26edo: Difference between revisions
Wikispaces>TallKite **Imported revision 613216037 - Original comment: ** |
Wikispaces>TallKite **Imported revision 621461935 - Original comment: ** |
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<h2>IMPORTED REVISION FROM WIKISPACES</h2> | <h2>IMPORTED REVISION FROM WIKISPACES</h2> | ||
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | ||
: This revision was by author [[User:TallKite|TallKite]] and made on <tt>2017- | : This revision was by author [[User:TallKite|TallKite]] and made on <tt>2017-11-11 19:01:32 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>621461935</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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*based on treating 26-EDO as a 13-limit temperament; other approaches are possible. | *based on treating 26-EDO as a 13-limit temperament; other approaches are possible. | ||
Using [[Kite's color notation|color notation]], qualities can be loosely associated with colors: | |||
||~ quality ||~ color ||~ monzo format ||~ examples || | |||
||= diminished ||= blue ||= {a, b, 0, 1} ||= 7/6, 7/4 || | |||
||= minor ||= fourthward white ||= {a, b}, b < -1 ||= 32/27, 16/9 || | |||
||= " ||= green ||= {a, b, -1} ||= 6/5, 9/5 || | |||
||= major ||= yellow ||= {a, b, 1} ||= 5/4, 5/3 || | |||
||= " ||= fifthward white ||= {a, b}, b > 1 ||= 9/8, 27/16 || | |||
||= augmented ||= red ||= {a, b, 0, -1} ||= 9/7, 12/7 || | |||
All 26edo chords can be named using conventional methods, expanded to include augmented and diminished 2nd, 3rds, 6ths and 7ths. Spelling certain chords properly may require triple sharps and flats, especially if the tonic is anything other than the 11 keys in the Eb-C# range. Here are the blue, green, yellow and red triads | |||
||~ color of the 3rd ||~ JI chord ||~ notes as edosteps ||~ notes of C chord ||~ written name ||~ spoken name || | |||
||= blue ||= 6:7:9 ||= 0-6-15 ||= C Ebb G ||= C(b3) or C(d3) ||= C flat-three or C dim-three || | |||
||= green ||= 10:12:15 ||= 0-7-15 ||= C Eb G ||= Cm ||= C minor || | |||
||= yellow ||= 4:5:6 ||= 0-8-15 ||= C E G ||= C ||= C major or C || | |||
||= red ||= 14:18:27 ||= 0-9-15 ||= C E# G ||= C(#3) or C(A3) ||= C sharp-three or C aug-three || | |||
For a more complete list, see [[xenharmonic/Ups and Downs Notation#Chord%20names%20in%20other%20EDOs|Ups and Downs Notation - Chord names in other EDOs]]. | |||
==Selected just intervals by error== | ==Selected just intervals by error== | ||
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*based on treating 26-EDO as a 13-limit temperament; other approaches are possible.<br /> | *based on treating 26-EDO as a 13-limit temperament; other approaches are possible.<br /> | ||
<br /> | <br /> | ||
Using <a class="wiki_link" href="/Kite%27s%20color%20notation">color notation</a>, qualities can be loosely associated with colors:<br /> | |||
<table class="wiki_table"> | |||
<tr> | |||
<th>quality<br /> | |||
</th> | |||
<th>color<br /> | |||
</th> | |||
<th>monzo format<br /> | |||
</th> | |||
<th>examples<br /> | |||
</th> | |||
</tr> | |||
<tr> | |||
<td style="text-align: center;">diminished<br /> | |||
</td> | |||
<td style="text-align: center;">blue<br /> | |||
</td> | |||
<td style="text-align: center;">{a, b, 0, 1}<br /> | |||
</td> | |||
<td style="text-align: center;">7/6, 7/4<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td style="text-align: center;">minor<br /> | |||
</td> | |||
<td style="text-align: center;">fourthward white<br /> | |||
</td> | |||
<td style="text-align: center;">{a, b}, b &lt; -1<br /> | |||
</td> | |||
<td style="text-align: center;">32/27, 16/9<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td style="text-align: center;">&quot;<br /> | |||
</td> | |||
<td style="text-align: center;">green<br /> | |||
</td> | |||
<td style="text-align: center;">{a, b, -1}<br /> | |||
</td> | |||
<td style="text-align: center;">6/5, 9/5<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td style="text-align: center;">major<br /> | |||
</td> | |||
<td style="text-align: center;">yellow<br /> | |||
</td> | |||
<td style="text-align: center;">{a, b, 1}<br /> | |||
</td> | |||
<td style="text-align: center;">5/4, 5/3<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td style="text-align: center;">&quot;<br /> | |||
</td> | |||
<td style="text-align: center;">fifthward white<br /> | |||
</td> | |||
<td style="text-align: center;">{a, b}, b &gt; 1<br /> | |||
</td> | |||
<td style="text-align: center;">9/8, 27/16<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td style="text-align: center;">augmented<br /> | |||
</td> | |||
<td style="text-align: center;">red<br /> | |||
</td> | |||
<td style="text-align: center;">{a, b, 0, -1}<br /> | |||
</td> | |||
<td style="text-align: center;">9/7, 12/7<br /> | |||
</td> | |||
</tr> | |||
</table> | |||
All 26edo chords can be named using conventional methods, expanded to include augmented and diminished 2nd, 3rds, 6ths and 7ths. Spelling certain chords properly may require triple sharps and flats, especially if the tonic is anything other than the 11 keys in the Eb-C# range. Here are the blue, green, yellow and red triads<br /> | |||
