13edo: Difference between revisions
Wikispaces>xenwolf **Imported revision 602739096 - Original comment: table formatting, unified precision of cent values** |
Wikispaces>TallKite **Imported revision 602809238 - 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:TallKite|TallKite]] and made on <tt>2016-12-25 21:54:47 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>602809238</tt>.<br> | ||
: The revision comment was: <tt> | : 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> | ||
<h4>Original Wikitext content:</h4> | <h4>Original Wikitext content:</h4> | ||
| Line 19: | Line 19: | ||
||= **Degree** ||= **Cents** ||= **Approximated 21-limit Ratios** * ||= **Erv Wilson** ||= **Archaeotonic** ||= **Oneirotonic** ||= **[[26edo]] names** ||= **Kentaku** || | ||= **Degree** ||= **Cents** ||= **Approximated 21-limit Ratios** * ||= **Erv Wilson** ||= **Archaeotonic** ||= **Oneirotonic** ||= **[[26edo]] names** ||= **Kentaku** || | ||
||= 0 ||= 0 ||= 1/1 ||= H || C || C || C || J || | ||= 0 ||= 0 ||= 1/1 ||= H ||= C ||= C ||= C ||= J || | ||
||= 1 || | ||= 1 ||= 92.31 ||= 17/16, 18/17, 19/18, 20/19, 21/20, 22/21 ||= <span style="background-color: #ffffff; color: #333333; font-family: Verdana; font-size: 12px;">β</span> ||= C#/Db ||= C#/Db ||= Cx/Dbb ||= J#/Kb || | ||
||= 2 || | ||= 2 ||= 184.62 ||= 9/8, 10/9, 11/10, 19/17, 21/19 ||= A ||= D ||= D ||= D ||= K || | ||
||= 3 || | ||= 3 ||= 276.92 ||= 7/6, 13/11, 20/17, 19/16, 22/19 ||= <span style="background-color: #ffffff; color: #333333; font-family: Verdana; font-size: 12px;">δ</span> ||= D#/Eb ||= D#/Eb ||= Dx/Ebb ||= K#/Lb || | ||
||= 4 || | ||= 4 ||= 369.23 ||= 5/4, 11/9, 16/13, 26/21 ||= C ||= E ||= E ||= E ||= L || | ||
||= 5 || | ||= 5 ||= 461.54 ||= 13/10, 17/13, 21/16, 22/17 ||= B ||= E#/Fb ||= F ||= Ex/Fb ||= M || | ||
||= 6 || | ||= 6 ||= 553.85 ||= 11/8, 18/13, 26/19 ||= <span style="background-color: #ffffff; color: #333333; font-family: Verdana; font-size: 12px;">ε</span> ||= F ||= F#/Gb ||= F# ||= M#/Nb || | ||
||= 7 || | ||= 7 ||= 646.15 ||= 16/11, 13/9, 19/13 ||= D ||= F#/Gb ||= G ||= Gb ||= N || | ||
||= 8 || | ||= 8 ||= 738.46 ||= 17/11, 20/13, 26/17, 32/21 ||= <span style="background-color: #ffffff; color: #333333; font-family: Verdana; font-size: 12px;">γ</span> ||= G ||= G#/Hb ||= G# ||= N#/Ob || | ||
||= 9 || | ||= 9 ||= 830.77 ||= 8/5, 13/8, 18/11, 21/13 ||= F ||= G#/Ab ||= H ||= Ab ||= O || | ||
||= 10 || | ||= 10 ||= 923.08 ||= [[17_10|17/10]], [[12_7|12/7]], [[22_13|22/13]], [[19_11|19/11]] ||= E ||= A ||= A ||= A# ||= P || | ||
||= 11 || | ||= 11 ||= 1015.38 ||= 9/5, 16/9, 20/11, 34/19, 38/21 ||= <span style="background-color: #ffffff; color: #333333; font-family: Verdana; font-size: 12px;">α</span> ||= A#/Bb ||= A#/Bb ||= Bb ||= P#/Qb || | ||
||= 12 || | ||= 12 ||= 1107.69 ||= 17/9, 19/10, 21/11, 32/17, 36/19, 40/21 ||= G ||= B/Cb ||= B ||= B#/Cbb ||= Q || | ||
||= 13 || | ||= 13 ||= 1200.00 ||= 2/1 ||= H ||= C/B# ||= C ||= C ||= J || | ||
||.............||.............||................................................................||...................||.......................||....................||.......................||................|| | ||= ............. ||= ............. ||= ................................................................ ||= ................... ||= ....................... ||= .................... ||= ....................... ||= ................ || | ||
*based on treating 13-EDO as a 2.5.9.11.13.21 subgroup temperament; other approaches are possible. | *based on treating 13-EDO as a 2.5.9.11.13.21 subgroup temperament; other approaches are possible. | ||
13edo can also be notated with ups and downs. The notational 5th is the 2nd-best approximation of 3/2, 7\13. Using this 5th allows conventional notation to be used, including the staff, note names, relative notation, etc. in two ways. The first preserves the __melodic__ meaning of sharp/flat, major/minor and aug/dim, in that sharp is higher pitched than flat, and major/aug is wider than minor/dim. The disadvantage to this approach is that conventional interval arithmetic no longer works. e.g. M2 + M2 isn't M3, and D + M2 isn't E. Chord names are different because C - E - G isn't P1 - M3 - P5. | |||
The second approach preserves the __harmonic__ meaning of sharp/flat, major/minor and aug/dim, in that the former is always further fifthwards on the chain of fifths than the latter. Sharp is lower in pitch than flat, and major/aug is narrower than minor/dim. While this approach may seem bizarre at first, interval arithmetic and chord names work as usual. Furthermore, conventional 12edo music can be directly translated to 13edo "on the fly". | |||
||= **Degree** ||= **Cents** ||= **Approximated 21-limit Ratios** * ||||= [[xenharmonic/Ups and Downs Notation|Up/down notation ]] | |||
with major wider | |||
than minor ||||= Up/down notation | |||
with major narrower | |||
than minor || | |||
||= 0 ||= 0 ||= 1/1 ||= P1 ||= D ||= P1 ||= D || | |||
||= 1 ||= 92.31 ||= 17/16, 18/17, 19/18, 20/19, 21/20, 22/21 ||= ||= ||= ||= || | |||
