Equal-step tuning: Difference between revisions

Revision as of 19:19, 15 September 2007

IMPORTED REVISION FROM WIKISPACES

This is an imported revision from Wikispaces. The revision metadata is included below for reference:

This revision was by author xenjacob and made on 2007-09-15 19:19:12 UTC.

The original revision id was 8011637.

The revision comment was:

The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.

Original Wikitext content:

=Equal= 

**Equal: a tuning in which every single step is the same interval; an equal-step scale.**

The size of this single step is given explicitly (e.g. 88 cent equal temperament) or as a fraction of a larger interval (e.g. 13 equal tones per octave). (When a just interval is equally divided, none of the resulting intervals are just. See [[roots]].)

When a tuning is called "X tone equal temperament" (abbreviated -tET or -ET), this usually means "X divisions of 2/1, the octave," but it also implies a mindset of [[Regular Temperaments|temperament]]—that is, of a harmony-centric, JI-approximation-based understanding of the scale.

The less loaded term //EDO//, meaning "equal divisions of the octave," is helpful for leaving comparison to JI completely out of the picture. (There are other less standard terms, many in the [[http://www.tonalsoft.com/enc/encyclopedia.aspx|Tonalsoft Encyclopedia]].)

**As there are infinite intervals, there are infinite equal scales.** Barring technicalities there are large quantities of perceivably different equal scales. Seeing such a diverse menagerie at their disposal, some composers choose to combine multiple equal tunings [[ET surveys|sequentially]] or [[Polymicrotonality|simultaneously]].

----
== == 
=Scale gallery= 

==Equal divisions...== 

===...of the Octave (2/1)=== 
(wildly popular; [[edo|dedicated page]])
|| [[1edo]] || [[2edo]] || [[3edo]] || [[4edo]] || [[5edo]] || [[6edo]] || [[7edo]] || [[8edo]] || [[9edo]] || [[10edo]] || [[11edo]] || [[12edo]] ||
|| [[13edo]] || [[14edo]] || [[15edo]] || [[16edo]] || [[17edo]] || [[18edo]] || [[19edo]] || [[20edo]] || [[21edo]] || [[22edo]] || [[23edo]] || [[24edo]] ||
|| [[25edo]] || [[26edo]] || [[27edo]] || [[28edo]] || [[29edo]] || [[30edo]] || [[31edo]] || [[32edo]] || [[33edo]] || [[34edo]] || [[35edo]] || [[36edo]] ||
|| [[37edo]] || [[38edo]] || [[39edo]] || [[40edo]] || [[41edo]] || [[42edo]] || [[43edo]] || [[44edo]] || [[45edo]] || [[46edo]] || [[47edo]] || [[48edo]] ||
|| [[49edo]] || [[50edo]] || [[51edo]] || [[52edo]] || [[53edo]] || [[54edo]] || [[55edo]] || [[56edo]] || [[57edo]] || [[58edo]] || [[59edo]] || [[60edo]] ||
and so on to less popular areas... [[76edo]]

===...of the Tritave (3/1)=== 
12
[[BohlenPierce|13 (Bohlen-Pierce)]]

===...of the Perfect Fifth (3/2)=== 
[[88cET|8 (88-cET)]]

===...of the Just Major 17th (5/1)=== 
25 (Stockhausen, McLaren)

==Equal multiplications?== 
88-cET, Alpha, Beta, Gamma

Original HTML content:

