39edo: Difference between revisions

Wikispaces>TallKite
**Imported revision 607131469 - Original comment: **
Wikispaces>TallKite
**Imported revision 607132865 - 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>2017-02-24 17:21:16 UTC</tt>.<br>
: This revision was by author [[User:TallKite|TallKite]] and made on <tt>2017-02-24 18:14:25 UTC</tt>.<br>
: The original revision id was <tt>607131469</tt>.<br>
: The original revision id was <tt>607132865</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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* **v** = Semiflat (1/5-tone down) ||
* **v** = Semiflat (1/5-tone down) ||


||~ **Degrees** ||~ **Cents size** ||~ **Armodue note** ||||~ [[xenharmonic/Ups and Downs Notation|ups and]]
||~ **Degrees** ||~ **Cents size** ||~ **Armodue note** ||||||~ [[xenharmonic/Ups and Downs Notation|ups and ]][[xenharmonic/Ups and Downs Notation|downs]]
[[xenharmonic/Ups and Downs Notation|downs]]
[[xenharmonic/Ups and Downs Notation|notation]] ||~ **[[xenharmonic/Nearest just interval|Nearest Just I]]nterval** ||~ **Cents value** ||~ **Error** ||~ 11-limit Ratio Assuming
[[xenharmonic/Ups and Downs Notation|notation]] ||~ **[[xenharmonic/Nearest just interval|Nearest Just I]]nterval** ||~ **Cents value** ||~ **Error** ||~ 11-limit Ratio Assuming
&lt;39 62 91 110 135| [[Val]] ||
&lt;39 62 91 110 135| [[Val]] ||
|| 0 || 0 || 1 ||= P1 ||= perfect unison || 1/1 || 0 || None || 1/1 ||
|| 0 || 0 || 1 ||= P1 ||= perfect unison ||= D || 1/1 || 0 || None || 1/1 ||
|| 1 || 30.7692 || 1‡ (9#) ||= ^1 ||= up unison || 57/56 || 30.6421 || +0.1271 ||  ||
|| 1 || 30.7692 || 1‡ (9#) ||= ^1 ||= up unison ||= D^ || 57/56 || 30.6421 || +0.1271 ||  ||
|| 2 || 61.5385 || 2b ||= m2 ||= minor 2nd || 29/28 || 60.7513 || +0.7872 ||  ||
|| 2 || 61.5385 || 2b ||= m2 ||= minor 2nd ||= Eb || 29/28 || 60.7513 || +0.7872 ||  ||
|| 3 || 92.3077 || 1# ||= ^m2 ||= upminor 2nd || 39/37 || 91.1386 || +1.1691 ||  ||
|| 3 || 92.3077 || 1# ||= ^m2 ||= upminor 2nd ||= Eb^ || 39/37 || 91.1386 || +1.1691 ||  ||
|| 4 || 123.0769 || 2v ||= v~2 ||= downmid 2nd || 44/41 || 122.2555 || +0.8214 ||  ||
|| 4 || 123.0769 || 2v ||= v~2 ||= downmid 2nd ||= Eb^^ || 44/41 || 122.2555 || +0.8214 ||  ||
|| 5 || 153.8462 || 2 ||= ^~2 ||= upmid 2nd || 35/32 || 155.1396 || -1.2934 || 12/11, 11/10 ||
