13edo: Difference between revisions
Wikispaces>TallKite **Imported revision 602809238 - Original comment: ** |
Wikispaces>TallKite **Imported revision 602809706 - Original comment: ** |
||
| Line 1: | Line 1: | ||
<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>2016-12-25 | : This revision was by author [[User:TallKite|TallKite]] and made on <tt>2016-12-25 22:53:14 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>602809706</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> | ||
| Line 36: | Line 36: | ||
*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. | 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 way 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". | 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** || | ||= **Degree** ||= **Cents** ||||||= [[xenharmonic/Ups and Downs Notation|Up/down notation]] with | ||
major wider than minor ||||||= Up/down notation with | |||
than minor ||||= Up/down notation | major narrower than minor || | ||
||= 0 ||= 0 ||= perfect unison ||= P1 ||= D ||= perfect unison ||= P1 ||= D || | |||
than minor || | ||= 1 ||= 92 ||= up unison, minor 2nd ||= ^1, m2 ||= D^, E ||= up unison, major 2nd ||= ^1, M2 ||= D^, E || | ||
||= 0 ||= 0 ||= | ||= 2 ||= 185 ||= upminor 2nd, minor 3rd ||= ^m2, m3 ||= E^, Fb ||= upmajor 2nd, major 3rd ||= ^M2, M3 ||= E^, F# || | ||
||= 1 ||= 92 | ||= 3 ||= 277 ||= downmajor 2nd, upminor 3rd ||= vM2, ^m3 ||= E#v, Fb^ ||= downminor 2nd, upmajor 3rd ||= vm2, ^M3 ||= Ebv, F#^ || | ||
||= 2 ||= | ||= 4 ||= 369 ||= major 2nd, downmajor 3rd ||= M2, vM3 ||= E#, Fv ||= minor 2nd, downminor 3rd ||= m2, vm3 ||= Eb, Fv || | ||
||= 3 ||= | ||= 5 ||= 462 ||= major 3rd, down 4th ||= M3, v4 ||= F, Gv ||= minor 3rd, down 4th ||= m3, v4 ||= F, Gv || | ||
||= 4 ||= 369 | ||= 6 ||= 554 ||= perfect 4th, down 5th ||= P4, v5 ||= G, Av ||= perfect 4th, down 5th ||= P4, v5 ||= G, Av || | ||
||= 5 ||= | ||= 7 ||= 646 ||= up 4th, perfect 5th ||= ^4, P5 ||= G^, A ||= up 4th, perfect 5th ||= ^4, P5 ||= G^, A || | ||
||= 6 ||= | ||= 8 ||= 738 ||= up 5th, minor 6th ||= ^5, m6 ||= A^, B ||= up 5th, major 6th ||= ^5, M6 ||= A^, B || | ||
||= 7 ||= 646 | ||= 9 ||= 831 ||= upminor 6th, minor 7th ||= ^m6, m7 ||= B^, Cb ||= upmajor 6th, major 7th ||= ^M6, M7 ||= B^, C# || | ||
||= 8 ||= 738 | ||= 10 ||= 923 ||= downmajor 6th, upminor 7th ||= vM6, ^m7 ||= B#v, Cb^ ||= downminor 6th, upmajor 7th ||= vm6, ^M7 ||= Bbv, C#^ || | ||
||= 9 ||= | ||= 11 ||= 1015 ||= major 6th, downmajor 7th ||= M6, vM7 ||= B#, Cv ||= minor 6th, downminor 7th ||= m6, vm7 ||= Bb, Cv || | ||
||= 10 ||= 923 | ||= 12 ||= 1108 ||= major 7th, down 8ve ||= M7, v8 ||= C, Dv ||= minor 7th, down 8ve ||= m7, v8 ||= C, Dv || | ||
||= 11 ||= 1015 | ||= 13 ||= 1200 ||= perfect 8ve ||= P8 ||= D ||= perfect 8ve ||= P8 ||= D || | ||
||= 12 ||= | |||
||= 13 ||= 1200 | |||
For alternative notations, see [[ | For alternative notations, see [[Ups and Downs Notation#Summary%20of%20EDO%20notation-%22Supersharp%22%20EDOs|Ups and Downs Notation -"Supersharp" EDOs]] (pentatonic and octotonic fifth-based) and [[Ups and Downs Notation#Natural%20Generators|Ups and Downs Notation - Natural Generators]] (heptatonic second-based). | ||
| Line 506: | Line 504: | ||
*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 /> | <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 /> | 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 way 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 /> | <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 /> | 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 /> | ||
| Line 518: | Line 516: | ||
<td style="text-align: center;"><strong>Cents</strong><br /> | <td style="text-align: center;"><strong>Cents</strong><br /> | ||
</td> | </td> | ||
<td style="text-align: center;">< | <td colspan="3" style="text-align: center;"><a class="wiki_link" href="http://xenharmonic.wikispaces.com/Ups%20and%20Downs%20Notation">Up/down notation</a> with<br /> | ||
major wider than minor<br /> | |||
</td> | </td> | ||
<td colspan=" | <td colspan="3" style="text-align: center;">Up/down notation with<br /> | ||
with | major narrower than minor<br /> | ||
than minor<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 534: | Line 528: | ||
<td style="text-align: center;">0<br /> | <td style="text-align: center;">0<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">perfect unison<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">P1<br /> | <td style="text-align: center;">P1<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">D<br /> | <td style="text-align: center;">D<br /> | ||
</td> | |||
<td style="text-align: center;">perfect unison<br /> | |||
</td> | </td> | ||
<td style="text-align: center;">P1<br /> | <td style="text-align: center;">P1<br /> | ||
| Line 548: | Line 544: | ||
<td style="text-align: center;">1<br /> | <td style="text-align: center;">1<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">92 | <td style="text-align: center;">92<br /> | ||
</td> | |||