<html><head><title>Equal-step Tuning</title></head><body><!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Equal"></a><!-- ws:end:WikiTextHeadingRule:0 -->Equal</h1>
 <br />
<strong>Equal: a tuning in which every single step is the same interval; an equal-step scale.</strong><br />
<br />
The size of this single step is given explicitly (e.g. 88 cent equal temperament) or as a fraction of a larger interval (e.g. 13 equal tones per octave). (When a just interval is equally divided, none of the resulting intervals are just. See <a class="wiki_link" href="/roots">roots</a>.)<br />
<br />
When a tuning is called &quot;X tone equal temperament&quot; (abbreviated -tET or -ET), this usually means &quot;X divisions of 2/1, the octave,&quot; but it also implies a mindset of <a class="wiki_link" href="/Regular%20Temperaments">temperament</a>—that is, of a harmony-centric, JI-approximation-based understanding of the scale.<br />
<br />
The less loaded term <em>EDO</em>, meaning &quot;equal divisions of the octave,&quot; is helpful for leaving comparison to JI completely out of the picture. (There are other less standard terms, many in the <a class="wiki_link_ext" href="http://www.tonalsoft.com/enc/encyclopedia.aspx" rel="nofollow">Tonalsoft Encyclopedia</a>.)<br />
<br />
<strong>As there are infinite intervals, there are infinite equal scales.</strong> Barring technicalities there are large quantities of perceivably different equal scales. Seeing such a diverse menagerie at their disposal, some composers choose to combine multiple equal tunings <a class="wiki_link" href="/ET%20surveys">sequentially</a> or <a class="wiki_link" href="/Polymicrotonality">simultaneously</a>.<br />
<br />
<hr />
<!-- ws:start:WikiTextHeadingRule:2:&lt;h2&gt; --><h2 id="toc1"><!-- ws:end:WikiTextHeadingRule:2 --> </h2>
 <!-- ws:start:WikiTextHeadingRule:4:&lt;h1&gt; --><h1 id="toc2"><a name="Scale gallery"></a><!-- ws:end:WikiTextHeadingRule:4 -->Scale gallery</h1>
 <br />
<!-- ws:start:WikiTextHeadingRule:6:&lt;h2&gt; --><h2 id="toc3"><a name="Scale gallery-Equal divisions..."></a><!-- ws:end:WikiTextHeadingRule:6 -->Equal divisions...</h2>
 <br />
<!-- ws:start:WikiTextHeadingRule:8:&lt;h3&gt; --><h3 id="toc4"><a name="Scale gallery-Equal divisions...-...of the Octave (2/1)"></a><!-- ws:end:WikiTextHeadingRule:8 -->...of the Octave (2/1)</h3>
 (wildly popular; <a class="wiki_link" href="/edo">dedicated page</a>)<br />


<table class="wiki_table">
    <tr>
        <td><a class="wiki_link" href="/1edo">1edo</a><br />
</td>
        <td><a class="wiki_link" href="/2edo">2edo</a><br />
</td>
        <td><a class="wiki_link" href="/3edo">3edo</a><br />
</td>
        <td><a class="wiki_link" href="/4edo">4edo</a><br />
</td>
        <td><a class="wiki_link" href="/5edo">5edo</a><br />
</td>
        <td><a class="wiki_link" href="/6edo">6edo</a><br />
</td>
        <td><a class="wiki_link" href="/7edo">7edo</a><br />
</td>
        <td><a class="wiki_link" href="/8edo">8edo</a><br />
</td>
        <td><a class="wiki_link" href="/9edo">9edo</a><br />
</td>
        <td><a class="wiki_link" href="/10edo">10edo</a><br />
</td>
        <td><a class="wiki_link" href="/11edo">11edo</a><br />
</td>
        <td><a class="wiki_link" href="/12edo">12edo</a><br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/13edo">13edo</a><br />
</td>
        <td><a class="wiki_link" href="/14edo">14edo</a><br />
</td>
        <td><a class="wiki_link" href="/15edo">15edo</a><br />
</td>
        <td><a class="wiki_link" href="/16edo">16edo</a><br />
</td>
        <td><a class="wiki_link" href="/17edo">17edo</a><br />
</td>
        <td><a class="wiki_link" href="/18edo">18edo</a><br />
</td>
        <td><a class="wiki_link" href="/19edo">19edo</a><br />
</td>
        <td><a class="wiki_link" href="/20edo">20edo</a><br />
</td>
        <td><a class="wiki_link" href="/21edo">21edo</a><br />
</td>
        <td><a class="wiki_link" href="/22edo">22edo</a><br />
</td>
        <td><a class="wiki_link" href="/23edo">23edo</a><br />
</td>
        <td><a class="wiki_link" href="/24edo">24edo</a><br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/25edo">25edo</a><br />
</td>
        <td><a class="wiki_link" href="/26edo">26edo</a><br />
</td>
        <td><a class="wiki_link" href="/27edo">27edo</a><br />
</td>
        <td><a class="wiki_link" href="/28edo">28edo</a><br />
</td>
        <td><a class="wiki_link" href="/29edo">29edo</a><br />
</td>
        <td><a class="wiki_link" href="/30edo">30edo</a><br />
</td>
        <td><a class="wiki_link" href="/31edo">31edo</a><br />
</td>
        <td><a class="wiki_link" href="/32edo">32edo</a><br />
</td>
        <td><a class="wiki_link" href="/33edo">33edo</a><br />
</td>
        <td><a class="wiki_link" href="/34edo">34edo</a><br />
</td>
        <td><a class="wiki_link" href="/35edo">35edo</a><br />
</td>
        <td><a class="wiki_link" href="/36edo">36edo</a><br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/37edo">37edo</a><br />
</td>
        <td><a class="wiki_link" href="/38edo">38edo</a><br />
</td>
        <td><a class="wiki_link" href="/39edo">39edo</a><br />
</td>
        <td><a class="wiki_link" href="/40edo">40edo</a><br />
</td>
        <td><a class="wiki_link" href="/41edo">41edo</a><br />
</td>
        <td><a class="wiki_link" href="/42edo">42edo</a><br />
</td>
        <td><a class="wiki_link" href="/43edo">43edo</a><br />
</td>
        <td><a class="wiki_link" href="/44edo">44edo</a><br />
</td>
        <td><a class="wiki_link" href="/45edo">45edo</a><br />
</td>
        <td><a class="wiki_link" href="/46edo">46edo</a><br />
</td>
        <td><a class="wiki_link" href="/47edo">47edo</a><br />
</td>
        <td><a class="wiki_link" href="/48edo">48edo</a><br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/49edo">49edo</a><br />
</td>
        <td><a class="wiki_link" href="/50edo">50edo</a><br />
</td>
        <td><a class="wiki_link" href="/51edo">51edo</a><br />
</td>
        <td><a class="wiki_link" href="/52edo">52edo</a><br />
</td>
        <td><a class="wiki_link" href="/53edo">53edo</a><br />
</td>
        <td><a class="wiki_link" href="/54edo">54edo</a><br />
</td>
        <td><a class="wiki_link" href="/55edo">55edo</a><br />
</td>
        <td><a class="wiki_link" href="/56edo">56edo</a><br />
</td>
        <td><a class="wiki_link" href="/57edo">57edo</a><br />
</td>
        <td><a class="wiki_link" href="/58edo">58edo</a><br />
</td>
        <td><a class="wiki_link" href="/59edo">59edo</a><br />
</td>
        <td><a class="wiki_link" href="/60edo">60edo</a><br />
</td>
    </tr>
</table>