|| 5 || 153.8462 || 2 ||= ^~2 ||= upmid 2nd ||= Evv || 35/32 || 155.1396 || -1.2934 || 12/11, 11/10 ||
|| 6 || 184.6154 || 2‡ ||= vM2 ||= downmajor 2nd || 10/9 || 182.4037 || +2.2117 || 10/9 ||
|| 6 || 184.6154 || 2‡ ||= vM2 ||= downmajor 2nd ||= Ev || 10/9 || 182.4037 || +2.2117 || 10/9 ||
|| 7**·** || 215.3846 || 3b ||= M2 ||= major 2nd || 17/15 || 216.6867 || -1.3021 || 8/7, 9/8 ||
|| 7**·** || 215.3846 || 3b ||= M2 ||= major 2nd ||= E || 17/15 || 216.6867 || -1.3021 || 8/7, 9/8 ||
|| 8 || 246.1538 || 2# ||= ^M2,
|| 8 || 246.1538 || 2# ||= ^M2,
vm3 ||= upmajor 2nd,
vm3 ||= upmajor 2nd,
downminor 3rd || 15/13 || 247.7411 || -1.5873 ||  ||
downminor 3rd ||= E^,
|| 9 || 276.9231 || 3v ||= m3 ||= minor 3rd || 27/23 || 277.5907 || -0.6676 || 7/6 ||
Fv || 15/13 || 247.7411 || -1.5873 ||  ||
|| 10 || 307.6923 || 3 ||= ^m3 ||= upminor 3rd || 43/36 || 307.6077 || +0.0846 || 6/5 ||
|| 9 || 276.9231 || 3v ||= m3 ||= minor 3rd ||= F || 27/23 || 277.5907 || -0.6676 || 7/6 ||
|| 11 || 338.4615 || 3‡ ||= v~3 ||= downmid 3rd || 17/14 || 336.1295 || +2.332 || 11/9 ||
|| 10 || 307.6923 || 3 ||= ^m3 ||= upminor 3rd ||= F^ || 43/36 || 307.6077 || +0.0846 || 6/5 ||
|| 12**·** || 369.2308 || 4b ||= ^~3 ||= upmid 3rd || 26/21 || 369.7468 || -0.516 ||  ||
|| 11 || 338.4615 || 3‡ ||= v~3 ||= downmid 3rd ||= F^^ || 17/14 || 336.1295 || +2.332 || 11/9 ||
|| 13 || 400 || 3# ||= vM3 ||= downmajor 3rd || 34/27 || 399.0904 || +0.9096 || 5/4 ||
|| 12**·** || 369.2308 || 4b ||= ^~3 ||= upmid 3rd ||= F#vv || 26/21 || 369.7468 || -0.516 ||  ||
|| 14 || 430.7692 || 4v (5b) ||= M3 ||= major 3rd || 41/32 || 429.0624 || +1.7068 || 9/7, 14/11 ||
|| 13 || 400 || 3# ||= vM3 ||= downmajor 3rd ||= F#v || 34/27 || 399.0904 || +0.9096 || 5/4 ||
|| 15 || 461.5385 || 4 ||= v4 ||= down 4th || 30/23 || 459.9944 || +1.5441 ||  ||
|| 14 || 430.7692 || 4v (5b) ||= M3 ||= major 3rd ||= F# || 41/32 || 429.0624 || +1.7068 || 9/7, 14/11 ||
|| 16 || 492.3077 || 4‡ (5v) ||= P4 ||= perfect 4th || 85/64 || 491.2691 || +1.0386 || 4/3 ||
|| 15 || 461.5385 || 4 ||= v4 ||= down 4th ||= Gv || 30/23 || 459.9944 || +1.5441 ||  ||
|| 17**·** || 523.0769 || 5 ||= ^4 ||= up 4th || 23/17 || 523.3189 || -0.242 ||  ||
|| 16 || 492.3077 || 4‡ (5v) ||= P4 ||= perfect 4th ||= G || 85/64 || 491.2691 || +1.0386 || 4/3 ||
|| 18 || 553.8462 || 5‡ (4#) ||= ^^4 ||= double-up 4th || 11/8 || 551.3179 || +2.5283 || 11/8 ||
