Equal-step tuning: Difference between revisions

Wikispaces>genewardsmith
**Imported revision 268591002 - Original comment: **
Wikispaces>Andrew_Heathwaite
**Imported revision 277294250 - 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:genewardsmith|genewardsmith]] and made on <tt>2011-10-25 21:27:34 UTC</tt>.<br>
: This revision was by author [[User:Andrew_Heathwaite|Andrew_Heathwaite]] and made on <tt>2011-11-19 21:14:43 UTC</tt>.<br>
: The original revision id was <tt>268591002</tt>.<br>
: The original revision id was <tt>277294250</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 22: Line 22:


==Equal divisions...==  
==Equal divisions...==  
===[[edo|...of the Octave/Duple (2/1)]]===  
===[[edo|...of the Octave/Duple (2/1)]]===  
by far the most widespread ones
by far the most widespread ones


===[[edt|...of the Tritave/Triple (3/1)]]===  
===[[edt|...of the Tritave/Triple (3/1)]]===  
most famously the [[BP]] scale, but lots of others, too


===[[edf|...of the Perfect Fifth (3/2)]]===  
===[[edf|...of the Perfect Fifth (3/2)]]===  
most famously Carlos Alpha, Beta and Gamma, but lots of others, too


===...of the Perfect Fourth (4/3)===  
===...of the Perfect Fourth (4/3)===  
Line 35: Line 36:


===[[ed5|...of the Just Major 17th (5/1)]]===  
===[[ed5|...of the Just Major 17th (5/1)]]===  
===[[ed4|...of the Double Octave (4/1)]]===
===...of the Tridecimal Ultramajor Third (13/10)===
[[Square root of 13 over 10]]
==Equal multiplications==
===...of a given cents value===
[[88cET|88-cET]]
[[65cET]]


===.....of various whole tones===  
===.....of various whole tones===  
[[9 8ths equal temperament|9:8]], 10:9, 12:11, 13:12
[[9 8ths equal temperament|9:8]], 10:9, 12:11, 13:12
==Equal multiplications?==
[[88cET|88-cET]], Alpha, Beta, Gamma


===See also:===  
===See also:===  
Line 62: Line 69:
  &lt;br /&gt;
  &lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc2"&gt;&lt;a name="Scale gallery-Equal divisions..."&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;Equal divisions...&lt;/h2&gt;
&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc2"&gt;&lt;a name="Scale gallery-Equal divisions..."&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;Equal divisions...&lt;/h2&gt;
  &lt;br /&gt;
  &lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc3"&gt;&lt;a name="Scale gallery-Equal divisions...-...of the Octave/Duple (2/1)"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;&lt;a class="wiki_link" href="/edo"&gt;...of the Octave/Duple (2/1)&lt;/a&gt;&lt;/h3&gt;
&lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc3"&gt;&lt;a name="Scale gallery-Equal divisions...-...of the Octave/Duple (2/1)"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;&lt;a class="wiki_link" href="/edo"&gt;...of the Octave/Duple (2/1)&lt;/a&gt;&lt;/h3&gt;
  by far the most widespread ones&lt;br /&gt;
  by far the most widespread ones&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:8:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc4"&gt;&lt;a name="Scale gallery-Equal divisions...-...of the Tritave/Triple (3/1)"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;&lt;a class="wiki_link" href="/edt"&gt;...of the Tritave/Triple (3/1)&lt;/a&gt;&lt;/h3&gt;
&lt;!-- ws:start:WikiTextHeadingRule:8:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc4"&gt;&lt;a name="Scale gallery-Equal divisions...-...of the Tritave/Triple (3/1)"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;&lt;a class="wiki_link" href="/edt"&gt;...of the Tritave/Triple (3/1)&lt;/a&gt;&lt;/h3&gt;
  &lt;br /&gt;
  most famously the &lt;a class="wiki_link" href="/BP"&gt;BP&lt;/a&gt; scale, but lots of others, too&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:10:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc5"&gt;&lt;a name="Scale gallery-Equal divisions...-...of the Perfect Fifth (3/2)"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:10 --&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:10:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc5"&gt;&lt;a name="Scale gallery-Equal divisions...-...of the Perfect Fifth (3/2)"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:10 --&gt;&lt;a class="wiki_link" href="/edf"&gt;...of the Perfect Fifth (3/2)&lt;/a&gt;&lt;/h3&gt;
  &lt;br /&gt;
  most famously Carlos Alpha, Beta and Gamma, but lots of others, too&lt;br /&gt;
&lt;br /&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 Perfect Fourth (4/3)"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:12 --&gt;...of the Perfect Fourth (4/3)&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 Perfect Fourth (4/3)"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:12 --&gt;...of the Perfect Fourth (4/3)&lt;/h3&gt;
  &lt;a class="wiki_link" href="/Cube%20Root%20of%20P4"&gt;Cube Root of 4/3&lt;/a&gt;&lt;br /&gt;
  &lt;a class="wiki_link" href="/Cube%20Root%20of%20P4"&gt;Cube Root of 4/3&lt;/a&gt;&lt;br /&gt;
Line 76: Line 84:
&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 Just Major 17th (5/1)"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:14 --&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:14:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc7"&gt;&lt;a name="Scale gallery-Equal divisions...-...of the Just Major 17th (5/1)"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:14 --&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:16:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc8"&gt;&lt;a name="Scale gallery-Equal divisions...-.....of various whole tones"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:16 --&gt;.....of various whole tones&lt;/h3&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 Double Octave (4/1)"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:16 --&gt;&lt;a class="wiki_link" href="/ed4"&gt;...of the Double Octave (4/1)&lt;/a&gt;&lt;/h3&gt;
  &lt;br /&gt;
  &lt;br /&gt;
&lt;a class="wiki_link" href="/9%208ths%20equal%20temperament"&gt;9:8&lt;/a&gt;, 10:9, 12:11, 13:12&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;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;!-- ws:start:WikiTextHeadingRule:20:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc10"&gt;&lt;a name="Scale gallery-Equal multiplications"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:20 --&gt;Equal multiplications&lt;/h2&gt;
&lt;!-- ws:start:WikiTextHeadingRule:22:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc11"&gt;&lt;a name="Scale gallery-Equal multiplications-...of a given cents value"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:22 --&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="/65cET"&gt;65cET&lt;/a&gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:18:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc9"&gt;&lt;a name="Scale gallery-Equal multiplications?"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:18 --&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 various whole tones"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:24 --&gt;.....of various whole tones&lt;/h3&gt;
  &lt;a class="wiki_link" href="/88cET"&gt;88-cET&lt;/a&gt;, Alpha, Beta, Gamma&lt;br /&gt;
  &lt;a class="wiki_link" href="/9%208ths%20equal%20temperament"&gt;9:8&lt;/a&gt;, 10:9, 12:11, 13:12&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 multiplications?-See also:"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:20 --&gt;See also:&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-See also:"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:26 --&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="/quasi-equal"&gt;quasi-equal&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="/quasi-equal"&gt;quasi-equal&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>