and so on to less popular areas... <a class="wiki_link" href="/76edo">76edo</a><br />
<br />
<!-- ws:start:WikiTextHeadingRule:10:&lt;h3&gt; --><h3 id="toc5"><a name="Scale gallery-Equal divisions...-...of the Tritave (3/1)"></a><!-- ws:end:WikiTextHeadingRule:10 -->...of the Tritave (3/1)</h3>
 12<br />
<a class="wiki_link" href="/BohlenPierce">13 (Bohlen-Pierce)</a><br />
<br />
<!-- ws:start:WikiTextHeadingRule:12:&lt;h3&gt; --><h3 id="toc6"><a name="Scale gallery-Equal divisions...-...of the Perfect Fifth (3/2)"></a><!-- ws:end:WikiTextHeadingRule:12 -->...of the Perfect Fifth (3/2)</h3>
 <a class="wiki_link" href="/88cET">8 (88-cET)</a><br />
<br />
<!-- ws:start:WikiTextHeadingRule:14:&lt;h3&gt; --><h3 id="toc7"><a name="Scale gallery-Equal divisions...-...of the Just Major 17th (5/1)"></a><!-- ws:end:WikiTextHeadingRule:14 -->...of the Just Major 17th (5/1)</h3>
 25 (Stockhausen, McLaren)<br />
<br />
<!-- ws:start:WikiTextHeadingRule:16:&lt;h2&gt; --><h2 id="toc8"><a name="Scale gallery-Equal multiplications?"></a><!-- ws:end:WikiTextHeadingRule:16 -->Equal multiplications?</h2>
 88-cET, Alpha, Beta, Gamma</body></html>