<td style="text-align: center;">up unison, minor 2nd<br /> | |||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">^1, m2<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><br /> | <td style="text-align: center;">D^, E<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><br /> | <td style="text-align: center;">up unison, major 2nd<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><br /> | <td style="text-align: center;">^1, M2<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><br /> | <td style="text-align: center;">D^, E<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 564: | Line 562: | ||
<td style="text-align: center;">2<br /> | <td style="text-align: center;">2<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">185<br /> | ||
</td> | |||
<td style="text-align: center;">upminor 2nd, minor 3rd<br /> | |||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">^m2, m3<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><br /> | <td style="text-align: center;">E^, Fb<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><br /> | <td style="text-align: center;">upmajor 2nd, major 3rd<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><br /> | <td style="text-align: center;">^M2, M3<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><br /> | <td style="text-align: center;">E^, F#<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 580: | Line 580: | ||
<td style="text-align: center;">3<br /> | <td style="text-align: center;">3<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">277<br /> | ||
</td> | |||
<td style="text-align: center;">downmajor 2nd, upminor 3rd<br /> | |||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">vM2, ^m3<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><br /> | <td style="text-align: center;">E#v, Fb^<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><br /> | <td style="text-align: center;">downminor 2nd, upmajor 3rd<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><br /> | <td style="text-align: center;">vm2, ^M3<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><br /> | <td style="text-align: center;">Ebv, F#^<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 596: | Line 598: | ||
<td style="text-align: center;">4<br /> | <td style="text-align: center;">4<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">369 | <td style="text-align: center;">369<br /> | ||
</td> | |||
<td style="text-align: center;">major 2nd, downmajor 3rd<br /> | |||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">M2, vM3<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><br /> | <td style="text-align: center;">E#, Fv<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><br /> | <td style="text-align: center;">minor 2nd, downminor 3rd<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><br /> | <td style="text-align: center;">m2, vm3<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><br /> | <td style="text-align: center;">Eb, Fv<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 612: | Line 616: | ||
<td style="text-align: center;">5<br /> | <td style="text-align: center;">5<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">462<br /> | ||
</td> | |||
<td style="text-align: center;">major 3rd, down 4th<br /> | |||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">M3, v4<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><br /> | <td style="text-align: center;">F, Gv<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><br /> | <td style="text-align: center;">minor 3rd, down 4th<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><br /> | <td style="text-align: center;">m3, v4<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><br /> | <td style="text-align: center;">F, Gv<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 628: | Line 634: | ||
<td style="text-align: center;">6<br /> | <td style="text-align: center;">6<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">554<br /> | ||
</td> | |||
<td style="text-align: center;">perfect 4th, down 5th<br /> | |||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">P4, v5<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">G, Av<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">perfect 4th, down 5th<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">P4<br /> | <td style="text-align: center;">P4, v5<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">G<br /> | <td style="text-align: center;">G, Av<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 644: | Line 652: | ||
<td style="text-align: center;">7<br /> | <td style="text-align: center;">7<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">646 | <td style="text-align: center;">646<br /> | ||
</td> | |||
<td style="text-align: center;">up 4th, perfect 5th<br /> | |||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">^4, P5<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">G^, A<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">up 4th, perfect 5th<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">P5<br /> | <td style="text-align: center;">^4, P5<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">A<br /> | <td style="text-align: center;">G^, A<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 660: | Line 670: | ||
