Equal-step tuning: Difference between revisions

Wikispaces>clumma
**Imported revision 578813701 - Original comment: **
Wikispaces>xenwolf
**Imported revision 587394487 - 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:clumma|clumma]] and made on <tt>2016-03-31 19:58:37 UTC</tt>.<br>
: This revision was by author [[User:xenwolf|xenwolf]] and made on <tt>2016-07-21 05:33:08 UTC</tt>.<br>
: The original revision id was <tt>578813701</tt>.<br>
: The original revision id was <tt>587394487</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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===[[ed5|...of the Just Major 17th (5/1)]]===  
===[[ed5|...of the Just Major 17th (5/1)]]===  
===[[ed7|...of the 7th Natural (7/1)]]===


===[[edf|...of the Perfect Fifth (3/2)]]===  
===[[edf|...of the Perfect Fifth (3/2)]]===  
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The following plot shows equal divisions of 2/1, 3/1, 5/1, and 7/1, and points out some instances when three or more of them happen to be close together. Note that any equal division of 2/1 is automatically an equal division of 4/1; and if something is simultaneously a good equal division of both 2/1 and 3/1, then it's a good equal division of 6/1 as well.&lt;br /&gt;
The following plot shows equal divisions of 2/1, 3/1, 5/1, and 7/1, and points out some instances when three or more of them happen to be close together. Note that any equal division of 2/1 is automatically an equal division of 4/1; and if something is simultaneously a good equal division of both 2/1 and 3/1, then it's a good equal division of 6/1 as well.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextLocalImageRule:31:&amp;lt;img src=&amp;quot;/file/view/equal.png/277409084/800x69/equal.png&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; style=&amp;quot;height: 69px; width: 800px;&amp;quot; /&amp;gt; --&gt;&lt;img src="/file/view/equal.png/277409084/800x69/equal.png" alt="equal.png" title="equal.png" style="height: 69px; width: 800px;" /&gt;&lt;!-- ws:end:WikiTextLocalImageRule:31 --&gt;&lt;br /&gt;
&lt;!-- ws:start:WikiTextLocalImageRule:33:&amp;lt;img src=&amp;quot;/file/view/equal.png/277409084/800x69/equal.png&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; style=&amp;quot;height: 69px; width: 800px;&amp;quot; /&amp;gt; --&gt;&lt;img src="/file/view/equal.png/277409084/800x69/equal.png" alt="equal.png" title="equal.png" style="height: 69px; width: 800px;" /&gt;&lt;!-- ws:end:WikiTextLocalImageRule:33 --&gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
(Unlimited resolution version: &lt;a href="http://xenharmonic.wikispaces.com/file/view/equal.svg/277406886/equal.svg" onclick="ws.common.trackFileLink('http://xenharmonic.wikispaces.com/file/view/equal.svg/277406886/equal.svg');"&gt;equal.svg&lt;/a&gt;)&lt;br /&gt;
(Unlimited resolution version: &lt;a href="http://xenharmonic.wikispaces.com/file/view/equal.svg/277406886/equal.svg" onclick="ws.common.trackFileLink('http://xenharmonic.wikispaces.com/file/view/equal.svg/277406886/equal.svg');"&gt;equal.svg&lt;/a&gt;)&lt;br /&gt;
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&lt;!-- ws:start:WikiTextHeadingRule:12:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc6"&gt;&lt;a name="Scale gallery-Equal divisions...-...of the Just Major 17th (5/1)"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:12 --&gt;&lt;a class="wiki_link" href="/ed5"&gt;...of the Just Major 17th (5/1)&lt;/a&gt;&lt;/h3&gt;
&lt;!-- ws:start:WikiTextHeadingRule:12:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc6"&gt;&lt;a name="Scale gallery-Equal divisions...-...of the Just Major 17th (5/1)"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:12 --&gt;&lt;a class="wiki_link" href="/ed5"&gt;...of the Just Major 17th (5/1)&lt;/a&gt;&lt;/h3&gt;
  &lt;br /&gt;
