6 - M6/m7 - ^m7 - ^^m7 - vvM7 - vM7 - P8<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:46:&lt;h3&gt; --><h3 id="toc23"><a name="Summary of EDO notation--Alternative pentatonic notation for pentatonic EDOs:"></a><!-- ws:end:WikiTextHeadingRule:46 --><u>Alternative pentatonic notation for pentatonic EDOs:</u></h3> | ||
<br /> | <br /> | ||
Pentatonic fourthwards chain of fifthoids: Ms3 - Ms7 - P4d - P1 - P5d - ms3 - ms7 - d4d etc.<br /> | Pentatonic fourthwards chain of fifthoids: Ms3 - Ms7 - P4d - P1 - P5d - ms3 - ms7 - d4d etc.<br /> | ||
| Line 3,559: | Line 3,557: | ||
<br /> | <br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:48:&lt;h3&gt; --><h3 id="toc24"><a name="Summary of EDO notation--&quot;Sweet&quot; EDOs (12, 17, 19, 22, 24, 26, 27, 29, 31-34, and all edos 36 or higher)"></a><!-- ws:end:WikiTextHeadingRule:48 --><u>&quot;Sweet&quot; EDOs (12, 17, 19, 22, 24, 26, 27, 29, 31-34, and all edos 36 or higher)</u></h3> | ||
<br /> | <br /> | ||
All sweet EDOs use the usual chain of fifths: m2 - m6 - m3 - m7 - P4 - P1 - P5 - M2 - M6 - M3 - M7 etc.<br /> | All sweet EDOs use the usual chain of fifths: m2 - m6 - m3 - m7 - P4 - P1 - P5 - M2 - M6 - M3 - M7 etc.<br /> | ||
| Line 3,592: | Line 3,590: | ||
<br /> | <br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:50:&lt;h2&gt; --><h2 id="toc25"><a name="Summary of EDO notation-Ups and downs solfege"></a><!-- ws:end:WikiTextHeadingRule:50 --><u>Ups and downs solfege</u></h2> | ||
<br /> | <br /> | ||
Solfege (do-re-mi) can be adapted to indicate sharp/flat and up/down:<br /> | Solfege (do-re-mi) can be adapted to indicate sharp/flat and up/down:<br /> | ||
| Line 3,623: | Line 3,621: | ||
<br /> | <br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:52:&lt;h2&gt; --><h2 id="toc26"><a name="Summary of EDO notation-Rank-2 Notation"></a><!-- ws:end:WikiTextHeadingRule:52 --><u>Rank-2 Notation</u></h2> | ||
<br /> | <br /> | ||
Ups and downs can be used to notate rank-2 scales. First we must distinguish between edos and sizing frameworks. For example, keyboards with 7 white keys and 5 black keys, and fretted instruments with 12 frets per octave, predate the use of 12edo by many centuries. Such instruments use a 12-tone framework. Traditional Western notation uses a 7-note naming framework and a 12-tone sizing framework. (See the first chapter of part V of Kite's book for more on frameworks.)<br /> | Ups and downs can be used to notate rank-2 scales. First we must distinguish between edos and sizing frameworks. For example, keyboards with 7 white keys and 5 black keys, and fretted instruments with 12 frets per octave, predate the use of 12edo by many centuries. Such instruments use a 12-tone framework. Traditional Western notation uses a 7-note naming framework and a 12-tone sizing framework. (See the first chapter of part V of Kite's book for more on frameworks.)<br /> | ||
| Line 5,783: | Line 5,781: | ||
There is no variant of D adjacent to C, and there is no 2nd with keyspan 1 or -1. Some other method of notation must be used for rank-2 fifth-generated tunings in these two frameworks.<br /> | There is no variant of D adjacent to C, and there is no 2nd with keyspan 1 or -1. Some other method of notation must be used for rank-2 fifth-generated tunings in these two frameworks.<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:54:&lt;h2&gt; --><h2 id="toc27"><!-- ws:end:WikiTextHeadingRule:54 --> </h2> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:56:&lt;h2&gt; --><h2 id="toc28"><a name="Summary of EDO notation-Generators other than a fifth"></a><!-- ws:end:WikiTextHeadingRule:56 --><u>Generators other than a fifth</u></h2> | ||
<br /> | <br /> | ||
The main reason to use ups and downs is to allow fifth-generated heptatonic notation in frameworks and EDOs that aren't fully compatible with such a notation, i.e. those not on the sides of the 4\7 kite. The main reason to use a generator other than a fifth is to use a notation more compatible with one's chosen framework or EDO. Thus there is little reason to use ups and downs in such a situation.<br /> | The main reason to use ups and downs is to allow fifth-generated heptatonic notation in frameworks and EDOs that aren't fully compatible with such a notation, i.e. those not on the sides of the 4\7 kite. The main reason to use a generator other than a fifth is to use a notation more compatible with one's chosen framework or EDO. Thus there is little reason to use ups and downs in such a situation.<br /> | ||