||= 2 ||= 184.62 ||= 9/8, 10/9, 11/10, 19/17, 21/19 ||= ||= ||= ||= || | |||
||= 3 ||= 276.92 ||= 7/6, 13/11, 20/17, 19/16, 22/19 ||= ||= ||= ||= || | |||
||= 4 ||= 369.23 ||= 5/4, 11/9, 16/13, 26/21 ||= ||= ||= ||= || | |||
||= 5 ||= 461.54 ||= 13/10, 17/13, 21/16, 22/17 ||= ||= ||= ||= || | |||
||= 6 ||= 553.85 ||= 11/8, 18/13, 26/19 ||= P4 ||= G ||= P4 ||= G || | |||
||= 7 ||= 646.15 ||= 16/11, 13/9, 19/13 ||= P5 ||= A ||= P5 ||= A || | |||
||= 8 ||= 738.46 ||= 17/11, 20/13, 26/17, 32/21 ||= ||= ||= ||= || | |||
||= 9 ||= 830.77 ||= 8/5, 13/8, 18/11, 21/13 ||= ||= ||= ||= || | |||
||= 10 ||= 923.08 ||= [[17_10|17/10]], [[12_7|12/7]], [[22_13|22/13]], [[19_11|19/11]] ||= ||= ||= ||= || | |||
||= 11 ||= 1015.38 ||= 9/5, 16/9, 20/11, 34/19, 38/21 ||= ||= ||= ||= || | |||
||= 12 ||= 1107.69 ||= 17/9, 19/10, 21/11, 32/17, 36/19, 40/21 ||= ||= ||= ||= || | |||
||= 13 ||= 1200.00 ||= 2/1 ||= P8 ||= D ||= P8 ||= D || | |||
For alternative notations, see [[xenharmonic/Ups and Downs Notation#Summary%20of%20EDO%20notation-%22Superflat%22%20EDOs|Ups and Downs Notation -"Superflat" EDOs]] and [[Ups and Downs Notation#Summary%20of%20EDO%20notation-%22Supersharp%22%20EDOs|Ups and Downs Notation -"Supersharp" EDOs]] and [[Ups and Downs Notation#Natural%20Generators|Ups and Downs Notation - Natural Generators]]. | For alternative notations, see [[xenharmonic/Ups and Downs Notation#Summary%20of%20EDO%20notation-%22Superflat%22%20EDOs|Ups and Downs Notation -"Superflat" EDOs]] and [[Ups and Downs Notation#Summary%20of%20EDO%20notation-%22Supersharp%22%20EDOs|Ups and Downs Notation -"Supersharp" EDOs]] and [[Ups and Downs Notation#Natural%20Generators|Ups and Downs Notation - Natural Generators]]. | ||
| Line 217: | Line 241: | ||
<td style="text-align: center;">H<br /> | <td style="text-align: center;">H<br /> | ||
</td> | </td> | ||
<td>C<br /> | <td style="text-align: center;">C<br /> | ||
</td> | </td> | ||
<td>C<br /> | <td style="text-align: center;">C<br /> | ||
</td> | </td> | ||
<td>C<br /> | <td style="text-align: center;">C<br /> | ||
</td> | </td> | ||
<td>J<br /> | <td style="text-align: center;">J<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 229: | Line 253: | ||
<td style="text-align: center;">1<br /> | <td style="text-align: center;">1<br /> | ||
</td> | </td> | ||
<td style="text-align: | <td style="text-align: center;">92.31<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">17/16, 18/17, 19/18, 20/19, 21/20, 22/21<br /> | <td style="text-align: center;">17/16, 18/17, 19/18, 20/19, 21/20, 22/21<br /> | ||
| Line 235: | Line 259: | ||
<td style="text-align: center;"><span style="background-color: #ffffff; color: #333333; font-family: Verdana; font-size: 12px;">β</span><br /> | <td style="text-align: center;"><span style="background-color: #ffffff; color: #333333; font-family: Verdana; font-size: 12px;">β</span><br /> | ||
</td> | </td> | ||
<td>C#/Db<br /> | <td style="text-align: center;">C#/Db<br /> | ||
</td> | </td> | ||
<td>C#/Db<br /> | <td style="text-align: center;">C#/Db<br /> | ||
</td> | </td> | ||
<td>Cx/Dbb<br /> | <td style="text-align: center;">Cx/Dbb<br /> | ||
</td> | </td> | ||
<td>J#/Kb<br /> | <td style="text-align: center;">J#/Kb<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 247: | Line 271: | ||
<td style="text-align: center;">2<br /> | <td style="text-align: center;">2<br /> | ||
</td> | </td> | ||
<td style="text-align: | <td style="text-align: center;">184.62<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">9/8, 10/9, 11/10, 19/17, 21/19<br /> | <td style="text-align: center;">9/8, 10/9, 11/10, 19/17, 21/19<br /> | ||
| Line 253: | Line 277: | ||
<td style="text-align: center;">A<br /> | <td style="text-align: center;">A<br /> | ||
</td> | </td> | ||
<td>D<br /> | <td style="text-align: center;">D<br /> | ||
</td> | </td> | ||
<td>D<br /> | <td style="text-align: center;">D<br /> | ||
</td> | </td> | ||
<td>D<br /> | <td style="text-align: center;">D<br /> | ||
</td> | </td> | ||
<td>K<br /> | <td style="text-align: center;">K<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 265: | Line 289: | ||
<td style="text-align: center;">3<br /> | <td style="text-align: center;">3<br /> | ||
</td> | </td> | ||
<td style="text-align: | <td style="text-align: center;">276.92<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">7/6, 13/11, 20/17, 19/16, 22/19<br /> | <td style="text-align: center;">7/6, 13/11, 20/17, 19/16, 22/19<br /> | ||
| Line 271: | Line 295: | ||
<td style="text-align: center;"><span style="background-color: #ffffff; color: #333333; font-family: Verdana; font-size: 12px;">δ</span><br /> | <td style="text-align: center;"><span style="background-color: #ffffff; color: #333333; font-family: Verdana; font-size: 12px;">δ</span><br /> | ||
</td> | </td> | ||
<td>D#/Eb<br /> | <td style="text-align: center;">D#/Eb<br /> | ||
</td> | </td> | ||
<td>D#/Eb<br /> | <td style="text-align: center;">D#/Eb<br /> | ||
</td> | </td> | ||
<td>Dx/Ebb<br /> | <td style="text-align: center;">Dx/Ebb<br /> | ||
</td> | </td> | ||
<td>K#/Lb<br /> | <td style="text-align: center;">K#/Lb<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 283: | Line 307: | ||