  &lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:14:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc7"&gt;&lt;a name="Scale gallery-Equal divisions...-...of the Perfect Fifth (3/2)"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:14 --&gt;&lt;a class="wiki_link" href="/edf"&gt;...of the Perfect Fifth (3/2)&lt;/a&gt;&lt;/h3&gt;
&lt;!-- ws:start:WikiTextHeadingRule:14:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc7"&gt;&lt;a name="Scale gallery-Equal divisions...-...of the 7th Natural (7/1)"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:14 --&gt;&lt;a class="wiki_link" href="/ed7"&gt;...of the 7th Natural (7/1)&lt;/a&gt;&lt;/h3&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:16:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc8"&gt;&lt;a name="Scale gallery-Equal divisions...-...of the Perfect Fifth (3/2)"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:16 --&gt;&lt;a class="wiki_link" href="/edf"&gt;...of the Perfect Fifth (3/2)&lt;/a&gt;&lt;/h3&gt;
  most famously Carlos Alpha, Beta and Gamma, but lots of others, too&lt;br /&gt;
  most famously Carlos Alpha, Beta and Gamma, but lots of others, too&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:16:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc8"&gt;&lt;a name="Scale gallery-Equal divisions...-...of the Perfect Fourth (4/3)"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:16 --&gt;...of the Perfect Fourth (4/3)&lt;/h3&gt;
&lt;!-- ws:start:WikiTextHeadingRule:18:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc9"&gt;&lt;a name="Scale gallery-Equal divisions...-...of the Perfect Fourth (4/3)"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:18 --&gt;...of the Perfect Fourth (4/3)&lt;/h3&gt;
  3 - &lt;a class="wiki_link" href="/Cube%20Root%20of%20P4"&gt;Cube Root of 4/3&lt;/a&gt;&lt;br /&gt;
  3 - &lt;a class="wiki_link" href="/Cube%20Root%20of%20P4"&gt;Cube Root of 4/3&lt;/a&gt;&lt;br /&gt;
9 - '&lt;a class="wiki_link" href="/Noleta"&gt;Noleta&lt;/a&gt;' Scale&lt;br /&gt;
9 - '&lt;a class="wiki_link" href="/Noleta"&gt;Noleta&lt;/a&gt;' Scale&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:18:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc9"&gt;&lt;a name="Scale gallery-Equal divisions...-...of the Tridecimal Ultramajor Third (13/10)"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:18 --&gt;...of the Tridecimal Ultramajor Third (13/10)&lt;/h3&gt;
&lt;!-- ws:start:WikiTextHeadingRule:20:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc10"&gt;&lt;a name="Scale gallery-Equal divisions...-...of the Tridecimal Ultramajor Third (13/10)"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:20 --&gt;...of the Tridecimal Ultramajor Third (13/10)&lt;/h3&gt;
  &lt;a class="wiki_link" href="/Square%20root%20of%2013%20over%2010"&gt;Square root of 13 over 10&lt;/a&gt;&lt;br /&gt;
  &lt;a class="wiki_link" href="/Square%20root%20of%2013%20over%2010"&gt;Square root of 13 over 10&lt;/a&gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:20:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc10"&gt;&lt;a name="Scale gallery-Equal divisions...-... of the Triple Octave (8/1)"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:20 --&gt;... of the Triple Octave (8/1)&lt;/h3&gt;
&lt;!-- ws:start:WikiTextHeadingRule:22:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc11"&gt;&lt;a name="Scale gallery-Equal divisions...-... of the Triple Octave (8/1)"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:22 --&gt;... of the Triple Octave (8/1)&lt;/h3&gt;
  &lt;a class="wiki_link" href="/31ed8"&gt;31ed8&lt;/a&gt;&lt;br /&gt;
  &lt;a class="wiki_link" href="/31ed8"&gt;31ed8&lt;/a&gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:22:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc11"&gt;&lt;a name="Scale gallery-Equal multiplications"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:22 --&gt;Equal multiplications&lt;/h2&gt;