|| 17**·** || 523.0769 || 5 ||= ^4 ||= up 4th ||= G^ || 23/17 || 523.3189 || -0.242 ||  ||
|| 18 || 553.8462 || 5‡ (4#) ||= ^^4 ||= double-up 4th ||= G^^ || 11/8 || 551.3179 || +2.5283 || 11/8 ||
|| 19 || 584.6154 || 6b ||= vvA4,
|| 19 || 584.6154 || 6b ||= vvA4,
^d5 ||= double-down aug 4th, updim 5th || 7/5 || 582.5122 || +2.1032 || 7/5 ||
^d5 ||= double-down aug 4th, updim 5th ||= G#vv,
Ab^ || 7/5 || 582.5122 || +2.1032 || 7/5 ||
|| 20 || 615.3846 || 5# ||= vA4,
|| 20 || 615.3846 || 5# ||= vA4,
^^d5 ||= downaug 4th, double-up dim 5th || 10/7 || 617.4878 || -2.1032 || 10/7 ||
^^d5 ||= downaug 4th, double-up dim 5th ||= G#v,
|| 21 || 646.1538 || 6v ||= vv5 ||= double-down 5th || 16/11 || 648.6821 || -2.5283 || 16/11 ||
Ab^^ || 10/7 || 617.4878 || -2.1032 || 10/7 ||
|| 22**·** || 676.9231 || 6 ||= v5 ||= down 5th || 34/23 || 676.6811 || +0.242 ||  ||
|| 21 || 646.1538 || 6v ||= vv5 ||= double-down 5th ||= Avv || 16/11 || 648.6821 || -2.5283 || 16/11 ||
|| 23 || 707.6923 || 6‡ ||= P5 ||= perfect 5th || 128/85 || 708.7309 || -1.0386 || 3/2 ||
|| 22**·** || 676.9231 || 6 ||= v5 ||= down 5th ||= Av || 34/23 || 676.6811 || +0.242 ||  ||
|| 24 || 738.4615 || 7b ||= ^5 ||= up 5th || 23/15 || 740.0056 || -1.5441 ||  ||
|| 23 || 707.6923 || 6‡ ||= P5 ||= perfect 5th ||= A || 128/85 || 708.7309 || -1.0386 || 3/2 ||
|| 25 || 769.2308 || 6# ||= m6 ||= minor 6th || 64/41 || 770.9376 || -1.7068 || 14/9, 11/7 ||
|| 24 || 738.4615 || 7b ||= ^5 ||= up 5th ||= A^ || 23/15 || 740.0056 || -1.5441 ||  ||
|| 26 || 800 || 7v ||= ^m6 ||= upminor 6th || 27/17 || 800.9096 || -0.9096 || 8/5 ||
|| 25 || 769.2308 || 6# ||= m6 ||= minor 6th ||= Bb || 64/41 || 770.9376 || -1.7068 || 14/9, 11/7 ||
|| 27**·** || 830.7692 || 7 ||= v~6 ||= downmid 6th || 21/13 || 830.2532 || +0.516 ||  ||
|| 26 || 800 || 7v ||= ^m6 ||= upminor 6th ||= Bb^ || 27/17 || 800.9096 || -0.9096 || 8/5 ||
|| 28 || 861.5385 || 7‡ ||= ^~6 ||= upmid 6th || 28/17 || 863.8705 || -2.332 || 18/11 ||
|| 27**·** || 830.7692 || 7 ||= v~6 ||= downmid 6th ||= Bb^^ || 21/13 || 830.2532 || +0.516 ||  ||
|| 29 || 892.3077 || 8b ||= vM6 ||= downmajor 6th || 72/43 || 892.3923 || -0.0846 || 5/3 ||
|| 28 || 861.5385 || 7‡ ||= ^~6 ||= upmid 6th ||= Bvv || 28/17 || 863.8705 || -2.332 || 18/11 ||
|| 30 || 923.0769 || 7# ||= M6 ||= major 6th || 46/27 || 922.4093 || +0.6676 || 12/7 ||