<td style="text-align: center;">4<br /> | <td style="text-align: center;">4<br /> | ||
</td> | </td> | ||
<td style="text-align: | <td style="text-align: center;">369.23<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">5/4, 11/9, 16/13, 26/21<br /> | <td style="text-align: center;">5/4, 11/9, 16/13, 26/21<br /> | ||
| Line 289: | Line 313: | ||
<td style="text-align: center;">C<br /> | <td style="text-align: center;">C<br /> | ||
</td> | </td> | ||
<td>E<br /> | <td style="text-align: center;">E<br /> | ||
</td> | </td> | ||
<td>E<br /> | <td style="text-align: center;">E<br /> | ||
</td> | </td> | ||
<td>E<br /> | <td style="text-align: center;">E<br /> | ||
</td> | </td> | ||
<td>L<br /> | <td style="text-align: center;">L<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 301: | Line 325: | ||
<td style="text-align: center;">5<br /> | <td style="text-align: center;">5<br /> | ||
</td> | </td> | ||
<td style="text-align: | <td style="text-align: center;">461.54<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">13/10, 17/13, 21/16, 22/17<br /> | <td style="text-align: center;">13/10, 17/13, 21/16, 22/17<br /> | ||
| Line 307: | Line 331: | ||
<td style="text-align: center;">B<br /> | <td style="text-align: center;">B<br /> | ||
</td> | </td> | ||
<td>E#/Fb<br /> | <td style="text-align: center;">E#/Fb<br /> | ||
</td> | </td> | ||
<td>F<br /> | <td style="text-align: center;">F<br /> | ||
</td> | </td> | ||
<td>Ex/Fb<br /> | <td style="text-align: center;">Ex/Fb<br /> | ||
</td> | </td> | ||
<td>M<br /> | <td style="text-align: center;">M<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 319: | Line 343: | ||
<td style="text-align: center;">6<br /> | <td style="text-align: center;">6<br /> | ||
</td> | </td> | ||
<td style="text-align: | <td style="text-align: center;">553.85<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">11/8, 18/13, 26/19<br /> | <td style="text-align: center;">11/8, 18/13, 26/19<br /> | ||
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<td style="text-align: center;"><span style="background-color: #ffffff; color: #333333; font-family: Verdana; font-size: 12px;">ε</span><br /> | <td style="text-align: center;"><span style="background-color: #ffffff; color: #333333; font-family: Verdana; font-size: 12px;">ε</span><br /> | ||
</td> | </td> | ||
<td>F<br /> | <td style="text-align: center;">F<br /> | ||
</td> | </td> | ||
<td>F#/Gb<br /> | <td style="text-align: center;">F#/Gb<br /> | ||
</td> | </td> | ||
<td>F#<br /> | <td style="text-align: center;">F#<br /> | ||
</td> | </td> | ||
<td>M#/Nb<br /> | <td style="text-align: center;">M#/Nb<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 337: | Line 361: | ||
<td style="text-align: center;">7<br /> | <td style="text-align: center;">7<br /> | ||
</td> | </td> | ||
<td style="text-align: | <td style="text-align: center;">646.15<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">16/11, 13/9, 19/13<br /> | <td style="text-align: center;">16/11, 13/9, 19/13<br /> | ||
| Line 343: | Line 367: | ||
<td style="text-align: center;">D<br /> | <td style="text-align: center;">D<br /> | ||
</td> | </td> | ||
<td>F#/Gb<br /> | <td style="text-align: center;">F#/Gb<br /> | ||
</td> | </td> | ||
<td>G<br /> | <td style="text-align: center;">G<br /> | ||
</td> | </td> | ||
<td>Gb<br /> | <td style="text-align: center;">Gb<br /> | ||
</td> | </td> | ||
<td>N<br /> | <td style="text-align: center;">N<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 355: | Line 379: | ||
<td style="text-align: center;">8<br /> | <td style="text-align: center;">8<br /> | ||
</td> | </td> | ||
<td style="text-align: | <td style="text-align: center;">738.46<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">17/11, 20/13, 26/17, 32/21<br /> | <td style="text-align: center;">17/11, 20/13, 26/17, 32/21<br /> | ||
| Line 361: | Line 385: | ||
<td style="text-align: center;"><span style="background-color: #ffffff; color: #333333; font-family: Verdana; font-size: 12px;">γ</span><br /> | <td style="text-align: center;"><span style="background-color: #ffffff; color: #333333; font-family: Verdana; font-size: 12px;">γ</span><br /> | ||
</td> | </td> | ||
<td>G<br /> | <td style="text-align: center;">G<br /> | ||
</td> | </td> | ||
<td>G#/Hb<br /> | <td style="text-align: center;">G#/Hb<br /> | ||
</td> | </td> | ||
<td>G#<br /> | <td style="text-align: center;">G#<br /> | ||
</td> | </td> | ||
<td>N#/Ob<br /> | <td style="text-align: center;">N#/Ob<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 373: | Line 397: | ||
<td style="text-align: center;">9<br /> | <td style="text-align: center;">9<br /> | ||
</td> | </td> | ||
<td style="text-align: | <td style="text-align: center;">830.77<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">8/5, 13/8, 18/11, 21/13<br /> | <td style="text-align: center;">8/5, 13/8, 18/11, 21/13<br /> | ||
| Line 379: | Line 403: | ||
<td style="text-align: center;">F<br /> | <td style="text-align: center;">F<br /> | ||
</td> | </td> | ||
