11edo: Difference between revisions

: This revision was by author [[User:xenwolf|xenwolf]] and made on <tt>2016-12-29 07:53:20 UTC</tt>.<br>

: The original revision id was <tt>602890256</tt>.<br>

11-tone equal temperament, or 11 [[edo]], divides the [[octave]] into eleven equal steps of approximately 109.09 [[cent]]s. It is the fifth [[prime numbers|prime]] edo, after [[2edo]], [[3edo]], [[5edo]], and [[7edo]].

Being less than twelve, 11edo maps easily to the standard keyboard. The suggested mapping disregards the Ab/G# key, leaving Orgone[7] on the whites.

(The superfluous Ab can be made a note of [[22edo]] and this tuning is known as "elevenplus".)

==11 edo solfege==  

11edo can be notated using ups and downs. Conventional notation, including the staff, note names, relative notation, etc. can be used 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 11edo "on the fly".

11 EDO tempers out the following commas. (Note: This assumes val &lt; 11 17 26 31 38 41 |.)

||= 9931568/9752117 || | -25 7 6 &gt; ||&gt; 31.57 ||= Ampersand's Comma ||=  ||=  ||

||= 1776337/1773750 || | -68 18 17 &gt; ||&gt; 2.52 ||= Vavoom ||=  ||=  ||

||= 9859966/9733137 || | -10 7 8 -7 &gt; ||&gt; 22.41 ||= Blackjackisma ||=  ||=  ||

11-tone equal temperament, or 11 &lt;a class="wiki_link" href="/edo"&gt;edo&lt;/a&gt;, divides the &lt;a class="wiki_link" href="/octave"&gt;octave&lt;/a&gt; into eleven equal steps of approximately 109.09 &lt;a class="wiki_link" href="/cent"&gt;cent&lt;/a&gt;s. It is the fifth &lt;a class="wiki_link" href="/prime%20numbers"&gt;prime&lt;/a&gt; edo, after &lt;a class="wiki_link" href="/2edo"&gt;2edo&lt;/a&gt;, &lt;a class="wiki_link" href="/3edo"&gt;3edo&lt;/a&gt;, &lt;a class="wiki_link" href="/5edo"&gt;5edo&lt;/a&gt;, and &lt;a class="wiki_link" href="/7edo"&gt;7edo&lt;/a&gt;.&lt;br /&gt;

Being less than twelve, 11edo maps easily to the standard keyboard. The suggested mapping disregards the Ab/G# key, leaving Orgone[7] on the whites.&lt;br /&gt;

(The superfluous Ab can be made a note of &lt;a class="wiki_link" href="/22edo"&gt;22edo&lt;/a&gt; and this tuning is known as &amp;quot;elevenplus&amp;quot;.)&lt;br /&gt;

&lt;!-- ws:start:WikiTextHeadingRule:11:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc5"&gt;&lt;a name="Intervals-11 edo solfege"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:11 --&gt;11 edo solfege&lt;/h2&gt;

11edo can be notated using ups and downs. Conventional notation, including the staff, note names, relative notation, etc. can be used in two ways. The first preserves the &lt;u&gt;melodic&lt;/u&gt; 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.&lt;br /&gt;

The second approach preserves the &lt;u&gt;harmonic&lt;/u&gt; 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 11edo &amp;quot;on the fly&amp;quot;.&lt;br /&gt;

  11 EDO tempers out the following commas. (Note: This assumes val &amp;lt; 11 17 26 31 38 41 |.)&lt;br /&gt;

         &lt;td style="text-align: center;"&gt;9931568/9752117&lt;br /&gt;

         &lt;td style="text-align: center;"&gt;1776337/1773750&lt;br /&gt;

         &lt;td style="text-align: center;"&gt;9859966/9733137&lt;br /&gt;