19edo: Difference between revisions

Wikispaces>TallKite
**Imported revision 602054164 - Original comment: **
Wikispaces>TallKite
**Imported revision 602737592 - 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>2016-12-13 07:19:28 UTC</tt>.<br>
: This revision was by author [[User:TallKite|TallKite]] and made on <tt>2016-12-22 03:28:14 UTC</tt>.<br>
: The original revision id was <tt>602054164</tt>.<br>
: The original revision id was <tt>602737592</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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Since 19 is prime, all rank two temperaments in 19edo have one period per octave. Therefore you can make a correspondence between intervals and the linear temperaments they generate.
Since 19 is prime, all rank two temperaments in 19edo have one period per octave. Therefore you can make a correspondence between intervals and the linear temperaments they generate.
||~ Degrees of 19edo ||~ Solfege ||~ Diatonic Category ||~ Dodecatonic category ||~ Cents coarse/fine ||||~ Ratios* ||~ Generator for ||
||~ Degrees of 19edo ||~ Solfege ||~ Diatonic Category ||~ Dodecatonic category ||~ Cents ||||~ Ratios* ||~ Generator for ||
|| 0 || do || P1 || P1 ||= 0 |||| 1 ||  ||
|| 0 || do || P1 || P1 ||= 0 |||| 1/1 ||  ||
|| 1 || di || A1, d2 || A1, m2 || 63.1579
|| 1 || di || A1, d2 || A1, m2 || 63.1579 |||| 25/24, 21/20, 28/27, 26/25, 27/26 || Unicorn/rhinocerus ||
75.7895 |||| 25/24, 21/20, 28/27, 26/25, 27/26 || Unicorn/rhinocerus ||
|| 2 || ra || m2 || M2, m3 || 126.326 |||| 15/14, 16/15, 13/12, 14/13 || [[xenharmonic/Negri|Negri]] ||
|| 2 || ra || m2 || M2, m3 || 126.326
|| 3 || re || M2 || M3 || 189.474 |||| 9/8, 10/9 || Deutone (2-meantone) / spell ||
151.579 |||| 15/14, 16/15, 13/12, 14/13 || [[xenharmonic/Negri|Negri]] ||
|| 4 || ri/ma || A2, d3 || m4, a3 || 252.632 |||| 7/6, 8/7, 15/13 || [[xenharmonic/Godzilla|Godzilla]] ||
|| 3 || re || M2 || M3 || 189.474
|| 5 || me || m3 || M4, m5 || 315.789 |||| 6/5, 25/21 || [[xenharmonic/Kleismic|Kleismic]] ([[xenharmonic/hanson|hanson]], [[xenharmonic/keemun|keemun]], [[xenharmonic/catakleismic|catakleismic]]) ||
227.368 |||| 9/8, 10/9 || Deutone (2-meantone) / spell ||
|| 6 || mi || M3 || M5 || 378.947 |||| 5/4, 16/13, 26/21 || [[xenharmonic/Magic|Magic]]/charisma/glamour ||
|| 4 || ri/ma || A2, d3 || m4, a3 || 252.632
|| 7 || mo || A3, d4 || A5, d6 || 442.105 |||| 32/25, 9/7, 13/10 || [[xenharmonic/Sensi|Sensi]] ||
303.158 |||| 7/6, 8/7, 15/13 || [[xenharmonic/Godzilla|Godzilla]] ||
|| 8 || fa || P4 || P6 || 505.263 |||| 4/3 || [[xenharmonic/Meantone|Meantone]]/[[xenharmonic/flattone|flattone]]/[[xenharmonic/meanennedecal|meanenneadecal]]/[[xenharmonic/meanpop|meanpop]] ||
|| 5 || me || m3 || M4, m5 || 315.7895/1
|| 9 || fi || A4 || A6, m7 || 568.421 |||| 25/18, 7/5, 18/13 || [[xenharmonic/Liese|Liese]]/[[xenharmonic/Triton|triton]]/lisa ||
378.947 |||| 6/5, 25/21 || [[xenharmonic/Kleismic|Kleismic]] ([[xenharmonic/hanson|hanson]], [[xenharmonic/keemun|keemun]], [[xenharmonic/catakleismic|catakleismic]]) ||