<td>G#/Ab<br /> | <td style="text-align: center;">G#/Ab<br /> | ||
</td> | </td> | ||
<td>H<br /> | <td style="text-align: center;">H<br /> | ||
</td> | </td> | ||
<td>Ab<br /> | <td style="text-align: center;">Ab<br /> | ||
</td> | </td> | ||
<td>O<br /> | <td style="text-align: center;">O<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 391: | Line 415: | ||
<td style="text-align: center;">10<br /> | <td style="text-align: center;">10<br /> | ||
</td> | </td> | ||
<td style="text-align: | <td style="text-align: center;">923.08<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><a class="wiki_link" href="/17_10">17/10</a>, <a class="wiki_link" href="/12_7">12/7</a>, <a class="wiki_link" href="/22_13">22/13</a>, <a class="wiki_link" href="/19_11">19/11</a><br /> | <td style="text-align: center;"><a class="wiki_link" href="/17_10">17/10</a>, <a class="wiki_link" href="/12_7">12/7</a>, <a class="wiki_link" href="/22_13">22/13</a>, <a class="wiki_link" href="/19_11">19/11</a><br /> | ||
| Line 397: | Line 421: | ||
<td style="text-align: center;">E<br /> | <td style="text-align: center;">E<br /> | ||
</td> | </td> | ||
<td>A<br /> | <td style="text-align: center;">A<br /> | ||
</td> | </td> | ||
<td>A<br /> | <td style="text-align: center;">A<br /> | ||
</td> | </td> | ||
<td>A#<br /> | <td style="text-align: center;">A#<br /> | ||
</td> | </td> | ||
<td>P<br /> | <td style="text-align: center;">P<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 409: | Line 433: | ||
<td style="text-align: center;">11<br /> | <td style="text-align: center;">11<br /> | ||
</td> | </td> | ||
<td style="text-align: | <td style="text-align: center;">1015.38<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">9/5, 16/9, 20/11, 34/19, 38/21<br /> | <td style="text-align: center;">9/5, 16/9, 20/11, 34/19, 38/21<br /> | ||
| Line 415: | Line 439: | ||
<td style="text-align: center;"><span style="background-color: #ffffff; color: #333333; font-family: Verdana; font-size: 12px;">α</span><br /> | <td style="text-align: center;"><span style="background-color: #ffffff; color: #333333; font-family: Verdana; font-size: 12px;">α</span><br /> | ||
</td> | </td> | ||
<td>A#/Bb<br /> | <td style="text-align: center;">A#/Bb<br /> | ||
</td> | </td> | ||
<td>A#/Bb<br /> | <td style="text-align: center;">A#/Bb<br /> | ||
</td> | </td> | ||
<td>Bb<br /> | <td style="text-align: center;">Bb<br /> | ||
</td> | </td> | ||
<td>P#/Qb<br /> | <td style="text-align: center;">P#/Qb<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 427: | Line 451: | ||
<td style="text-align: center;">12<br /> | <td style="text-align: center;">12<br /> | ||
</td> | </td> | ||
<td style="text-align: | <td style="text-align: center;">1107.69<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">17/9, 19/10, 21/11, 32/17, 36/19, 40/21<br /> | <td style="text-align: center;">17/9, 19/10, 21/11, 32/17, 36/19, 40/21<br /> | ||
| Line 433: | Line 457: | ||
<td style="text-align: center;">G<br /> | <td style="text-align: center;">G<br /> | ||
</td> | </td> | ||
<td>B/Cb<br /> | <td style="text-align: center;">B/Cb<br /> | ||
</td> | </td> | ||
<td>B<br /> | <td style="text-align: center;">B<br /> | ||
</td> | </td> | ||
<td>B#/Cbb<br /> | <td style="text-align: center;">B#/Cbb<br /> | ||
</td> | </td> | ||
<td>Q<br /> | <td style="text-align: center;">Q<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 445: | Line 469: | ||
<td style="text-align: center;">13<br /> | <td style="text-align: center;">13<br /> | ||
</td> | </td> | ||
<td style="text-align: | <td style="text-align: center;">1200.00<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">2/1<br /> | <td style="text-align: center;">2/1<br /> | ||
| Line 451: | Line 475: | ||
<td style="text-align: center;">H<br /> | <td style="text-align: center;">H<br /> | ||
</td> | </td> | ||
<td>C/B#<br /> | <td style="text-align: center;">C/B#<br /> | ||
</td> | </td> | ||
<td>C<br /> | <td style="text-align: center;">C<br /> | ||
</td> | </td> | ||
<td>C<br /> | <td style="text-align: center;">C<br /> | ||
</td> | </td> | ||
<td>J<br /> | <td style="text-align: center;">J<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>.............<br /> | <td style="text-align: center;">.............<br /> | ||
</td> | </td> | ||
<td>.............<br /> | <td style="text-align: center;">.............<br /> | ||
</td> | </td> | ||
<td>................................................................<br /> | <td style="text-align: center;">................................................................<br /> | ||
</td> | </td> | ||
<td>...................<br /> | <td style="text-align: center;">...................<br /> | ||
</td> | </td> | ||
<td>.......................<br /> | <td style="text-align: center;">.......................<br /> | ||
</td> | </td> | ||
<td>....................<br /> | <td style="text-align: center;">....................<br /> | ||
</td> | </td> | ||
<td>.......................<br /> | <td style="text-align: center;">.......................<br /> | ||
</td> | </td> | ||