|| 29 || 892.3077 || 8b ||= vM6 ||= downmajor 6th ||= Bv || 72/43 || 892.3923 || -0.0846 || 5/3 ||
|| 30 || 923.0769 || 7# ||= M6 ||= major 6th ||= B || 46/27 || 922.4093 || +0.6676 || 12/7 ||
|| 31 || 953.8462 || 8v ||= ^M6,
|| 31 || 953.8462 || 8v ||= ^M6,
vm7 ||= upmajor 6th,
vm7 ||= upmajor 6th,
downminor 7th || 26/15 || 952.2589 || +1.5873 ||  ||
downminor 7th ||= B^,
|| 32**·** || 984.6154 || 8 ||= m7 ||= minor 7th || 30/17 || 983.3133 || +1.3021 || 7/4, 16/9 ||
Cv || 26/15 || 952.2589 || +1.5873 ||  ||
|| 33 || 1015.3846 || 8‡ ||= ^m7 ||= upminor 7th || 9/5 || 1017.5963 || -2.2117 || 9/5 ||
|| 32**·** || 984.6154 || 8 ||= m7 ||= minor 7th ||= C || 30/17 || 983.3133 || +1.3021 || 7/4, 16/9 ||
|| 34 || 1046.1538 || 9b ||= v~7 ||= downmid 7th || 64/35 || 1044.8604 || +1.2934 || 11/6, 20/11 ||
|| 33 || 1015.3846 || 8‡ ||= ^m7 ||= upminor 7th ||= C^ || 9/5 || 1017.5963 || -2.2117 || 9/5 ||
|| 35 || 1076.9231 || 8# ||= ^~7 ||= upmid 7th || 41/22 || 1077.7445 || -0.8214 ||  ||
|| 34 || 1046.1538 || 9b ||= v~7 ||= downmid 7th ||= C^^ || 64/35 || 1044.8604 || +1.2934 || 11/6, 20/11 ||
|| 36 || 1107.6923 || 9v (1b) ||= vM7 ||= downmajor 7th || 74/39 || 1108.8614 || -1.1691 ||  ||
|| 35 || 1076.9231 || 8# ||= ^~7 ||= upmid 7th ||= C#vv || 41/22 || 1077.7445 || -0.8214 ||  ||
|| 37 || 1138.4615 || 9 ||= M7 ||= major 7th || 56/29 || 1139.2487 || -0.7872 ||  ||
|| 36 || 1107.6923 || 9v (1b) ||= vM7 ||= downmajor 7th ||= C#v || 74/39 || 1108.8614 || -1.1691 ||  ||
|| 38 || 1169.2308 || 9‡ (1v) ||= v8 ||= down-8ve || 112/57 || 1169.3579 || -0.1271 ||  ||
|| 37 || 1138.4615 || 9 ||= M7 ||= major 7th ||= C# || 56/29 || 1139.2487 || -0.7872 ||  ||
|| 39**··**(or 0) || 1200 || 1 ||= P8 ||= perfect 8ve || 2/1 || 1200 || None ||  ||
|| 38 || 1169.2308 || 9‡ (1v) ||= v8 ||= down-8ve ||= Dv || 112/57 || 1169.3579 || -0.1271 ||  ||
|| 39**··**(or 0) || 1200 || 1 ||= P8 ||= perfect 8ve ||= D || 2/1 || 1200 || None ||  ||
Chords can be named using ups and downs as C upminor, D downmajor seven, etc. See [[xenharmonic/Ups and Downs Notation#Chord%20names%20in%20other%20EDOs|Ups and Downs Notation - Chord names in other EDOs]].
Chords can be named using ups and downs as C upminor, D downmajor seven, etc. See [[xenharmonic/Ups and Downs Notation#Chord%20names%20in%20other%20EDOs|Ups and Downs Notation - Chord names in other EDOs]].