|| 10 || se || d5 || M7, d8 || 631.579 |||| 36/25, 10/7, 13/9 || Liese/triton/lisa ||
|| 6 || mi || M3 || M5 || 378.947
|| 11 || sol || P5 || P8 || 694.737 |||| 3/2 || Meantone ||
454.737 |||| 5/4, 16/13, 26/21 || [[xenharmonic/Magic|Magic]]/charisma/glamour ||
|| 12 || lo || A5, d6 || A8, m9 || 757.895 |||| 25/16, 14/9, &lt;span style="line-height: 1.5;"&gt;20/13&lt;/span&gt; || Sensi ||
|| 7 || mo || A3, d4 || A5, d6 || 442.105
|| 13 || le || m6 || M9, m10 || 821.053 |||| 8/5, &lt;span style="line-height: 1.5;"&gt;13/8, 21/13&lt;/span&gt; || Magic ||
530.526 |||| 32/25, 9/7, 13/10 || [[xenharmonic/Sensi|Sensi]] ||
|| 14 || la || M6 || M10 || 884.210 |||| 5/3, 42/25 || Kleismic (hanson, keemun, catakleismic) ||
|| 8 || fa || P4 || P6 || 505.263
|| 15 || li/ta || A6, d7 || m11, A10 || 947.368 |||| 7/4, 12/7, 26/15 || Godzilla ||
606.316 |||| 4/3 || [[xenharmonic/Meantone|Meantone]]/[[xenharmonic/flattone|flattone]]/[[xenharmonic/meanennedecal|meanenneadecal]]/[[xenharmonic/meanpop|meanpop]] ||
|| 16 || te || m7 || M11, m12 || 1010.53 |||| 9/5, 16/9 || Deutone / spell ||
|| 9 || fi || A4 || A6, m7 || 568.421
|| 17 || ti || M7 || M12 || 1073.68 |||| 15/8, 13/7, &lt;span style="line-height: 1.5;"&gt;28/15, 24/13&lt;/span&gt; || Negri ||
682.105 |||| 25/18, 7/5, 18/13 || [[xenharmonic/Liese|Liese]]/[[xenharmonic/Triton|triton]]/lisa ||
|| 18 || da || A7, d8 || A12, d13 || 1136.84 |||| &lt;span style="line-height: 1.5;"&gt;48/25, &lt;/span&gt;40/21, 27/14, &lt;span style="line-height: 1.5;"&gt;25/13, 52/27&lt;/span&gt; || Unicorn/rhinocerus ||
|| 10 || se || d5 || M7, d8 || 631.579
|| 19 || do || P8 || P13 || 1200 || 2/1 ||  ||  ||
757.895 |||| 36/25, 10/7, 13/9 || Liese/triton/lisa ||
|| 11 || sol || P5 || P8 || 694.737
833.684 |||| 3/2 || Meantone ||
|| 12 || lo || A5, d6 || A8, m9 || 757.895
909.484 |||| 25/16, 14/9, &lt;span style="line-height: 1.5;"&gt;20/13&lt;/span&gt; || Sensi ||
|| 13 || le || m6 || M9, m10 || 821.053
985.263 |||| 8/5, &lt;span style="line-height: 1.5;"&gt;13/8, 21/13&lt;/span&gt; || Magic ||
|| 14 || la || M6 || M10 || 884.2105/1
1061.05 |||| 5/3, 42/25 || Kleismic (hanson, keemun, catakleismic) ||
|| 15 || li/ta || A6, d7 || m11, A10 || 947.368
1136.84 |||| 7/4, 12/7, 26/15 || Godzilla ||
|| 16 || te || m7 || M11, m12 || 1010.53
1212.63 |||| 9/5, 16/9 || Deutone / spell ||
|| 17 || ti || M7 || M12 || 1073.68
1288.42 |||| 15/8, 13/7, &lt;span style="line-height: 1.5;"&gt;28/15, 24/13&lt;/span&gt; || Negri ||
|| 18 || da || A7, d8 || A12, d13 || 1136.84
1364.21 |||| &lt;span style="line-height: 1.5;"&gt;48/25, &lt;/span&gt;40/21, 27/14, &lt;span style="line-height: 1.5;"&gt;25/13, 52/27&lt;/span&gt; || Unicorn/rhinocerus ||
*based on treating 19-EDO as a 2.3.5.7.13 subgroup temperament; other approaches are possible.
*based on treating 19-EDO as a 2.3.5.7.13 subgroup temperament; other approaches are possible.


=Chord Names=  
=Chord Names=  


Chords can be named using conventional methods, expanded to include augmented and diminished 3rds, 6ths, 7ths, etc.