<td>................<br /> | <td style="text-align: center;">................<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 481: | Line 505: | ||
*based on treating 13-EDO as a 2.5.9.11.13.21 subgroup temperament; other approaches are possible.<br /> | *based on treating 13-EDO as a 2.5.9.11.13.21 subgroup temperament; other approaches are possible.<br /> | ||
<br /> | |||
13edo can also be notated with ups and downs. The notational 5th is the 2nd-best approximation of 3/2, 7\13. Using this 5th allows conventional notation to be used, including the staff, note names, relative notation, etc. in two ways. The first preserves the <u>melodic</u> meaning of sharp/flat, major/minor and aug/dim, in that sharp is higher pitched than flat, and major/aug is wider than minor/dim. The disadvantage to this approach is that conventional interval arithmetic no longer works. e.g. M2 + M2 isn't M3, and D + M2 isn't E. Chord names are different because C - E - G isn't P1 - M3 - P5.<br /> | |||
<br /> | |||
The second approach preserves the <u>harmonic</u> meaning of sharp/flat, major/minor and aug/dim, in that the former is always further fifthwards on the chain of fifths than the latter. Sharp is lower in pitch than flat, and major/aug is narrower than minor/dim. While this approach may seem bizarre at first, interval arithmetic and chord names work as usual. Furthermore, conventional 12edo music can be directly translated to 13edo &quot;on the fly&quot;.<br /> | |||
<br /> | |||
<table class="wiki_table"> | |||
<tr> | |||
<td style="text-align: center;"><strong>Degree</strong><br /> | |||
</td> | |||
<td style="text-align: center;"><strong>Cents</strong><br /> | |||
</td> | |||
<td style="text-align: center;"><strong>Approximated 21-limit Ratios</strong> *<br /> | |||
</td> | |||
<td colspan="2" style="text-align: center;"><a class="wiki_link" href="http://xenharmonic.wikispaces.com/Ups%20and%20Downs%20Notation">Up/down notation </a><br /> | |||
with major wider<br /> | |||
than minor<br /> | |||
</td> | |||
<td colspan="2" style="text-align: center;">Up/down notation<br /> | |||
with major narrower<br /> | |||
than minor<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td style="text-align: center;">0<br /> | |||
</td> | |||
<td style="text-align: center;">0<br /> | |||
</td> | |||
<td style="text-align: center;">1/1<br /> | |||
</td> | |||
<td style="text-align: center;">P1<br /> | |||
</td> | |||
<td style="text-align: center;">D<br /> | |||
</td> | |||
<td style="text-align: center;">P1<br /> | |||
</td> | |||
<td style="text-align: center;">D<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td style="text-align: center;">1<br /> | |||
</td> | |||
<td style="text-align: center;">92.31<br /> | |||
</td> | |||
<td style="text-align: center;">17/16, 18/17, 19/18, 20/19, 21/20, 22/21<br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td style="text-align: center;">2<br /> | |||
</td> | |||
<td style="text-align: center;">184.62<br /> | |||
</td> | |||
<td style="text-align: center;">9/8, 10/9, 11/10, 19/17, 21/19<br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td style="text-align: center;">3<br /> | |||
</td> | |||
<td style="text-align: center;">276.92<br /> | |||
</td> | |||
<td style="text-align: center;">7/6, 13/11, 20/17, 19/16, 22/19<br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td style="text-align: center;">4<br /> | |||
</td> | |||
<td style="text-align: center;">369.23<br /> | |||
</td> | |||
<td style="text-align: center;">5/4, 11/9, 16/13, 26/21<br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td style="text-align: center;">5<br /> | |||
</td> | |||
<td style="text-align: center;">461.54<br /> | |||
</td> | |||
<td style="text-align: center;">13/10, 17/13, 21/16, 22/17<br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td style="text-align: center;">6<br /> | |||
</td> | |||
<td style="text-align: center;">553.85<br /> | |||
</td> | |||
<td style="text-align: center;">11/8, 18/13, 26/19<br /> | |||
</td> | |||
<td style="text-align: center;">P4<br /> | |||
</td> | |||
<td style="text-align: center;">G<br /> | |||
</td> | |||
<td style="text-align: center;">P4<br /> | |||
</td> | |||
<td style="text-align: center;">G<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td style="text-align: center;">7<br /> | |||
</td> | |||
<td style="text-align: center;">646.15<br /> | |||
</td> | |||
<td style="text-align: center;">16/11, 13/9, 19/13<br /> | |||
</td> | |||
<td style="text-align: center;">P5<br /> | |||
</td> | |||
<td style="text-align: center;">A<br /> | |||
</td> | |||
<td style="text-align: center;">P5<br /> | |||
</td> | |||
<td style="text-align: center;">A<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td style="text-align: center;">8<br /> | |||
</td> | |||
<td style="text-align: center;">738.46<br /> | |||
</td> | |||
<td style="text-align: center;">17/11, 20/13, 26/17, 32/21<br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td style="text-align: center;">9<br /> | |||
</td> | |||
<td style="text-align: center;">830.77<br /> | |||
</td> | |||