<table class="wiki_table"> | |||
<tr> | |||
<th>color of the 3rd<br /> | |||
</th> | |||
<th>JI chord<br /> | |||
</th> | |||
<th>notes as edosteps<br /> | |||
</th> | |||
<th>notes of C chord<br /> | |||
</th> | |||
<th>written name<br /> | |||
</th> | |||
<th>spoken name<br /> | |||
</th> | |||
</tr> | |||
<tr> | |||
<td style="text-align: center;">blue<br /> | |||
</td> | |||
<td style="text-align: center;">6:7:9<br /> | |||
</td> | |||
<td style="text-align: center;">0-6-15<br /> | |||
</td> | |||
<td style="text-align: center;">C Ebb G<br /> | |||
</td> | |||
<td style="text-align: center;">C(b3) or C(d3)<br /> | |||
</td> | |||
<td style="text-align: center;">C flat-three or C dim-three<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td style="text-align: center;">green<br /> | |||
</td> | |||
<td style="text-align: center;">10:12:15<br /> | |||
</td> | |||
<td style="text-align: center;">0-7-15<br /> | |||
</td> | |||
<td style="text-align: center;">C Eb G<br /> | |||
</td> | |||
<td style="text-align: center;">Cm<br /> | |||
</td> | |||
<td style="text-align: center;">C minor<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td style="text-align: center;">yellow<br /> | |||
</td> | |||
<td style="text-align: center;">4:5:6<br /> | |||
</td> | |||
<td style="text-align: center;">0-8-15<br /> | |||
</td> | |||
<td style="text-align: center;">C E G<br /> | |||
</td> | |||
<td style="text-align: center;">C<br /> | |||
</td> | |||
<td style="text-align: center;">C major or C<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td style="text-align: center;">red<br /> | |||
</td> | |||
<td style="text-align: center;">14:18:27<br /> | |||
</td> | |||
<td style="text-align: center;">0-9-15<br /> | |||
</td> | |||
<td style="text-align: center;">C E# G<br /> | |||
</td> | |||
<td style="text-align: center;">C(#3) or C(A3)<br /> | |||
</td> | |||
<td style="text-align: center;">C sharp-three or C aug-three<br /> | |||
</td> | |||
</tr> | |||
</table> | |||
For a more complete list, see <a class="wiki_link" href="https://xenharmonic.wikispaces.com/Ups%20and%20Downs%20Notation#Chord%20names%20in%20other%20EDOs">Ups and Downs Notation - Chord names in other EDOs</a>.<br /> | |||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:5:&lt;h2&gt; --><h2 id="toc2"><a name="x-Selected just intervals by error"></a><!-- ws:end:WikiTextHeadingRule:5 -->Selected just intervals by error</h2> | <!-- ws:start:WikiTextHeadingRule:5:&lt;h2&gt; --><h2 id="toc2"><a name="x-Selected just intervals by error"></a><!-- ws:end:WikiTextHeadingRule:5 -->Selected just intervals by error</h2> | ||
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Orgone has a minimax tuning which sharpens both 7 and 11 by 1/5 of an orgonisma, or 1.679 cents. This makes the generator g a 77/64 sharp by 2/5 of the orgonisma. From this we may conclude that 24/89 or 31/115 would be reasonable alternatives to the 7/26 generator.<br /> | Orgone has a minimax tuning which sharpens both 7 and 11 by 1/5 of an orgonisma, or 1.679 cents. This makes the generator g a 77/64 sharp by 2/5 of the orgonisma. From this we may conclude that 24/89 or 31/115 would be reasonable alternatives to the 7/26 generator.<br /> | ||
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<span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><a class="wiki_link_ext" href="http://soonlabel.com/xenharmonic/wp-content/uploads/2011/11/26-tone-fugue.mp3" rel="nofollow">26 tone fugue (unfinished)</a></span> by Peter Kosmorsky (based on the melody he was singing in the shower, in orgone, to the presumed confusion of those in earshot)<br /> | <span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><a class="wiki_link_ext" href="http://soonlabel.com/xenharmonic/wp-content/uploads/2011/11/26-tone-fugue.mp3" rel="nofollow">26 tone fugue (unfinished)</a></span> by Peter Kosmorsky (based on the melody he was singing in the shower, in orgone, to the presumed confusion of those in earshot)<br /> | ||
<span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><a class="wiki_link_ext" href="http://www.96edo.com/music/micro900607.mp3" rel="nofollow">Microtonal music in 26-EDO</a></span> by <a class="wiki_link" href="/Shaahin%20Mohajeri">Shaahin Mohajeri</a><br /> | <span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><a class="wiki_link_ext" href="http://www.96edo.com/music/micro900607.mp3" rel="nofollow">Microtonal music in 26-EDO</a></span> by <a class="wiki_link" href="/Shaahin%20Mohajeri">Shaahin Mohajeri</a><br /> | ||
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<span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Curley/Zach%20Curley%20-%20Injera%20Jam.mp3" rel="nofollow">Injera Jam</a></span> by <a class="wiki_link" href="/Zach%20Curley">Zach Curley</a><br /> | <span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Curley/Zach%20Curley%20-%20Injera%20Jam.mp3" rel="nofollow">Injera Jam</a></span> by <a class="wiki_link" href="/Zach%20Curley">Zach Curley</a><br /> | ||