Chords can be named using conventional methods, expanded to include augmented and diminished 2nd, 3rds, 6ths and 7ths.


0-6-11 = C E G = C = C major (approximate 4:5:6)
0-6-11 = C E G = C = C major (approximate 4:5:6)
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         &lt;th&gt;Dodecatonic category&lt;br /&gt;
         &lt;th&gt;Dodecatonic category&lt;br /&gt;
&lt;/th&gt;
&lt;/th&gt;
         &lt;th&gt;Cents coarse/fine&lt;br /&gt;
         &lt;th&gt;Cents&lt;br /&gt;
&lt;/th&gt;
&lt;/th&gt;
         &lt;th colspan="2"&gt;Ratios*&lt;br /&gt;
         &lt;th colspan="2"&gt;Ratios*&lt;br /&gt;
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         &lt;td style="text-align: center;"&gt;0&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;0&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td colspan="2"&gt;1&lt;br /&gt;
         &lt;td colspan="2"&gt;1/1&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;br /&gt;
         &lt;td&gt;&lt;br /&gt;
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&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;63.1579&lt;br /&gt;
         &lt;td&gt;63.1579&lt;br /&gt;
75.7895&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td colspan="2"&gt;25/24, 21/20, 28/27, 26/25, 27/26&lt;br /&gt;
         &lt;td colspan="2"&gt;25/24, 21/20, 28/27, 26/25, 27/26&lt;br /&gt;
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&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;126.326&lt;br /&gt;
         &lt;td&gt;126.326&lt;br /&gt;
151.579&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td colspan="2"&gt;15/14, 16/15, 13/12, 14/13&lt;br /&gt;
         &lt;td colspan="2"&gt;15/14, 16/15, 13/12, 14/13&lt;br /&gt;
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&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;189.474&lt;br /&gt;
         &lt;td&gt;189.474&lt;br /&gt;
227.368&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td colspan="2"&gt;9/8, 10/9&lt;br /&gt;
         &lt;td colspan="2"&gt;9/8, 10/9&lt;br /&gt;
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&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;252.632&lt;br /&gt;
         &lt;td&gt;252.632&lt;br /&gt;
303.158&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td colspan="2"&gt;7/6, 8/7, 15/13&lt;br /&gt;
         &lt;td colspan="2"&gt;7/6, 8/7, 15/13&lt;br /&gt;
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         &lt;td&gt;M4, m5&lt;br /&gt;
         &lt;td&gt;M4, m5&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;315.7895/1&lt;br /&gt;
         &lt;td&gt;315.789&lt;br /&gt;
378.947&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td colspan="2"&gt;6/5, 25/21&lt;br /&gt;
         &lt;td colspan="2"&gt;6/5, 25/21&lt;br /&gt;
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&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;378.947&lt;br /&gt;
         &lt;td&gt;378.947&lt;br /&gt;
454.737&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td colspan="2"&gt;5/4, 16/13, 26/21&lt;br /&gt;
         &lt;td colspan="2"&gt;5/4, 16/13, 26/21&lt;br /&gt;
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&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;442.105&lt;br /&gt;
         &lt;td&gt;442.105&lt;br /&gt;
530.526&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td colspan="2"&gt;32/25, 9/7, 13/10&lt;br /&gt;
         &lt;td colspan="2"&gt;32/25, 9/7, 13/10&lt;br /&gt;
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&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;505.263&lt;br /&gt;
         &lt;td&gt;505.263&lt;br /&gt;
606.316&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td colspan="2"&gt;4/3&lt;br /&gt;
         &lt;td colspan="2"&gt;4/3&lt;br /&gt;
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&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;568.421&lt;br /&gt;
         &lt;td&gt;568.421&lt;br /&gt;
682.105&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td colspan="2"&gt;25/18, 7/5, 18/13&lt;br /&gt;
         &lt;td colspan="2"&gt;25/18, 7/5, 18/13&lt;br /&gt;
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&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;631.579&lt;br /&gt;
         &lt;td&gt;631.579&lt;br /&gt;
757.895&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td colspan="2"&gt;36/25, 10/7, 13/9&lt;br /&gt;
         &lt;td colspan="2"&gt;36/25, 10/7, 13/9&lt;br /&gt;
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&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;694.737&lt;br /&gt;
         &lt;td&gt;694.737&lt;br /&gt;
833.684&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td colspan="2"&gt;3/2&lt;br /&gt;
         &lt;td colspan="2"&gt;3/2&lt;br /&gt;