<td style="text-align: center;">8/5, 13/8, 18/11, 21/13<br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td style="text-align: center;">10<br /> | |||
</td> | |||
<td style="text-align: center;">923.08<br /> | |||
</td> | |||
<td style="text-align: center;"><a class="wiki_link" href="/17_10">17/10</a>, <a class="wiki_link" href="/12_7">12/7</a>, <a class="wiki_link" href="/22_13">22/13</a>, <a class="wiki_link" href="/19_11">19/11</a><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td style="text-align: center;">11<br /> | |||
</td> | |||
<td style="text-align: center;">1015.38<br /> | |||
</td> | |||
<td style="text-align: center;">9/5, 16/9, 20/11, 34/19, 38/21<br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td style="text-align: center;">12<br /> | |||
</td> | |||
<td style="text-align: center;">1107.69<br /> | |||
</td> | |||
<td style="text-align: center;">17/9, 19/10, 21/11, 32/17, 36/19, 40/21<br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td style="text-align: center;">13<br /> | |||
</td> | |||
<td style="text-align: center;">1200.00<br /> | |||
</td> | |||
<td style="text-align: center;">2/1<br /> | |||
</td> | |||
<td style="text-align: center;">P8<br /> | |||
</td> | |||
<td style="text-align: center;">D<br /> | |||
</td> | |||
<td style="text-align: center;">P8<br /> | |||
</td> | |||
<td style="text-align: center;">D<br /> | |||
</td> | |||
</tr> | |||
</table> | |||
<br /> | <br /> | ||
For alternative notations, see <a class="wiki_link" href="http://xenharmonic.wikispaces.com/Ups%20and%20Downs%20Notation#Summary%20of%20EDO%20notation-%22Superflat%22%20EDOs">Ups and Downs Notation -&quot;Superflat&quot; EDOs</a> and <a class="wiki_link" href="/Ups%20and%20Downs%20Notation#Summary%20of%20EDO%20notation-%22Supersharp%22%20EDOs">Ups and Downs Notation -&quot;Supersharp&quot; EDOs</a> and <a class="wiki_link" href="/Ups%20and%20Downs%20Notation#Natural%20Generators">Ups and Downs Notation - Natural Generators</a>.<br /> | For alternative notations, see <a class="wiki_link" href="http://xenharmonic.wikispaces.com/Ups%20and%20Downs%20Notation#Summary%20of%20EDO%20notation-%22Superflat%22%20EDOs">Ups and Downs Notation -&quot;Superflat&quot; EDOs</a> and <a class="wiki_link" href="/Ups%20and%20Downs%20Notation#Summary%20of%20EDO%20notation-%22Supersharp%22%20EDOs">Ups and Downs Notation -&quot;Supersharp&quot; EDOs</a> and <a class="wiki_link" href="/Ups%20and%20Downs%20Notation#Natural%20Generators">Ups and Downs Notation - Natural Generators</a>.<br /> | ||
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<!-- ws:start:WikiTextHeadingRule:13:&lt;h1&gt; --><h1 id="toc2"><a name="Scales in 13edo"></a><!-- ws:end:WikiTextHeadingRule:13 -->Scales in 13edo</h1> | <!-- ws:start:WikiTextHeadingRule:13:&lt;h1&gt; --><h1 id="toc2"><a name="Scales in 13edo"></a><!-- ws:end:WikiTextHeadingRule:13 -->Scales in 13edo</h1> | ||
Due to the prime character of the number 13, 13edo can form several xenharmonic <a class="wiki_link" href="/MOSScales">moment of symmetry scales</a>. The diagram below shows five &quot;families&quot; of MOS scales: those generated by making a chain of 2\13 (two <u><a class="wiki_link" href="/degree">degree</a>s of</u> 13edo), 3\13, 4\13, 5\13, &amp; 6\13, respectively.<br /> | Due to the prime character of the number 13, 13edo can form several xenharmonic <a class="wiki_link" href="/MOSScales">moment of symmetry scales</a>. The diagram below shows five &quot;families&quot; of MOS scales: those generated by making a chain of 2\13 (two <u><a class="wiki_link" href="/degree">degree</a>s of</u> 13edo), 3\13, 4\13, 5\13, &amp; 6\13, respectively.<br /> | ||
<br /> | <br /> | ||
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~diagram by Andrew Heathwaite, based on horagrams pioneered by Erv Wilson<br /> | ~diagram by Andrew Heathwaite, based on horagrams pioneered by Erv Wilson<br /> | ||
<br /> | <br /> | ||
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<!-- ws:start:WikiTextHeadingRule:21:&lt;h3&gt; --><h3 id="toc6"><a name="Notational and Compositional Approaches to 13edo-The Cryptic Ruse Methods-Modes and Harmony in The Archaeotonic Scale"></a><!-- ws:end:WikiTextHeadingRule:21 -->Modes and Harmony in The Archaeotonic Scale</h3> | <!-- ws:start:WikiTextHeadingRule:21:&lt;h3&gt; --><h3 id="toc6"><a name="Notational and Compositional Approaches to 13edo-The Cryptic Ruse Methods-Modes and Harmony in The Archaeotonic Scale"></a><!-- ws:end:WikiTextHeadingRule:21 -->Modes and Harmony in The Archaeotonic Scale</h3> | ||
A 7-nominal notaiton is proposed, using the letters A-G. The &quot;C natural&quot; scale is proposed to be degrees 0-2-4-6-8-10-12-(13), with the note &quot;C&quot; tuned to a reference pitch of concert middle C. The modes are laid out in the following table, excerpted from an unfinished paper on 13edo.<br /> | A 7-nominal notaiton is proposed, using the letters A-G. The &quot;C natural&quot; scale is proposed to be degrees 0-2-4-6-8-10-12-(13), with the note &quot;C&quot; tuned to a reference pitch of concert middle C. The modes are laid out in the following table, excerpted from an unfinished paper on 13edo.<br /> | ||