<td style="text-align: center;">8<br /> | <td style="text-align: center;">8<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">738 | <td style="text-align: center;">738<br /> | ||
</td> | |||
<td style="text-align: center;">up 5th, minor 6th<br /> | |||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">^5, m6<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><br /> | <td style="text-align: center;">A^, B<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><br /> | <td style="text-align: center;">up 5th, major 6th<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><br /> | <td style="text-align: center;">^5, M6<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><br /> | <td style="text-align: center;">A^, B<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 676: | Line 688: | ||
<td style="text-align: center;">9<br /> | <td style="text-align: center;">9<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">831<br /> | ||
</td> | |||
<td style="text-align: center;">upminor 6th, minor 7th<br /> | |||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">^m6, m7<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><br /> | <td style="text-align: center;">B^, Cb<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><br /> | <td style="text-align: center;">upmajor 6th, major 7th<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><br /> | <td style="text-align: center;">^M6, M7<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><br /> | <td style="text-align: center;">B^, C#<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 692: | Line 706: | ||
<td style="text-align: center;">10<br /> | <td style="text-align: center;">10<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">923 | <td style="text-align: center;">923<br /> | ||
</td> | |||
<td style="text-align: center;">downmajor 6th, upminor 7th<br /> | |||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">vM6, ^m7<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><br /> | <td style="text-align: center;">B#v, Cb^<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><br /> | <td style="text-align: center;">downminor 6th, upmajor 7th<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><br /> | <td style="text-align: center;">vm6, ^M7<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><br /> | <td style="text-align: center;">Bbv, C#^<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 708: | Line 724: | ||
<td style="text-align: center;">11<br /> | <td style="text-align: center;">11<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">1015 | <td style="text-align: center;">1015<br /> | ||
</td> | |||
<td style="text-align: center;">major 6th, downmajor 7th<br /> | |||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">M6, vM7<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><br /> | <td style="text-align: center;">B#, Cv<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><br /> | <td style="text-align: center;">minor 6th, downminor 7th<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><br /> | <td style="text-align: center;">m6, vm7<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><br /> | <td style="text-align: center;">Bb, Cv<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 724: | Line 742: | ||
<td style="text-align: center;">12<br /> | <td style="text-align: center;">12<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">1108<br /> | ||
</td> | |||
<td style="text-align: center;">major 7th, down 8ve<br /> | |||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">M7, v8<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><br /> | <td style="text-align: center;">C, Dv<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><br /> | <td style="text-align: center;">minor 7th, down 8ve<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><br /> | <td style="text-align: center;">m7, v8<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><br /> | <td style="text-align: center;">C, Dv<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 740: | Line 760: | ||
<td style="text-align: center;">13<br /> | <td style="text-align: center;">13<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">1200 | <td style="text-align: center;">1200<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">perfect 8ve<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">P8<br /> | <td style="text-align: center;">P8<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">D<br /> | <td style="text-align: center;">D<br /> | ||
</td> | |||
<td style="text-align: center;">perfect 8ve<br /> | |||
</td> | </td> | ||
<td style="text-align: center;">P8<br /> | <td style="text-align: center;">P8<br /> | ||
| Line 756: | Line 778: | ||
<br /> | <br /> | ||
For alternative notations, see <a class="wiki_link" href=" | For alternative notations, see <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> (pentatonic and octotonic fifth-based) and <a class="wiki_link" href="/Ups%20and%20Downs%20Notation#Natural%20Generators">Ups and Downs Notation - Natural Generators</a> (heptatonic second-based).<br /> | ||
