19edo: Difference between revisions
Wikispaces>csvargas31 **Imported revision 531624902 - Original comment: ** |
Wikispaces>JosephRuhf **Imported revision 537682672 - 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: | : This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2015-01-17 18:35:41 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>537682672</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 ||~ Cents value ||~ Ratios* ||~ Generator for || | ||~ Degrees of 19edo ||~ Solfege ||~ **Dodecatonic notation A** ||~ **<span style="text-align: center;">Dodecatonic notation B</span>** ||~ **<span style="text-align: center;">Dodecatonic notation C</span>** ||~ **<span style="font-size: 13.3333339691162px; text-align: center;">Dodecatonic notation D</span>** ||~ Cents value ||~ Ratios* ||~ Generator for || | ||
|| 0 || do ||= 0 || 1/1 || || | || 0 || do || C || C || C || C ||= 0 || 1/1 || || | ||
|| 1 || di || 63.1579 || 25/24, 26/25, 28/27 || Unicorn/rhinocerus || | || 1 || di || Ç || C#/Δb || <span style="font-size: 13.3333339691162px;">Ç</span> || <span style="font-size: 13.3333339691162px;">C#/Δb</span> || 63.1579 || 25/24, 26/25, 27/26, 28/27 || Unicorn/rhinocerus || | ||
|| 2 || ra || 126.326 || 13/12, 14/13, 15/14, 16/15 || [[xenharmonic/Negri|Negri]] || | || 2 || ra || Ç#/Db || Δ || <span style="font-size: 13.3333339691162px;">Ç#/Db</span> || <span style="font-size: 13.3333339691162px;">Δ</span> || 126.326 || 13/12, 14/13, 15/14, 16/15 || [[xenharmonic/Negri|Negri]] || | ||
|| 3 || re || 189.474 || 9/8, 10/9 || Deutone (2-meantone) / spell || | || 3 || re || D || D || D || D || 189.474 || 9/8, 10/9 || Deutone (2-meantone) / spell || | ||
|| 4 || ri/ma || 252.632 || 7/6, 8/7, 15/13 || [[xenharmonic/Godzilla|Godzilla]] || | || 4 || ri/ma || Þ || D#/εb || <span style="font-size: 13.3333339691162px;">Þ</span> || <span style="font-size: 13.3333339691162px;">D#/εb</span> || 252.632 || 7/6, 8/7, 15/13 || [[xenharmonic/Godzilla|Godzilla]] || | ||
|| 5 || me || 315.789 || 6/5 || [[xenharmonic/Kleismic|Kleismic]] ([[xenharmonic/hanson|hanson]], [[xenharmonic/keemun|keemun]], [[xenharmonic/catakleismic|catakleismic]]) || | || 5 || me || Þ#/Eb || ε || <span style="font-size: 13.3333339691162px;">Þ#/Eb</span> || <span style="font-size: 13.3333339691162px;">ε</span> || 315.789 || 6/5 || [[xenharmonic/Kleismic|Kleismic]] ([[xenharmonic/hanson|hanson]], [[xenharmonic/keemun|keemun]], [[xenharmonic/catakleismic|catakleismic]]) || | ||
|| 6 || mi || 378.947 || 5/4, 16/13 || [[xenharmonic/Magic|Magic]]/charisma/glamour || | || 6 || mi || E || E || E || E || 378.947 || 5/4, 16/13 || [[xenharmonic/Magic|Magic]]/charisma/glamour || | ||
|| 7 || mo || 442.105 || 9/7, 13/10 || [[xenharmonic/Sensi|Sensi]] || | || 7 || mo || E#/Fb || E#/Fb || <span style="font-size: 13.3333339691162px;">E#/Fb</span> || E#/Fb || 442.105 || 9/7, 13/10 || [[xenharmonic/Sensi|Sensi]] || | ||
|| 8 || fa || 505.263 || 4/3 || [[xenharmonic/Meantone|Meantone]]/[[xenharmonic/flattone|flattone]]/[[xenharmonic/meanennedecal|meanenneadecal]]/[[xenharmonic/meanpop|meanpop]] || | || 8 || fa || F || F || F || F || 505.263 || 4/3 || [[xenharmonic/Meantone|Meantone]]/[[xenharmonic/flattone|flattone]]/[[xenharmonic/meanennedecal|meanenneadecal]]/[[xenharmonic/meanpop|meanpop]] || | ||
