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- | : 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> | : 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 | ||~ 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 || | ||
|| 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 || | ||
|| 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]]) || | ||
|| 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]] || | ||
|| 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. | || 9 || fi || A4 || A6, m7 || 568.421 |||| 25/18, 7/5, 18/13 || [[xenharmonic/Liese|Liese]]/[[xenharmonic/Triton|triton]]/lisa || | ||
|| 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 || | ||
|| 12 || lo || A5, d6 || A8, m9 || 757.895 |||| 25/16, 14/9, <span style="line-height: 1.5;">20/13</span> || Sensi || | |||
|| 7 || mo || A3, d4 || A5, d6 || 442.105 | || 13 || le || m6 || M9, m10 || 821.053 |||| 8/5, <span style="line-height: 1.5;">13/8, 21/13</span> || Magic || | ||
|| 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 || | ||
|| 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, <span style="line-height: 1.5;">28/15, 24/13</span> || Negri || | ||
|| 18 || da || A7, d8 || A12, d13 || 1136.84 |||| <span style="line-height: 1.5;">48/25, </span>40/21, 27/14, <span style="line-height: 1.5;">25/13, 52/27</span> || Unicorn/rhinocerus || | |||
|| 10 || se || d5 || M7, d8 || 631.579 | || 19 || do || P8 || P13 || 1200 || 2/1 || || || | ||
|| 11 || sol || P5 || P8 || 694.737 | |||
|| 12 || lo || A5, d6 || A8, m9 || 757.895 | |||
|| 13 || le || m6 || M9, m10 || 821.053 | |||
|| 14 || la || M6 || M10 || 884. | |||
|| 15 || li/ta || A6, d7 || m11, A10 || 947.368 | |||
|| 16 || te || m7 || M11, m12 || 1010.53 | |||
|| 17 || ti || M7 || M12 || 1073.68 | |||
|| 18 || da || A7, d8 || A12, d13 || 1136.84 | |||
*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 | 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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<th>Dodecatonic category<br /> | <th>Dodecatonic category<br /> | ||
</th> | </th> | ||
<th>Cents | <th>Cents<br /> | ||
</th> | </th> | ||
<th colspan="2">Ratios*<br /> | <th colspan="2">Ratios*<br /> | ||
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<td style="text-align: center;">0<br /> | <td style="text-align: center;">0<br /> | ||
</td> | </td> | ||
<td colspan="2">1<br /> | <td colspan="2">1/1<br /> | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
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</td> | </td> | ||
<td>63.1579<br /> | <td>63.1579<br /> | ||
</td> | </td> | ||
<td colspan="2">25/24, 21/20, 28/27, 26/25, 27/26<br /> | <td colspan="2">25/24, 21/20, 28/27, 26/25, 27/26<br /> | ||
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</td> | </td> | ||
<td>126.326<br /> | <td>126.326<br /> | ||
</td> | </td> | ||
<td colspan="2">15/14, 16/15, 13/12, 14/13<br /> | <td colspan="2">15/14, 16/15, 13/12, 14/13<br /> | ||
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</td> | </td> | ||
<td>189.474<br /> | <td>189.474<br /> | ||
</td> | </td> | ||
<td colspan="2">9/8, 10/9<br /> | <td colspan="2">9/8, 10/9<br /> | ||
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</td> | </td> | ||
<td>252.632<br /> | <td>252.632<br /> | ||
</td> | </td> | ||
<td colspan="2">7/6, 8/7, 15/13<br /> | <td colspan="2">7/6, 8/7, 15/13<br /> | ||
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<td>M4, m5<br /> | <td>M4, m5<br /> | ||
</td> | </td> | ||
<td>315. | <td>315.789<br /> | ||
</td> | </td> | ||
<td colspan="2">6/5, 25/21<br /> | <td colspan="2">6/5, 25/21<br /> | ||
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</td> | </td> | ||
<td>378.947<br /> | <td>378.947<br /> | ||
</td> | </td> | ||
<td colspan="2">5/4, 16/13, 26/21<br /> | <td colspan="2">5/4, 16/13, 26/21<br /> | ||
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</td> | </td> | ||
<td>442.105<br /> | <td>442.105<br /> | ||
</td> | </td> | ||
<td colspan="2">32/25, 9/7, 13/10<br /> | <td colspan="2">32/25, 9/7, 13/10<br /> | ||
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</td> | </td> | ||
<td>505.263<br /> | <td>505.263<br /> | ||
</td> | </td> | ||
<td colspan="2">4/3<br /> | <td colspan="2">4/3<br /> | ||