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         &lt;th&gt;&lt;strong&gt;Armodue note&lt;/strong&gt;&lt;br /&gt;
         &lt;th&gt;&lt;strong&gt;Armodue note&lt;/strong&gt;&lt;br /&gt;
&lt;/th&gt;
&lt;/th&gt;
         &lt;th colspan="2"&gt;&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/Ups%20and%20Downs%20Notation"&gt;ups and&lt;/a&gt;&lt;br /&gt;
         &lt;th colspan="3"&gt;&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/Ups%20and%20Downs%20Notation"&gt;ups and &lt;/a&gt;&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/Ups%20and%20Downs%20Notation"&gt;downs&lt;/a&gt;&lt;br /&gt;
&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/Ups%20and%20Downs%20Notation"&gt;downs&lt;/a&gt;&lt;br /&gt;
&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/Ups%20and%20Downs%20Notation"&gt;notation&lt;/a&gt;&lt;br /&gt;
&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/Ups%20and%20Downs%20Notation"&gt;notation&lt;/a&gt;&lt;br /&gt;
&lt;/th&gt;
&lt;/th&gt;
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&lt;/td&gt;
&lt;/td&gt;
         &lt;td style="text-align: center;"&gt;perfect unison&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;perfect unison&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;D&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;1/1&lt;br /&gt;
         &lt;td&gt;1/1&lt;br /&gt;
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&lt;/td&gt;
&lt;/td&gt;
         &lt;td style="text-align: center;"&gt;up unison&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;up unison&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;D^&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;57/56&lt;br /&gt;
         &lt;td&gt;57/56&lt;br /&gt;
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&lt;/td&gt;
&lt;/td&gt;
         &lt;td style="text-align: center;"&gt;minor 2nd&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;minor 2nd&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Eb&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;29/28&lt;br /&gt;
         &lt;td&gt;29/28&lt;br /&gt;
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&lt;/td&gt;
&lt;/td&gt;
         &lt;td style="text-align: center;"&gt;upminor 2nd&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;upminor 2nd&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Eb^&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;39/37&lt;br /&gt;
         &lt;td&gt;39/37&lt;br /&gt;
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&lt;/td&gt;
&lt;/td&gt;
         &lt;td style="text-align: center;"&gt;downmid 2nd&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;downmid 2nd&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Eb^^&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;44/41&lt;br /&gt;
         &lt;td&gt;44/41&lt;br /&gt;
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&lt;/td&gt;
&lt;/td&gt;
         &lt;td style="text-align: center;"&gt;upmid 2nd&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;upmid 2nd&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Evv&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;35/32&lt;br /&gt;
         &lt;td&gt;35/32&lt;br /&gt;
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&lt;/td&gt;
&lt;/td&gt;
         &lt;td style="text-align: center;"&gt;downmajor 2nd&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;downmajor 2nd&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Ev&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;10/9&lt;br /&gt;
         &lt;td&gt;10/9&lt;br /&gt;
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&lt;/td&gt;
&lt;/td&gt;
         &lt;td style="text-align: center;"&gt;major 2nd&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;major 2nd&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;E&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;17/15&lt;br /&gt;
         &lt;td&gt;17/15&lt;br /&gt;
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         &lt;td style="text-align: center;"&gt;upmajor 2nd,&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;upmajor 2nd,&lt;br /&gt;
downminor 3rd&lt;br /&gt;
downminor 3rd&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;E^,&lt;br /&gt;
Fv&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;15/13&lt;br /&gt;
         &lt;td&gt;15/13&lt;br /&gt;
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&lt;/td&gt;
&lt;/td&gt;
         &lt;td style="text-align: center;"&gt;minor 3rd&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;minor 3rd&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;F&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;27/23&lt;br /&gt;
         &lt;td&gt;27/23&lt;br /&gt;
