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: | : 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> | : 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.<br /> | 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.<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextLocalImageRule: | <!-- ws:start:WikiTextLocalImageRule:33:&lt;img src=&quot;/file/view/equal.png/277409084/800x69/equal.png&quot; alt=&quot;&quot; title=&quot;&quot; style=&quot;height: 69px; width: 800px;&quot; /&gt; --><img src="/file/view/equal.png/277409084/800x69/equal.png" alt="equal.png" title="equal.png" style="height: 69px; width: 800px;" /><!-- ws:end:WikiTextLocalImageRule:33 --><br /> | ||
<br /> | <br /> | ||
(Unlimited resolution version: <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');">equal.svg</a>)<br /> | (Unlimited resolution version: <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');">equal.svg</a>)<br /> | ||
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<!-- ws:start:WikiTextHeadingRule:12:&lt;h3&gt; --><h3 id="toc6"><a name="Scale gallery-Equal divisions...-...of the Just Major 17th (5/1)"></a><!-- ws:end:WikiTextHeadingRule:12 --><a class="wiki_link" href="/ed5">...of the Just Major 17th (5/1)</a></h3> | <!-- ws:start:WikiTextHeadingRule:12:&lt;h3&gt; --><h3 id="toc6"><a name="Scale gallery-Equal divisions...-...of the Just Major 17th (5/1)"></a><!-- ws:end:WikiTextHeadingRule:12 --><a class="wiki_link" href="/ed5">...of the Just Major 17th (5/1)</a></h3> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:14:&lt;h3&gt; --><h3 id="toc7"><a name="Scale gallery-Equal divisions...-...of the Perfect Fifth (3/2)"></a><!-- ws:end:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:14:&lt;h3&gt; --><h3 id="toc7"><a name="Scale gallery-Equal divisions...-...of the 7th Natural (7/1)"></a><!-- ws:end:WikiTextHeadingRule:14 --><a class="wiki_link" href="/ed7">...of the 7th Natural (7/1)</a></h3> | ||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:16:&lt;h3&gt; --><h3 id="toc8"><a name="Scale gallery-Equal divisions...-...of the Perfect Fifth (3/2)"></a><!-- ws:end:WikiTextHeadingRule:16 --><a class="wiki_link" href="/edf">...of the Perfect Fifth (3/2)</a></h3> | |||
most famously Carlos Alpha, Beta and Gamma, but lots of others, too<br /> | most famously Carlos Alpha, Beta and Gamma, but lots of others, too<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:18:&lt;h3&gt; --><h3 id="toc9"><a name="Scale gallery-Equal divisions...-...of the Perfect Fourth (4/3)"></a><!-- ws:end:WikiTextHeadingRule:18 -->...of the Perfect Fourth (4/3)</h3> | ||
3 - <a class="wiki_link" href="/Cube%20Root%20of%20P4">Cube Root of 4/3</a><br /> | 3 - <a class="wiki_link" href="/Cube%20Root%20of%20P4">Cube Root of 4/3</a><br /> | ||
9 - '<a class="wiki_link" href="/Noleta">Noleta</a>' Scale<br /> | 9 - '<a class="wiki_link" href="/Noleta">Noleta</a>' Scale<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:20:&lt;h3&gt; --><h3 id="toc10"><a name="Scale gallery-Equal divisions...-...of the Tridecimal Ultramajor Third (13/10)"></a><!-- ws:end:WikiTextHeadingRule:20 -->...of the Tridecimal Ultramajor Third (13/10)</h3> | ||
<a class="wiki_link" href="/Square%20root%20of%2013%20over%2010">Square root of 13 over 10</a><br /> | <a class="wiki_link" href="/Square%20root%20of%2013%20over%2010">Square root of 13 over 10</a><br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:22:&lt;h3&gt; --><h3 id="toc11"><a name="Scale gallery-Equal divisions...-... of the Triple Octave (8/1)"></a><!-- ws:end:WikiTextHeadingRule:22 -->... of the Triple Octave (8/1)</h3> | ||
<a class="wiki_link" href="/31ed8">31ed8</a><br /> | <a class="wiki_link" href="/31ed8">31ed8</a><br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:24:&lt;h2&gt; --><h2 id="toc12"><a name="Scale gallery-Equal multiplications"></a><!-- ws:end:WikiTextHeadingRule:24 -->Equal multiplications</h2> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:26:&lt;h3&gt; --><h3 id="toc13"><a name="Scale gallery-Equal multiplications-...of a given cents value"></a><!-- ws:end:WikiTextHeadingRule:26 -->...of a given cents value</h3> | ||
<a class="wiki_link" href="/88cET">88-cET</a><br /> | <a class="wiki_link" href="/88cET">88-cET</a><br /> | ||
<a class="wiki_link" href="/65cET">65cET</a><br /> | <a class="wiki_link" href="/65cET">65cET</a><br /> | ||
<a class="wiki_link" href="/125cET">125cET</a><br /> | <a class="wiki_link" href="/125cET">125cET</a><br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:28:&lt;h3&gt; --><h3 id="toc14"><a name="Scale gallery-Equal multiplications-.....of various whole tones"></a><!-- ws:end:WikiTextHeadingRule:28 -->.....of various whole tones</h3> | ||
<a class="wiki_link" href="/9%208ths%20equal%20temperament">9:8</a>, <a class="wiki_link" href="/10%209ths%20equal%20temperament">10:9</a>, <a class="wiki_link" href="/12%2011th%20equal%20temperament">12:11</a>, <a class="wiki_link" href="/13%2012ths%20equal%20temperament">13:12</a><br /> | <a class="wiki_link" href="/9%208ths%20equal%20temperament">9:8</a>, <a class="wiki_link" href="/10%209ths%20equal%20temperament">10:9</a>, <a class="wiki_link" href="/12%2011th%20equal%20temperament">12:11</a>, <a class="wiki_link" href="/13%2012ths%20equal%20temperament">13:12</a><br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:30:&lt;h3&gt; --><h3 id="toc15"><a name="Scale gallery-Equal multiplications-See also:"></a><!-- ws:end:WikiTextHeadingRule:30 -->See also:</h3> | ||
<a class="wiki_link" href="/edo%20anatomy">edo anatomy</a>, <a class="wiki_link" href="/macrotonal%20edos">macrotonal edos</a>, <a class="wiki_link" href="/maximal%20evenness">maximal evenness</a>, <a class="wiki_link" href="/Toctave">Toctave</a>, <a class="wiki_link" href="/The%20Riemann%20Zeta%20Function%20and%20Tuning">The Riemann Zeta Function and Tuning</a></body></html></pre></div> | <a class="wiki_link" href="/edo%20anatomy">edo anatomy</a>, <a class="wiki_link" href="/macrotonal%20edos">macrotonal edos</a>, <a class="wiki_link" href="/maximal%20evenness">maximal evenness</a>, <a class="wiki_link" href="/Toctave">Toctave</a>, <a class="wiki_link" href="/The%20Riemann%20Zeta%20Function%20and%20Tuning">The Riemann Zeta Function and Tuning</a></body></html></pre></div> | ||