|| 9 || fi || 568.421 || 7/5, 18/13 || [[xenharmonic/Liese|Liese]]/[[xenharmonic/Triton|triton]]/lisa || | || 9 || fi || ϕ || ϕ || <span style="font-size: 13.3333339691162px;">ϕ</span> || F#/Γb || 568.421 || 7/5, 18/13 || [[xenharmonic/Liese|Liese]]/[[xenharmonic/Triton|triton]]/lisa || | ||
|| 10 || se || 631.579 || 10/7, 13/9 || Liese/triton/lisa || | || 10 || se || ϕ#/Gb || <span style="font-size: 12.8000001907349px;">ϕ#/Gb</span> || <span style="font-size: 13.3333339691162px;">ϕ#/Gb</span> || Γ || 631.579 || 10/7, 13/9 || Liese/triton/lisa || | ||
|| 11 || sol || 694.737 || 3/2 || Meantone || | || 11 || sol || G || G || G || G || 694.737 || 3/2 || Meantone || | ||
|| 12 || lo || 757.895 || 14/9, 20/13 || Sensi || | || 12 || lo || Z || G#/αb || Z || <span style="font-size: 13.3333339691162px;">G#/αb</span> || 757.895 || 14/9, 20/13 || Sensi || | ||
|| 13 || le || 821.053 || 8/5, 13/8 || Magic || | || 13 || le || Z#/Ab || α || <span style="font-size: 13.3333339691162px;">Z#/Ab</span> || <span style="font-size: 13.3333339691162px;">α</span> || 821.053 || 8/5, 13/8 || Magic || | ||
|| 14 || la || 884.211 || 5/3 || Kleismic (hanson, keemun, catakleismic) || | || 14 || la || A || A || A || A || 884.211 || 5/3 || Kleismic (hanson, keemun, catakleismic) || | ||
|| 15 || li/ta || 947.368 || 7/4, 12/7, 26/15 || Godzilla || | || 15 || li/ta || Æ || A#/βb, A#/Bb || <span style="font-size: 13.3333339691162px;">A#/βb, A#/Bb</span> || <span style="font-size: 13.3333339691162px;">A#/βb, A#/Bb</span> || 947.368 || 7/4, 12/7, 26/15 || Godzilla || | ||
|| 16 || te || 1010.53 || 9/5, 16/9 || Deutone / spell || | || 16 || te || Æ#/Bb || β, B || <span style="font-size: 13.3333339691162px;">β, B</span> || <span style="font-size: 13.3333339691162px;">β, B</span> || 1010.53 || 9/5, 16/9 || Deutone / spell || | ||
|| 17 || ti || 1073.68 || 13/7, 15/8, 24/13, 28/15 || Negri || | || 17 || ti || B || B, H || <span style="font-size: 13.3333339691162px;">B, H</span> || <span style="font-size: 13.3333339691162px;">B, H</span> || 1073.68 || 13/7, 15/8, 24/13, 28/15 || Negri || | ||
|| 18 || da || 1136.84 || | || 18 || da || B#/Cb || B#, H#/Cb || <span style="font-size: 13.3333339691162px;">B#, H#/Cb</span> || <span style="font-size: 13.3333339691162px;">B#, H#/Cb</span> || 1136.84 || 48/25, 25/13, 52/27, 27/14 || 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. | ||
| Line 214: | Line 214: | ||
</th> | </th> | ||
<th>Solfege<br /> | <th>Solfege<br /> | ||
</th> | |||
<th><strong>Dodecatonic notation A</strong><br /> | |||
</th> | |||
<th><strong><span style="text-align: center;">Dodecatonic notation B</span></strong><br /> | |||
</th> | |||
<th><strong><span style="text-align: center;">Dodecatonic notation C</span></strong><br /> | |||
</th> | |||
<th><strong><span style="font-size: 13.3333339691162px; text-align: center;">Dodecatonic notation D</span></strong><br /> | |||
</th> | </th> | ||
<th>Cents value<br /> | <th>Cents value<br /> | ||
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</td> | </td> | ||
<td>do<br /> | <td>do<br /> | ||
</td> | |||
<td>C<br /> | |||
</td> | |||
<td>C<br /> | |||
</td> | |||
<td>C<br /> | |||
</td> | |||
<td>C<br /> | |||
</td> | </td> | ||
<td style="text-align: center;">0<br /> | <td style="text-align: center;">0<br /> | ||
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</td> | </td> | ||
<td>di<br /> | <td>di<br /> | ||
</td> | |||
<td>Ç<br /> | |||
</td> | |||
<td>C#/Δb<br /> | |||
</td> | |||
<td><span style="font-size: 13.3333339691162px;">Ç</span><br /> | |||