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&lt;/td&gt;
&lt;/td&gt;
         &lt;td style="text-align: center;"&gt;upminor 3rd&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;upminor 3rd&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;F^&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;43/36&lt;br /&gt;
         &lt;td&gt;43/36&lt;br /&gt;
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&lt;/td&gt;
&lt;/td&gt;
         &lt;td style="text-align: center;"&gt;downmid 3rd&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;downmid 3rd&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;F^^&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;17/14&lt;br /&gt;
         &lt;td&gt;17/14&lt;br /&gt;
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&lt;/td&gt;
&lt;/td&gt;
         &lt;td style="text-align: center;"&gt;upmid 3rd&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;upmid 3rd&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;F#vv&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;26/21&lt;br /&gt;
         &lt;td&gt;26/21&lt;br /&gt;
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&lt;/td&gt;
&lt;/td&gt;
         &lt;td style="text-align: center;"&gt;downmajor 3rd&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;downmajor 3rd&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;F#v&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;34/27&lt;br /&gt;
         &lt;td&gt;34/27&lt;br /&gt;
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&lt;/td&gt;
&lt;/td&gt;
         &lt;td style="text-align: center;"&gt;major 3rd&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;major 3rd&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;F#&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;41/32&lt;br /&gt;
         &lt;td&gt;41/32&lt;br /&gt;
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&lt;/td&gt;
&lt;/td&gt;
         &lt;td style="text-align: center;"&gt;down 4th&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;down 4th&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Gv&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;30/23&lt;br /&gt;
         &lt;td&gt;30/23&lt;br /&gt;
Line 543: Line 578:
&lt;/td&gt;
&lt;/td&gt;
         &lt;td style="text-align: center;"&gt;perfect 4th&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;perfect 4th&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;G&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;85/64&lt;br /&gt;
         &lt;td&gt;85/64&lt;br /&gt;
Line 563: Line 600:
&lt;/td&gt;
&lt;/td&gt;
         &lt;td style="text-align: center;"&gt;up 4th&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;up 4th&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;G^&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;23/17&lt;br /&gt;
         &lt;td&gt;23/17&lt;br /&gt;
Line 583: Line 622:
&lt;/td&gt;
&lt;/td&gt;
         &lt;td style="text-align: center;"&gt;double-up 4th&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;double-up 4th&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;G^^&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;11/8&lt;br /&gt;
         &lt;td&gt;11/8&lt;br /&gt;
Line 604: Line 645:
&lt;/td&gt;
&lt;/td&gt;
         &lt;td style="text-align: center;"&gt;double-down aug 4th, updim 5th&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;double-down aug 4th, updim 5th&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;G#vv,&lt;br /&gt;
Ab^&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;7/5&lt;br /&gt;
         &lt;td&gt;7/5&lt;br /&gt;
Line 625: Line 669:
&lt;/td&gt;
&lt;/td&gt;
         &lt;td style="text-align: center;"&gt;downaug 4th, double-up dim 5th&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;downaug 4th, double-up dim 5th&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;G#v,&lt;br /&gt;
Ab^^&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;10/7&lt;br /&gt;
         &lt;td&gt;10/7&lt;br /&gt;
Line 645: Line 692:
&lt;/td&gt;
&lt;/td&gt;
         &lt;td style="text-align: center;"&gt;double-down 5th&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;double-down 5th&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Avv&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;16/11&lt;br /&gt;
         &lt;td&gt;16/11&lt;br /&gt;
Line 665: Line 714:
&lt;/td&gt;
&lt;/td&gt;
         &lt;td style="text-align: center;"&gt;down 5th&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;down 5th&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Av&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;34/23&lt;br /&gt;
         &lt;td&gt;34/23&lt;br /&gt;
Line 685: Line 736:
&lt;/td&gt;
&lt;/td&gt;