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</td> | </td> | ||
<td>568.421<br /> | <td>568.421<br /> | ||
</td> | </td> | ||
<td colspan="2">25/18, 7/5, 18/13<br /> | <td colspan="2">25/18, 7/5, 18/13<br /> | ||
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</td> | </td> | ||
<td>631.579<br /> | <td>631.579<br /> | ||
</td> | </td> | ||
<td colspan="2">36/25, 10/7, 13/9<br /> | <td colspan="2">36/25, 10/7, 13/9<br /> | ||
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</td> | </td> | ||
<td>694.737<br /> | <td>694.737<br /> | ||
</td> | </td> | ||
<td colspan="2">3/2<br /> | <td colspan="2">3/2<br /> | ||
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</td> | </td> | ||
<td>757.895<br /> | <td>757.895<br /> | ||
</td> | </td> | ||
<td colspan="2">25/16, 14/9, <span style="line-height: 1.5;">20/13</span><br /> | <td colspan="2">25/16, 14/9, <span style="line-height: 1.5;">20/13</span><br /> | ||
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</td> | </td> | ||
<td>821.053<br /> | <td>821.053<br /> | ||
</td> | </td> | ||
<td colspan="2">8/5, <span style="line-height: 1.5;">13/8, 21/13</span><br /> | <td colspan="2">8/5, <span style="line-height: 1.5;">13/8, 21/13</span><br /> | ||
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<td>M10<br /> | <td>M10<br /> | ||
</td> | </td> | ||
<td>884. | <td>884.210<br /> | ||
</td> | </td> | ||
<td colspan="2">5/3, 42/25<br /> | <td colspan="2">5/3, 42/25<br /> | ||
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</td> | </td> | ||
<td>947.368<br /> | <td>947.368<br /> | ||
</td> | </td> | ||
<td colspan="2">7/4, 12/7, 26/15<br /> | <td colspan="2">7/4, 12/7, 26/15<br /> | ||
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</td> | </td> | ||
<td>1010.53<br /> | <td>1010.53<br /> | ||
</td> | </td> | ||
<td colspan="2">9/5, 16/9<br /> | <td colspan="2">9/5, 16/9<br /> | ||
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</td> | </td> | ||
<td>1073.68<br /> | <td>1073.68<br /> | ||
</td> | </td> | ||
<td colspan="2">15/8, 13/7, <span style="line-height: 1.5;">28/15, 24/13</span><br /> | <td colspan="2">15/8, 13/7, <span style="line-height: 1.5;">28/15, 24/13</span><br /> | ||
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</td> | </td> | ||
<td>1136.84<br /> | <td>1136.84<br /> | ||
</td> | </td> | ||
<td colspan="2"><span style="line-height: 1.5;">48/25, </span>40/21, 27/14, <span style="line-height: 1.5;">25/13, 52/27</span><br /> | <td colspan="2"><span style="line-height: 1.5;">48/25, </span>40/21, 27/14, <span style="line-height: 1.5;">25/13, 52/27</span><br /> | ||
</td> | </td> | ||
<td>Unicorn/rhinocerus<br /> | <td>Unicorn/rhinocerus<br /> | ||
</td> | |||
</tr> | |||
<tr> | |||
<td>19<br /> | |||
</td> | |||
<td>do<br /> | |||
</td> | |||
<td>P8<br /> | |||
</td> | |||
<td>P13<br /> | |||
</td> | |||
<td>1200<br /> | |||
</td> | |||
<td>2/1<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
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<!-- ws:start:WikiTextHeadingRule:10:&lt;h1&gt; --><h1 id="toc4"><a name="Chord Names"></a><!-- ws:end:WikiTextHeadingRule:10 -->Chord Names</h1> | <!-- ws:start:WikiTextHeadingRule:10:&lt;h1&gt; --><h1 id="toc4"><a name="Chord Names"></a><!-- ws:end:WikiTextHeadingRule:10 -->Chord Names</h1> | ||
<br /> | <br /> | ||
Chords can be named using conventional methods, expanded to include augmented and diminished 3rds, 6ths | Chords can be named using conventional methods, expanded to include augmented and diminished 2nd, 3rds, 6ths and 7ths.<br /> | ||
<br /> | <br /> | ||
0-6-11 = C E G = C = C major (approximate 4:5:6)<br /> | 0-6-11 = C E G = C = C major (approximate 4:5:6)<br /> | ||
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<!-- ws:start:WikiTextHeadingRule:14:&lt;h2&gt; --><h2 id="toc6"><a name="Chord Names-Commas"></a><!-- ws:end:WikiTextHeadingRule:14 -->Commas</h2> | <!-- ws:start:WikiTextHeadingRule:14:&lt;h2&gt; --><h2 id="toc6"><a name="Chord Names-Commas"></a><!-- ws:end:WikiTextHeadingRule:14 -->Commas</h2> | ||
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19 note per octave Ibanez conversion by Brad Smith (Indianapolis)<br /> | 19 note per octave Ibanez conversion by Brad Smith (Indianapolis)<br /> | ||
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