<!-- ws:start:WikiTextLocalImageRule: | <!-- ws:start:WikiTextLocalImageRule:1111:&lt;img src=&quot;/file/view/Archeotonic.png/252639498/Archeotonic.png&quot; alt=&quot;&quot; title=&quot;&quot; /&gt; --><img src="/file/view/Archeotonic.png/252639498/Archeotonic.png" alt="Archeotonic.png" title="Archeotonic.png" /><!-- ws:end:WikiTextLocalImageRule:1111 --><br /> | ||
Treating 13edo as a temperament as proposed above leads to a chord of degrees 0-2-4-6-9 representing the JI harmony 8:9:10:11:13; two such pentads exist in this scale, on E and F. Smaller harmonic units exist as follows: 8:9:10:11 on C, D, E, and F; 8:9:10:13 on E, F and G; 8:9:10 on C, D, E, F, and G; 8:9:11 on C, D, E, and F; 8:9:13 on E, F, G, and A. Finally, on B we have the relatively-discordant 16:17:21:26 (0-1-5-9, or the notes B-C-E-G), which can be octave-inverted into a more concordant 8:13:17:21.<br /> | Treating 13edo as a temperament as proposed above leads to a chord of degrees 0-2-4-6-9 representing the JI harmony 8:9:10:11:13; two such pentads exist in this scale, on E and F. Smaller harmonic units exist as follows: 8:9:10:11 on C, D, E, and F; 8:9:10:13 on E, F and G; 8:9:10 on C, D, E, F, and G; 8:9:11 on C, D, E, and F; 8:9:13 on E, F, G, and A. Finally, on B we have the relatively-discordant 16:17:21:26 (0-1-5-9, or the notes B-C-E-G), which can be octave-inverted into a more concordant 8:13:17:21.<br /> | ||
<br /> | <br /> | ||
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<!-- ws:start:WikiTextHeadingRule:23:&lt;h3&gt; --><h3 id="toc7"><a name="Notational and Compositional Approaches to 13edo-The Cryptic Ruse Methods-Modes and Harmony in the Oneirotonic Scale"></a><!-- ws:end:WikiTextHeadingRule:23 -->Modes and Harmony in the Oneirotonic Scale</h3> | <!-- ws:start:WikiTextHeadingRule:23:&lt;h3&gt; --><h3 id="toc7"><a name="Notational and Compositional Approaches to 13edo-The Cryptic Ruse Methods-Modes and Harmony in the Oneirotonic Scale"></a><!-- ws:end:WikiTextHeadingRule:23 -->Modes and Harmony in the Oneirotonic Scale</h3> | ||
Here an 8-nominal notation is proposed, using letters A-H. The &quot;C natural&quot; scale is proposed to be degrees 0-2-4-5-7-9-10-12-(13), with the note &quot;C&quot; tuned to concert middle C. The modes are laid out in the following table, excerpted from an unfinished paper on 13edo.<br /> | Here an 8-nominal notation is proposed, using letters A-H. The &quot;C natural&quot; scale is proposed to be degrees 0-2-4-5-7-9-10-12-(13), with the note &quot;C&quot; tuned to concert middle C. The modes are laid out in the following table, excerpted from an unfinished paper on 13edo.<br /> | ||
<!-- ws:start:WikiTextLocalImageRule: | <!-- ws:start:WikiTextLocalImageRule:1112:&lt;img src=&quot;/file/view/Oneirotonic.png/252639860/Oneirotonic.png&quot; alt=&quot;&quot; title=&quot;&quot; /&gt; --><img src="/file/view/Oneirotonic.png/252639860/Oneirotonic.png" alt="Oneirotonic.png" title="Oneirotonic.png" /><!-- ws:end:WikiTextLocalImageRule:1112 --><br /> | ||
There is a great number of potential consonant harmonies in this scale. A dedicated article on harmony and tonality in the oneirotonic scale is forthcoming.<br /> | There is a great number of potential consonant harmonies in this scale. A dedicated article on harmony and tonality in the oneirotonic scale is forthcoming.<br /> | ||
<!-- ws:start:WikiTextHeadingRule:25:&lt;h2&gt; --><h2 id="toc8"><!-- ws:end:WikiTextHeadingRule:25 --> </h2> | <!-- ws:start:WikiTextHeadingRule:25:&lt;h2&gt; --><h2 id="toc8"><!-- ws:end:WikiTextHeadingRule:25 --> </h2> | ||
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This new approach simply modifies the way 13 edo is systematized and notated but is based on the exact same 8 tone scale that cryptic ruse uses.<br /> | This new approach simply modifies the way 13 edo is systematized and notated but is based on the exact same 8 tone scale that cryptic ruse uses.<br /> | ||
<!-- ws:start:WikiTextLocalImageRule: | <!-- ws:start:WikiTextLocalImageRule:1113:&lt;img src=&quot;/file/view/13%20edo%20alphabet.PNG/506083616/13%20edo%20alphabet.PNG&quot; alt=&quot;&quot; title=&quot;&quot; /&gt; --><img src="/file/view/13%20edo%20alphabet.PNG/506083616/13%20edo%20alphabet.PNG" alt="13 edo alphabet.PNG" title="13 edo alphabet.PNG" /><!-- ws:end:WikiTextLocalImageRule:1113 --><br /> | ||
Notation written on the staff looks nearly the same as 12 edo notation except that because there are 8 letters instead of 7, the notes offset themselves to where space to space and line to line is now octaves rather than line to space. This actually makes learning the system much, much easier because a letter that is on a line is always on a line.<br /> | Notation written on the staff looks nearly the same as 12 edo notation except that because there are 8 letters instead of 7, the notes offset themselves to where space to space and line to line is now octaves rather than line to space. This actually makes learning the system much, much easier because a letter that is on a line is always on a line.<br /> | ||
<br /> | <br /> | ||