         &lt;td style="text-align: center;"&gt;perfect 5th&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;perfect 5th&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;A&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;128/85&lt;br /&gt;
         &lt;td&gt;128/85&lt;br /&gt;
Line 705: Line 758:
&lt;/td&gt;
&lt;/td&gt;
         &lt;td style="text-align: center;"&gt;up 5th&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;up 5th&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;A^&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;23/15&lt;br /&gt;
         &lt;td&gt;23/15&lt;br /&gt;
Line 725: Line 780:
&lt;/td&gt;
&lt;/td&gt;
         &lt;td style="text-align: center;"&gt;minor 6th&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;minor 6th&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Bb&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;64/41&lt;br /&gt;
         &lt;td&gt;64/41&lt;br /&gt;
Line 745: Line 802:
&lt;/td&gt;
&lt;/td&gt;
         &lt;td style="text-align: center;"&gt;upminor 6th&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;upminor 6th&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Bb^&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;27/17&lt;br /&gt;
         &lt;td&gt;27/17&lt;br /&gt;
Line 765: Line 824:
&lt;/td&gt;
&lt;/td&gt;
         &lt;td style="text-align: center;"&gt;downmid 6th&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;downmid 6th&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Bb^^&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;21/13&lt;br /&gt;
         &lt;td&gt;21/13&lt;br /&gt;
Line 785: Line 846:
&lt;/td&gt;
&lt;/td&gt;
         &lt;td style="text-align: center;"&gt;upmid 6th&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;upmid 6th&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Bvv&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;28/17&lt;br /&gt;
         &lt;td&gt;28/17&lt;br /&gt;
Line 805: Line 868:
&lt;/td&gt;
&lt;/td&gt;
         &lt;td style="text-align: center;"&gt;downmajor 6th&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;downmajor 6th&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Bv&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;72/43&lt;br /&gt;
         &lt;td&gt;72/43&lt;br /&gt;
Line 825: Line 890:
&lt;/td&gt;
&lt;/td&gt;
         &lt;td style="text-align: center;"&gt;major 6th&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;major 6th&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;B&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;46/27&lt;br /&gt;
         &lt;td&gt;46/27&lt;br /&gt;
Line 847: Line 914:
         &lt;td style="text-align: center;"&gt;upmajor 6th,&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;upmajor 6th,&lt;br /&gt;
downminor 7th&lt;br /&gt;
downminor 7th&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;B^,&lt;br /&gt;
Cv&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;26/15&lt;br /&gt;
         &lt;td&gt;26/15&lt;br /&gt;
Line 867: Line 937:
&lt;/td&gt;
&lt;/td&gt;
         &lt;td style="text-align: center;"&gt;minor 7th&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;minor 7th&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;C&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;30/17&lt;br /&gt;
         &lt;td&gt;30/17&lt;br /&gt;
Line 887: Line 959:
&lt;/td&gt;
&lt;/td&gt;
         &lt;td style="text-align: center;"&gt;upminor 7th&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;upminor 7th&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;C^&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;9/5&lt;br /&gt;
         &lt;td&gt;9/5&lt;br /&gt;
Line 907: Line 981:
&lt;/td&gt;
&lt;/td&gt;
         &lt;td style="text-align: center;"&gt;downmid 7th&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;downmid 7th&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;C^^&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;64/35&lt;br /&gt;
         &lt;td&gt;64/35&lt;br /&gt;
Line 927: Line 1,003:
&lt;/td&gt;
&lt;/td&gt;
         &lt;td style="text-align: center;"&gt;upmid 7th&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;upmid 7th&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;C#vv&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;41/22&lt;br /&gt;
         &lt;td&gt;41/22&lt;br /&gt;
Line 947: Line 1,025:
&lt;/td&gt;
&lt;/td&gt;
         &lt;td style="text-align: center;"&gt;downmajor 7th&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;downmajor 7th&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;C#v&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;74/39&lt;br /&gt;
         &lt;td&gt;74/39&lt;br /&gt;
Line 967: Line 1,047:
&lt;/td&gt;
&lt;/td&gt;