<br /> | <br /> | ||
<br /> | <br /> | ||
| Line 764: | Line 786: | ||
<!-- ws:start:WikiTextMediaRule:2:&lt;img src=&quot;http://www.wikispaces.com/site/embedthumbnail/custom/24802800?h=0&amp;w=0&quot; class=&quot;WikiMedia WikiMediaCustom&quot; id=&quot;wikitext@@media@@type=&amp;quot;custom&amp;quot; key=&amp;quot;24802800&amp;quot;&quot; title=&quot;Custom Media&quot;/&gt; --><object id="example" type="image/svg+xml" data="http://xenharmonic.wikispaces.com/file/view/13ed2-001.svg">alt : Your browser has no SVG support.</object><!-- ws:end:WikiTextMediaRule:2 --><br /> | <!-- ws:start:WikiTextMediaRule:2:&lt;img src=&quot;http://www.wikispaces.com/site/embedthumbnail/custom/24802800?h=0&amp;w=0&quot; class=&quot;WikiMedia WikiMediaCustom&quot; id=&quot;wikitext@@media@@type=&amp;quot;custom&amp;quot; key=&amp;quot;24802800&amp;quot;&quot; title=&quot;Custom Media&quot;/&gt; --><object id="example" type="image/svg+xml" data="http://xenharmonic.wikispaces.com/file/view/13ed2-001.svg">alt : Your browser has no SVG support.</object><!-- ws:end:WikiTextMediaRule:2 --><br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextFileRule: | <!-- ws:start:WikiTextFileRule:1144:&lt;img src=&quot;http://www.wikispaces.com/site/embedthumbnail/file/13ed2-001.svg?h=52&amp;w=320&quot; class=&quot;WikiFile&quot; id=&quot;wikitext@@file@@13ed2-001.svg&quot; title=&quot;File: 13ed2-001.svg&quot; width=&quot;320&quot; height=&quot;52&quot; /&gt; --><div class="objectEmbed"><a href="/file/view/13ed2-001.svg/480712008/13ed2-001.svg" onclick="ws.common.trackFileLink('/file/view/13ed2-001.svg/480712008/13ed2-001.svg');"><img src="http://www.wikispaces.com/i/mime/32/empty.png" height="32" width="32" alt="13ed2-001.svg" /></a><div><a href="/file/view/13ed2-001.svg/480712008/13ed2-001.svg" onclick="ws.common.trackFileLink('/file/view/13ed2-001.svg/480712008/13ed2-001.svg');" class="filename" title="13ed2-001.svg">13ed2-001.svg</a><br /><ul><li><a href="/file/detail/13ed2-001.svg">Details</a></li><li><a href="/file/view/13ed2-001.svg/480712008/13ed2-001.svg">Download</a></li><li style="color: #666">15 KB</li></ul></div></div><!-- ws:end:WikiTextFileRule:1144 --><br /> | ||
<!-- 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 /> | ||
<!-- ws:start:WikiTextLocalImageRule: | <!-- ws:start:WikiTextLocalImageRule:1136:&lt;img src=&quot;/file/view/13edo_horograms.jpg/104015789/13edo_horograms.jpg&quot; alt=&quot;&quot; title=&quot;&quot; /&gt; --><img src="/file/view/13edo_horograms.jpg/104015789/13edo_horograms.jpg" alt="13edo_horograms.jpg" title="13edo_horograms.jpg" /><!-- ws:end:WikiTextLocalImageRule:1136 --><br /> | ||
<!-- ws:start:WikiTextFileRule: | <!-- ws:start:WikiTextFileRule:1145:&lt;img src=&quot;http://www.wikispaces.com/site/embedthumbnail/file/13edo%20horograms.pdf?h=52&amp;w=320&quot; class=&quot;WikiFile&quot; id=&quot;wikitext@@file@@13edo horograms.pdf&quot; title=&quot;File: 13edo horograms.pdf&quot; width=&quot;320&quot; height=&quot;52&quot; /&gt; --><div class="objectEmbed"><a href="/file/view/13edo%20horograms.pdf/104047129/13edo%20horograms.pdf" onclick="ws.common.trackFileLink('/file/view/13edo%20horograms.pdf/104047129/13edo%20horograms.pdf');"><img src="http://www.wikispaces.com/i/mime/32/application/pdf.png" height="32" width="32" alt="13edo horograms.pdf" /></a><div><a href="/file/view/13edo%20horograms.pdf/104047129/13edo%20horograms.pdf" onclick="ws.common.trackFileLink('/file/view/13edo%20horograms.pdf/104047129/13edo%20horograms.pdf');" class="filename" title="13edo horograms.pdf">13edo horograms.pdf</a><br /><ul><li><a href="/file/detail/13edo%20horograms.pdf">Details</a></li><li><a href="/file/view/13edo%20horograms.pdf/104047129/13edo%20horograms.pdf">Download</a></li><li style="color: #666">242 KB</li></ul></div></div><!-- ws:end:WikiTextFileRule:1145 --><br /> | ||
~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 /> | ||
| Line 800: | Line 822: | ||
<!-- 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:1137:&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:1137 --><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 /> | ||
| Line 807: | Line 829: | ||
<!-- 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:1138:&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:1138 --><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> | ||
| Line 816: | Line 838: | ||
<br /> | <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 /> | 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:1139:&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:1139 --><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:1140:&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:1140 --><br /> | ||
<!-- ws:start:WikiTextLocalImageRule: | <!-- ws:start:WikiTextLocalImageRule:1141:&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:1141 --><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:1142:&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:1142 --><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 /> | ||