3 EDO Chromatic Scale in Octatonic Notation:<br /> | 3 EDO Chromatic Scale in Octatonic Notation:<br /> | ||
<!-- ws:start:WikiTextLocalImageRule: | <!-- ws:start:WikiTextLocalImageRule:1114:&lt;img src=&quot;/file/view/8%20tone%20scale%2013%20edo.PNG/506382886/8%20tone%20scale%2013%20edo.PNG&quot; alt=&quot;&quot; title=&quot;&quot; /&gt; --><img src="/file/view/8%20tone%20scale%2013%20edo.PNG/506382886/8%20tone%20scale%2013%20edo.PNG" alt="8 tone scale 13 edo.PNG" title="8 tone scale 13 edo.PNG" /><!-- ws:end:WikiTextLocalImageRule:1114 --><br /> | ||
<!-- ws:start:WikiTextLocalImageRule: | <!-- ws:start:WikiTextLocalImageRule:1115:&lt;img src=&quot;/file/view/13%20edo%20chromatic%20scale.PNG/506089524/13%20edo%20chromatic%20scale.PNG&quot; alt=&quot;&quot; title=&quot;&quot; /&gt; --><img src="/file/view/13%20edo%20chromatic%20scale.PNG/506089524/13%20edo%20chromatic%20scale.PNG" alt="13 edo chromatic scale.PNG" title="13 edo chromatic scale.PNG" /><!-- ws:end:WikiTextLocalImageRule:1115 --><br /> | ||
Also, this approach allows for a circle of fourths to be produced:<br /> | Also, this approach allows for a circle of fourths to be produced:<br /> | ||
<!-- ws:start:WikiTextLocalImageRule: | <!-- ws:start:WikiTextLocalImageRule:1116:&lt;img src=&quot;http://xenharmonic.wikispaces.com/file/view/13%20ET%20circle%20of%20fourths.PNG/506093224/13%20ET%20circle%20of%20fourths.PNG&quot; alt=&quot;&quot; title=&quot;&quot; /&gt; --><img src="http://xenharmonic.wikispaces.com/file/view/13%20ET%20circle%20of%20fourths.PNG/506093224/13%20ET%20circle%20of%20fourths.PNG" alt="13 ET circle of fourths.PNG" title="13 ET circle of fourths.PNG" /><!-- ws:end:WikiTextLocalImageRule:1116 --><br /> | ||
Listen to Ryonian on J (F#) <!-- ws:start:WikiTextMediaRule:7:&lt;img src=&quot;http://www.wikispaces.com/site/embedthumbnail/file-audio/13%20edo%20Ryo%20mode.wav?h=50&amp;w=300&quot; class=&quot;WikiMedia WikiMediaFile&quot; id=&quot;wikitext@@media@@type=&amp;quot;file&amp;quot; key=&amp;quot;13 edo Ryo mode.wav&amp;quot; width=&amp;quot;300&amp;quot; height=&amp;quot;50&amp;quot;&quot; title=&quot;Local Media File&quot;height=&quot;50&quot; width=&quot;300&quot;/&gt; --><embed type="audio/wav" style="cursor:hand; cursor:pointer;" src="http://xenharmonic.wikispaces.com/file/view/13+edo+Ryo+mode.wav" width="300" height="50" autoplay="false" target="myself" controller="true" loop="false" scale="aspect" bgcolor="#FFFFFF" pluginspage="http://www.apple.com/quicktime/download/"></embed><!-- ws:end:WikiTextMediaRule:7 --><br /> | Listen to Ryonian on J (F#) <!-- ws:start:WikiTextMediaRule:7:&lt;img src=&quot;http://www.wikispaces.com/site/embedthumbnail/file-audio/13%20edo%20Ryo%20mode.wav?h=50&amp;w=300&quot; class=&quot;WikiMedia WikiMediaFile&quot; id=&quot;wikitext@@media@@type=&amp;quot;file&amp;quot; key=&amp;quot;13 edo Ryo mode.wav&amp;quot; width=&amp;quot;300&amp;quot; height=&amp;quot;50&amp;quot;&quot; title=&quot;Local Media File&quot;height=&quot;50&quot; width=&quot;300&quot;/&gt; --><embed type="audio/wav" style="cursor:hand; cursor:pointer;" src="http://xenharmonic.wikispaces.com/file/view/13+edo+Ryo+mode.wav" width="300" height="50" autoplay="false" target="myself" controller="true" loop="false" scale="aspect" bgcolor="#FFFFFF" pluginspage="http://www.apple.com/quicktime/download/"></embed><!-- ws:end:WikiTextMediaRule:7 --><br /> | ||
Listen to Dylathian on J: (F#) <!-- ws:start:WikiTextMediaRule:8:&lt;img src=&quot;http://www.wikispaces.com/site/embedthumbnail/file-audio/13%20edo%208%20tone%20mode%201.wav?h=50&amp;w=300&quot; class=&quot;WikiMedia WikiMediaFile&quot; id=&quot;wikitext@@media@@type=&amp;quot;file&amp;quot; key=&amp;quot;13 edo 8 tone mode 1.wav&amp;quot; width=&amp;quot;300&amp;quot; height=&amp;quot;50&amp;quot;&quot; title=&quot;Local Media File&quot;height=&quot;50&quot; width=&quot;300&quot;/&gt; --><embed type="audio/wav" style="cursor:hand; cursor:pointer;" src="http://xenharmonic.wikispaces.com/file/view/13+edo+8+tone+mode+1.wav" width="300" height="50" autoplay="false" target="myself" controller="true" loop="false" scale="aspect" bgcolor="#FFFFFF" pluginspage="http://www.apple.com/quicktime/download/"></embed><!-- ws:end:WikiTextMediaRule:8 --><br /> | Listen to Dylathian on J: (F#) <!-- ws:start:WikiTextMediaRule:8:&lt;img src=&quot;http://www.wikispaces.com/site/embedthumbnail/file-audio/13%20edo%208%20tone%20mode%201.wav?h=50&amp;w=300&quot; class=&quot;WikiMedia WikiMediaFile&quot; id=&quot;wikitext@@media@@type=&amp;quot;file&amp;quot; key=&amp;quot;13 edo 8 tone mode 1.wav&amp;quot; width=&amp;quot;300&amp;quot; height=&amp;quot;50&amp;quot;&quot; title=&quot;Local Media File&quot;height=&quot;50&quot; width=&quot;300&quot;/&gt; --><embed type="audio/wav" style="cursor:hand; cursor:pointer;" src="http://xenharmonic.wikispaces.com/file/view/13+edo+8+tone+mode+1.wav" width="300" height="50" autoplay="false" target="myself" controller="true" loop="false" scale="aspect" bgcolor="#FFFFFF" pluginspage="http://www.apple.com/quicktime/download/"></embed><!-- ws:end:WikiTextMediaRule:8 --><br /> | ||