         &lt;td style="text-align: center;"&gt;major 7th&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;major 7th&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;C#&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;56/29&lt;br /&gt;
         &lt;td&gt;56/29&lt;br /&gt;
Line 987: Line 1,069:
&lt;/td&gt;
&lt;/td&gt;
         &lt;td style="text-align: center;"&gt;down-8ve&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;down-8ve&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Dv&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;112/57&lt;br /&gt;
         &lt;td&gt;112/57&lt;br /&gt;
Line 1,007: Line 1,091:
&lt;/td&gt;
&lt;/td&gt;
         &lt;td style="text-align: center;"&gt;perfect 8ve&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;perfect 8ve&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;D&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;2/1&lt;br /&gt;
         &lt;td&gt;2/1&lt;br /&gt;
Line 1,023: Line 1,109:
&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc2"&gt;&lt;a name="x39 tone equal temperament-Instruments (prototypes):"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;&lt;u&gt;Instruments (prototypes):&lt;/u&gt;&lt;/h2&gt;
&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc2"&gt;&lt;a name="x39 tone equal temperament-Instruments (prototypes):"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;&lt;u&gt;Instruments (prototypes):&lt;/u&gt;&lt;/h2&gt;
  &lt;br /&gt;
  &lt;br /&gt;
&lt;!-- ws:start:WikiTextLocalImageRule:866:&amp;lt;img src=&amp;quot;/file/view/TECLADO%2039-EDD.PNG/390052498/800x467/TECLADO%2039-EDD.PNG&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; style=&amp;quot;height: 467px; width: 800px;&amp;quot; /&amp;gt; --&gt;&lt;img src="/file/view/TECLADO%2039-EDD.PNG/390052498/800x467/TECLADO%2039-EDD.PNG" alt="TECLADO 39-EDD.PNG" title="TECLADO 39-EDD.PNG" style="height: 467px; width: 800px;" /&gt;&lt;!-- ws:end:WikiTextLocalImageRule:866 --&gt;&lt;br /&gt;
&lt;!-- ws:start:WikiTextLocalImageRule:946:&amp;lt;img src=&amp;quot;/file/view/TECLADO%2039-EDD.PNG/390052498/800x467/TECLADO%2039-EDD.PNG&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; style=&amp;quot;height: 467px; width: 800px;&amp;quot; /&amp;gt; --&gt;&lt;img src="/file/view/TECLADO%2039-EDD.PNG/390052498/800x467/TECLADO%2039-EDD.PNG" alt="TECLADO 39-EDD.PNG" title="TECLADO 39-EDD.PNG" style="height: 467px; width: 800px;" /&gt;&lt;!-- ws:end:WikiTextLocalImageRule:946 --&gt;&lt;br /&gt;
&lt;em&gt;An illustrative image of a 39-ED2 keyboard&lt;/em&gt;&lt;br /&gt;
&lt;em&gt;An illustrative image of a 39-ED2 keyboard&lt;/em&gt;&lt;br /&gt;
&lt;!-- ws:start:WikiTextLocalImageRule:867:&amp;lt;img src=&amp;quot;http://xenharmonic.wikispaces.com/file/view/Custom_700mm_5-str_Tricesanonaphonic_Guitar.png/258445130/826x203/Custom_700mm_5-str_Tricesanonaphonic_Guitar.png&amp;quot; alt=&amp;quot;39-EDD fretboard visualization&amp;quot; title=&amp;quot;39-EDD fretboard visualization&amp;quot; style=&amp;quot;height: 203px; width: 826px;&amp;quot; /&amp;gt; --&gt;&lt;table class="captionBox"&gt;&lt;tr&gt;&lt;td class="captionedImage"&gt;&lt;img src="http://xenharmonic.wikispaces.com/file/view/Custom_700mm_5-str_Tricesanonaphonic_Guitar.png/258445130/826x203/Custom_700mm_5-str_Tricesanonaphonic_Guitar.png" alt="Custom_700mm_5-str_Tricesanonaphonic_Guitar.png" title="Custom_700mm_5-str_Tricesanonaphonic_Guitar.png" style="height: 203px; width: 826px;" /&gt;&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td class="imageCaption"&gt;39-EDD fretboard visualization&lt;/td&gt;&lt;/tr&gt;&lt;/table&gt;&lt;!-- ws:end:WikiTextLocalImageRule:867 --&gt;&lt;br /&gt;
&lt;!-- ws:start:WikiTextLocalImageRule:947:&amp;lt;img src=&amp;quot;http://xenharmonic.wikispaces.com/file/view/Custom_700mm_5-str_Tricesanonaphonic_Guitar.png/258445130/826x203/Custom_700mm_5-str_Tricesanonaphonic_Guitar.png&amp;quot; alt=&amp;quot;39-EDD fretboard visualization&amp;quot; title=&amp;quot;39-EDD fretboard visualization&amp;quot; style=&amp;quot;height: 203px; width: 826px;&amp;quot; /&amp;gt; --&gt;&lt;table class="captionBox"&gt;&lt;tr&gt;&lt;td class="captionedImage"&gt;&lt;img src="http://xenharmonic.wikispaces.com/file/view/Custom_700mm_5-str_Tricesanonaphonic_Guitar.png/258445130/826x203/Custom_700mm_5-str_Tricesanonaphonic_Guitar.png" alt="Custom_700mm_5-str_Tricesanonaphonic_Guitar.png" title="Custom_700mm_5-str_Tricesanonaphonic_Guitar.png" style="height: 203px; width: 826px;" /&gt;&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td class="imageCaption"&gt;39-EDD fretboard visualization&lt;/td&gt;&lt;/tr&gt;&lt;/table&gt;&lt;!-- ws:end:WikiTextLocalImageRule:947 --&gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;