&lt;!-- ws:start:WikiTextHeadingRule:24:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc12"&gt;&lt;a name="Scale gallery-Equal multiplications"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:24 --&gt;Equal multiplications&lt;/h2&gt;
  &lt;!-- ws:start:WikiTextHeadingRule:24:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc12"&gt;&lt;a name="Scale gallery-Equal multiplications-...of a given cents value"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:24 --&gt;...of a given cents value&lt;/h3&gt;
  &lt;!-- ws:start:WikiTextHeadingRule:26:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc13"&gt;&lt;a name="Scale gallery-Equal multiplications-...of a given cents value"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:26 --&gt;...of a given cents value&lt;/h3&gt;
  &lt;a class="wiki_link" href="/88cET"&gt;88-cET&lt;/a&gt;&lt;br /&gt;
  &lt;a class="wiki_link" href="/88cET"&gt;88-cET&lt;/a&gt;&lt;br /&gt;
&lt;a class="wiki_link" href="/65cET"&gt;65cET&lt;/a&gt;&lt;br /&gt;
&lt;a class="wiki_link" href="/65cET"&gt;65cET&lt;/a&gt;&lt;br /&gt;
&lt;a class="wiki_link" href="/125cET"&gt;125cET&lt;/a&gt;&lt;br /&gt;
&lt;a class="wiki_link" href="/125cET"&gt;125cET&lt;/a&gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:26:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc13"&gt;&lt;a name="Scale gallery-Equal multiplications-.....of various whole tones"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:26 --&gt;.....of various whole tones&lt;/h3&gt;
&lt;!-- ws:start:WikiTextHeadingRule:28:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc14"&gt;&lt;a name="Scale gallery-Equal multiplications-.....of various whole tones"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:28 --&gt;.....of various whole tones&lt;/h3&gt;
  &lt;a class="wiki_link" href="/9%208ths%20equal%20temperament"&gt;9:8&lt;/a&gt;, &lt;a class="wiki_link" href="/10%209ths%20equal%20temperament"&gt;10:9&lt;/a&gt;, &lt;a class="wiki_link" href="/12%2011th%20equal%20temperament"&gt;12:11&lt;/a&gt;, &lt;a class="wiki_link" href="/13%2012ths%20equal%20temperament"&gt;13:12&lt;/a&gt;&lt;br /&gt;
  &lt;a class="wiki_link" href="/9%208ths%20equal%20temperament"&gt;9:8&lt;/a&gt;, &lt;a class="wiki_link" href="/10%209ths%20equal%20temperament"&gt;10:9&lt;/a&gt;, &lt;a class="wiki_link" href="/12%2011th%20equal%20temperament"&gt;12:11&lt;/a&gt;, &lt;a class="wiki_link" href="/13%2012ths%20equal%20temperament"&gt;13:12&lt;/a&gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:28:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc14"&gt;&lt;a name="Scale gallery-Equal multiplications-See also:"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:28 --&gt;See also:&lt;/h3&gt;
&lt;!-- ws:start:WikiTextHeadingRule:30:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc15"&gt;&lt;a name="Scale gallery-Equal multiplications-See also:"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:30 --&gt;See also:&lt;/h3&gt;
  &lt;a class="wiki_link" href="/edo%20anatomy"&gt;edo anatomy&lt;/a&gt;, &lt;a class="wiki_link" href="/macrotonal%20edos"&gt;macrotonal edos&lt;/a&gt;, &lt;a class="wiki_link" href="/maximal%20evenness"&gt;maximal evenness&lt;/a&gt;, &lt;a class="wiki_link" href="/Toctave"&gt;Toctave&lt;/a&gt;, &lt;a class="wiki_link" href="/The%20Riemann%20Zeta%20Function%20and%20Tuning"&gt;The Riemann Zeta Function and Tuning&lt;/a&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>
  &lt;a class="wiki_link" href="/edo%20anatomy"&gt;edo anatomy&lt;/a&gt;, &lt;a class="wiki_link" href="/macrotonal%20edos"&gt;macrotonal edos&lt;/a&gt;, &lt;a class="wiki_link" href="/maximal%20evenness"&gt;maximal evenness&lt;/a&gt;, &lt;a class="wiki_link" href="/Toctave"&gt;Toctave&lt;/a&gt;, &lt;a class="wiki_link" href="/The%20Riemann%20Zeta%20Function%20and%20Tuning"&gt;The Riemann Zeta Function and Tuning&lt;/a&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>