</td> | |||
<td><span style="font-size: 13.3333339691162px;">C#/Δb</span><br /> | |||
</td> | </td> | ||
<td>63.1579<br /> | <td>63.1579<br /> | ||
</td> | </td> | ||
<td>25/24, 26/25, 28/27<br /> | <td>25/24, 26/25, 27/26, 28/27<br /> | ||
</td> | </td> | ||
<td>Unicorn/rhinocerus<br /> | <td>Unicorn/rhinocerus<br /> | ||
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</td> | </td> | ||
<td>ra<br /> | <td>ra<br /> | ||
</td> | |||
<td>Ç#/Db<br /> | |||
</td> | |||
<td>Δ<br /> | |||
</td> | |||
<td><span style="font-size: 13.3333339691162px;">Ç#/Db</span><br /> | |||
</td> | |||
<td><span style="font-size: 13.3333339691162px;">Δ</span><br /> | |||
</td> | </td> | ||
<td>126.326<br /> | <td>126.326<br /> | ||
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</td> | </td> | ||
<td>re<br /> | <td>re<br /> | ||
</td> | |||
<td>D<br /> | |||
</td> | |||
<td>D<br /> | |||
</td> | |||
<td>D<br /> | |||
</td> | |||
<td>D<br /> | |||
</td> | </td> | ||
<td>189.474<br /> | <td>189.474<br /> | ||
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</td> | </td> | ||
<td>ri/ma<br /> | <td>ri/ma<br /> | ||
</td> | |||
<td>Þ<br /> | |||
</td> | |||
<td>D#/εb<br /> | |||
</td> | |||
<td><span style="font-size: 13.3333339691162px;">Þ</span><br /> | |||
</td> | |||
<td><span style="font-size: 13.3333339691162px;">D#/εb</span><br /> | |||
</td> | </td> | ||
<td>252.632<br /> | <td>252.632<br /> | ||
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</td> | </td> | ||
<td>me<br /> | <td>me<br /> | ||
</td> | |||
<td>Þ#/Eb<br /> | |||
</td> | |||
<td>ε<br /> | |||
</td> | |||
<td><span style="font-size: 13.3333339691162px;">Þ#/Eb</span><br /> | |||
</td> | |||
<td><span style="font-size: 13.3333339691162px;">ε</span><br /> | |||
</td> | </td> | ||
<td>315.789<br /> | <td>315.789<br /> | ||
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</td> | </td> | ||
<td>mi<br /> | <td>mi<br /> | ||
</td> | |||
<td>E<br /> | |||
</td> | |||
<td>E<br /> | |||
</td> | |||
<td>E<br /> | |||
</td> | |||
<td>E<br /> | |||
</td> | </td> | ||
<td>378.947<br /> | <td>378.947<br /> | ||
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</td> | </td> | ||
<td>mo<br /> | <td>mo<br /> | ||
</td> | |||
<td>E#/Fb<br /> | |||
</td> | |||
<td>E#/Fb<br /> | |||
</td> | |||
<td><span style="font-size: 13.3333339691162px;">E#/Fb</span><br /> | |||
</td> | |||
<td>E#/Fb<br /> | |||
</td> | </td> | ||
<td>442.105<br /> | <td>442.105<br /> | ||
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</td> | </td> | ||
<td>fa<br /> | <td>fa<br /> | ||
</td> | |||
<td>F<br /> | |||
</td> | |||
<td>F<br /> | |||
</td> | |||
<td>F<br /> | |||
</td> | |||
<td>F<br /> | |||
</td> | </td> | ||
<td>505.263<br /> | <td>505.263<br /> | ||
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</td> | </td> | ||
<td>fi<br /> | <td>fi<br /> | ||
</td> | |||
<td>ϕ<br /> | |||
</td> | |||
<td>ϕ<br /> | |||
</td> | |||
<td><span style="font-size: 13.3333339691162px;">ϕ</span><br /> | |||
</td> | |||
<td>F#/Γb<br /> | |||
</td> | </td> | ||
<td>568.421<br /> | <td>568.421<br /> | ||
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</td> | </td> | ||
<td>se<br /> | <td>se<br /> | ||
</td> | |||
<td>ϕ#/Gb<br /> | |||
</td> | |||
<td><span style="font-size: 12.8000001907349px;">ϕ#/Gb</span><br /> | |||
</td> | |||
<td><span style="font-size: 13.3333339691162px;">ϕ#/Gb</span><br /> | |||
</td> | |||