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&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;757.895&lt;br /&gt;
         &lt;td&gt;757.895&lt;br /&gt;
909.484&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td colspan="2"&gt;25/16, 14/9, &lt;span style="line-height: 1.5;"&gt;20/13&lt;/span&gt;&lt;br /&gt;
         &lt;td colspan="2"&gt;25/16, 14/9, &lt;span style="line-height: 1.5;"&gt;20/13&lt;/span&gt;&lt;br /&gt;
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&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;821.053&lt;br /&gt;
         &lt;td&gt;821.053&lt;br /&gt;
985.263&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td colspan="2"&gt;8/5, &lt;span style="line-height: 1.5;"&gt;13/8, 21/13&lt;/span&gt;&lt;br /&gt;
         &lt;td colspan="2"&gt;8/5, &lt;span style="line-height: 1.5;"&gt;13/8, 21/13&lt;/span&gt;&lt;br /&gt;
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         &lt;td&gt;M10&lt;br /&gt;
         &lt;td&gt;M10&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;884.2105/1&lt;br /&gt;
         &lt;td&gt;884.210&lt;br /&gt;
1061.05&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td colspan="2"&gt;5/3, 42/25&lt;br /&gt;
         &lt;td colspan="2"&gt;5/3, 42/25&lt;br /&gt;
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&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;947.368&lt;br /&gt;
         &lt;td&gt;947.368&lt;br /&gt;
1136.84&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td colspan="2"&gt;7/4, 12/7, 26/15&lt;br /&gt;
         &lt;td colspan="2"&gt;7/4, 12/7, 26/15&lt;br /&gt;
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&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;1010.53&lt;br /&gt;
         &lt;td&gt;1010.53&lt;br /&gt;
1212.63&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td colspan="2"&gt;9/5, 16/9&lt;br /&gt;
         &lt;td colspan="2"&gt;9/5, 16/9&lt;br /&gt;
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&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;1073.68&lt;br /&gt;
         &lt;td&gt;1073.68&lt;br /&gt;
1288.42&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td colspan="2"&gt;15/8, 13/7, &lt;span style="line-height: 1.5;"&gt;28/15, 24/13&lt;/span&gt;&lt;br /&gt;
         &lt;td colspan="2"&gt;15/8, 13/7, &lt;span style="line-height: 1.5;"&gt;28/15, 24/13&lt;/span&gt;&lt;br /&gt;
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&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;1136.84&lt;br /&gt;
         &lt;td&gt;1136.84&lt;br /&gt;
1364.21&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td colspan="2"&gt;&lt;span style="line-height: 1.5;"&gt;48/25, &lt;/span&gt;40/21, 27/14, &lt;span style="line-height: 1.5;"&gt;25/13, 52/27&lt;/span&gt;&lt;br /&gt;
         &lt;td colspan="2"&gt;&lt;span style="line-height: 1.5;"&gt;48/25, &lt;/span&gt;40/21, 27/14, &lt;span style="line-height: 1.5;"&gt;25/13, 52/27&lt;/span&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;Unicorn/rhinocerus&lt;br /&gt;
         &lt;td&gt;Unicorn/rhinocerus&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;19&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;do&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;P8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;P13&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1200&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;2/1&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
     &lt;/tr&gt;
     &lt;/tr&gt;
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&lt;!-- ws:start:WikiTextHeadingRule:10:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc4"&gt;&lt;a name="Chord Names"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:10 --&gt;Chord Names&lt;/h1&gt;
&lt;!-- ws:start:WikiTextHeadingRule:10:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc4"&gt;&lt;a name="Chord Names"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:10 --&gt;Chord Names&lt;/h1&gt;
  &lt;br /&gt;
  &lt;br /&gt;
Chords can be named using conventional methods, expanded to include augmented and diminished 3rds, 6ths, 7ths, etc.&lt;br /&gt;
Chords can be named using conventional methods, expanded to include augmented and diminished 2nd, 3rds, 6ths and 7ths.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
0-6-11 = C E G = C = C major (approximate 4:5:6)&lt;br /&gt;
0-6-11 = C E G = C = C major (approximate 4:5:6)&lt;br /&gt;
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&lt;br /&gt;
&lt;br /&gt;
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  19 note per octave Ibanez conversion by Brad Smith (Indianapolis)&lt;br /&gt;
  19 note per octave Ibanez conversion by Brad Smith (Indianapolis)&lt;br /&gt;
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