<td>Γ<br /> | |||
</td> | </td> | ||
<td>631.579<br /> | <td>631.579<br /> | ||
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</td> | </td> | ||
<td>sol<br /> | <td>sol<br /> | ||
</td> | |||
<td>G<br /> | |||
</td> | |||
<td>G<br /> | |||
</td> | |||
<td>G<br /> | |||
</td> | |||
<td>G<br /> | |||
</td> | </td> | ||
<td>694.737<br /> | <td>694.737<br /> | ||
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</td> | </td> | ||
<td>lo<br /> | <td>lo<br /> | ||
</td> | |||
<td>Z<br /> | |||
</td> | |||
<td>G#/αb<br /> | |||
</td> | |||
<td>Z<br /> | |||
</td> | |||
<td><span style="font-size: 13.3333339691162px;">G#/αb</span><br /> | |||
</td> | </td> | ||
<td>757.895<br /> | <td>757.895<br /> | ||
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</td> | </td> | ||
<td>le<br /> | <td>le<br /> | ||
</td> | |||
<td>Z#/Ab<br /> | |||
</td> | |||
<td>α<br /> | |||
</td> | |||
<td><span style="font-size: 13.3333339691162px;">Z#/Ab</span><br /> | |||
</td> | |||
<td><span style="font-size: 13.3333339691162px;">α</span><br /> | |||
</td> | </td> | ||
<td>821.053<br /> | <td>821.053<br /> | ||
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</td> | </td> | ||
<td>la<br /> | <td>la<br /> | ||
</td> | |||
<td>A<br /> | |||
</td> | |||
<td>A<br /> | |||
</td> | |||
<td>A<br /> | |||
</td> | |||
<td>A<br /> | |||
</td> | </td> | ||
<td>884.211<br /> | <td>884.211<br /> | ||
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</td> | </td> | ||
<td>li/ta<br /> | <td>li/ta<br /> | ||
</td> | |||
<td>Æ<br /> | |||
</td> | |||
<td>A#/βb, A#/Bb<br /> | |||
</td> | |||
<td><span style="font-size: 13.3333339691162px;">A#/βb, A#/Bb</span><br /> | |||
</td> | |||
<td><span style="font-size: 13.3333339691162px;">A#/βb, A#/Bb</span><br /> | |||
</td> | </td> | ||
<td>947.368<br /> | <td>947.368<br /> | ||
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</td> | </td> | ||
<td>te<br /> | <td>te<br /> | ||
</td> | |||
<td>Æ#/Bb<br /> | |||
</td> | |||
<td>β, B<br /> | |||
</td> | |||
<td><span style="font-size: 13.3333339691162px;">β, B</span><br /> | |||
</td> | |||
<td><span style="font-size: 13.3333339691162px;">β, B</span><br /> | |||
</td> | </td> | ||
<td>1010.53<br /> | <td>1010.53<br /> | ||
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</td> | </td> | ||
<td>ti<br /> | <td>ti<br /> | ||
</td> | |||
<td>B<br /> | |||
</td> | |||
<td>B, H<br /> | |||
</td> | |||
<td><span style="font-size: 13.3333339691162px;">B, H</span><br /> | |||
</td> | |||
<td><span style="font-size: 13.3333339691162px;">B, H</span><br /> | |||
</td> | </td> | ||
<td>1073.68<br /> | <td>1073.68<br /> | ||
| Line 442: | Line 594: | ||
</td> | </td> | ||
<td>da<br /> | <td>da<br /> | ||
</td> | |||
<td>B#/Cb<br /> | |||
</td> | |||
<td>B#, H#/Cb<br /> | |||
</td> | |||
<td><span style="font-size: 13.3333339691162px;">B#, H#/Cb</span><br /> | |||
</td> | |||
<td><span style="font-size: 13.3333339691162px;">B#, H#/Cb</span><br /> | |||
</td> | </td> | ||
<td>1136.84<br /> | <td>1136.84<br /> | ||
</td> | </td> | ||
<td><br /> | <td>48/25, 25/13, 52/27, 27/14<br /> | ||
</td> | </td> | ||
<td>Unicorn/rhinocerus<br /> | <td>Unicorn/rhinocerus<br /> | ||
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<br /> | <br /> | ||
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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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