@@ Line 1: / Line 1: @@
 <h2>IMPORTED REVISION FROM WIKISPACES</h2>
 This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
-: This revision was by author [[User:xenjacob|xenjacob]] and made on <tt>2007-09-15 19:00:27 UTC</tt>.<br>
+: This revision was by author [[User:xenjacob|xenjacob]] and made on <tt>2007-09-15 19:19:12 UTC</tt>.<br>
-: The original revision id was <tt>8011225</tt>.<br>
+: The original revision id was <tt>8011637</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>
@@ Line 8: / Line 8: @@
 <div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">=Equal=
-Equal: a tuning in which every single step is the same interval; an equal-step scale.
+**Equal: a tuning in which every single step is the same interval; an equal-step scale.**
 The size of this single step is given explicitly (e.g. 88 cent equal temperament) or as a fraction of a larger interval (e.g. 13 equal tones per octave). (When a just interval is equally divided, none of the resulting intervals are just. See [[roots]].)
@@ Line 14: / Line 14: @@
 When a tuning is called "X tone equal temperament" (abbreviated -tET or -ET), this usually means "X divisions of 2/1, the octave," but it also implies a mindset of [[Regular Temperaments|temperament]]—that is, of a harmony-centric, JI-approximation-based understanding of the scale.
-The less loaded term //EDO//, meaning "equal divisions of the octave," is helpful for leaving comparison to JI completely out of the picture.
+The less loaded term //EDO//, meaning "equal divisions of the octave," is helpful for leaving comparison to JI completely out of the picture. (There are other less standard terms, many in the [[http://www.tonalsoft.com/enc/encyclopedia.aspx|Tonalsoft Encyclopedia]].)
-There are other less standard terms, many in the [[http://www.tonalsoft.com/enc/encyclopedia.aspx|Tonalsoft Encyclopedia]].
+**As there are infinite intervals, there are infinite equal scales.** Barring technicalities there are large quantities of perceivably different equal scales. Seeing such a diverse menagerie at their disposal, some composers choose to combine multiple equal tunings [[ET surveys|sequentially]] or [[Polymicrotonality|simultaneously]].
 ----
 == ==
+=Scale gallery=
 ==Equal divisions...==
 ===...of the Octave (2/1)===
-[[edo|(wildly popular; dedicated page on e.d.o.)]]
+(wildly popular; [[edo|dedicated page]])
 || [[1edo]] || [[2edo]] || [[3edo]] || [[4edo]] || [[5edo]] || [[6edo]] || [[7edo]] || [[8edo]] || [[9edo]] || [[10edo]] || [[11edo]] || [[12edo]] ||
 || [[13edo]] || [[14edo]] || [[15edo]] || [[16edo]] || [[17edo]] || [[18edo]] || [[19edo]] || [[20edo]] || [[21edo]] || [[22edo]] || [[23edo]] || [[24edo]] ||
@@ Line 40: / Line 43: @@
 (Stockhausen, McLaren)
-==Equal multiplications==
+==Equal multiplications?==
--cET, Alpha, Beta, Gamma
+-cET, Alpha, Beta, Gamma</pre></div>
-----
-=Equal temperament surveys=
-A rather strange emerging genre. Some curious composers, wishing to test the Darregian notion that each equal temperament, to a certain extent, possesses a certain quality or mood to it, endeavor to compose entire series of pieces which sample the field, often sequentially. Easley Blackwood's rather neoclassical //Microtonal Etudes// (1980-1), in EDO's 13 through 24, was one of the first such surveys. [[McLaren|Brian McLaren]]'s idiosyncratic //240 Piano Pieces// from the 90's, with 5 pieces in each tuning from 5/oct to 53/oct (excepting 12!), might be the most extensive, so much that each set of 5 pieces might be thought of as a whole. [[Warren Burt]]'s //39 Dissonant Etudes// (1992-8) (5/oct to 43/oct) all use the same type of technique to generate "dissonance."
-Daniel Wolf has a series of etudes from ET's 8 through 23, excepting 10, 12, and 20, written between 1994 and 2004. Jacob Barton's //Moods// and //Xenharmonic Variations on a Theme by Mozart// from 2004 progress sequentially in sections (ET's 1-13 and 12-19). Igliashon Jones is currently at work on an album of electronic pop songs in EDOs 10-23 in which the time signature matches the tuning(!), an idea from Hans Straub, who has written such works in 5- and 17-EDO.
-In addition to the proper surveys, many individuals have made forays into a wide range of EDOs that don't necessarily constitute suites or "thorough" surveys. Ivor Darreg, Marc Jones, Gene Ward Smith, X. J. Scott, Andrew Heathwaite, and Aaron Hunt come to mind, as well as more music by Brian McLaren and Warren Burt.
-=[[Polymicrotonality]] with equal temperaments=
-You are invited to share your experiences with combining equal temperaments with each other and with unequal temperaments.</pre></div>
 <h4>Original HTML content:</h4>
 <div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html">&lt;html&gt;&lt;head&gt;&lt;title&gt;Equal-step Tuning&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="Equal"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Equal&lt;/h1&gt;
   &lt;br /&gt;
-Equal: a tuning in which every single step is the same interval; an equal-step scale.&lt;br /&gt;
+&lt;strong&gt;Equal: a tuning in which every single step is the same interval; an equal-step scale.&lt;/strong&gt;&lt;br /&gt;
 &lt;br /&gt;
 The size of this single step is given explicitly (e.g. 88 cent equal temperament) or as a fraction of a larger interval (e.g. 13 equal tones per octave). (When a just interval is equally divided, none of the resulting intervals are just. See &lt;a class="wiki_link" href="/roots"&gt;roots&lt;/a&gt;.)&lt;br /&gt;
@@ Line 64: / Line 54: @@
 When a tuning is called &amp;quot;X tone equal temperament&amp;quot; (abbreviated -tET or -ET), this usually means &amp;quot;X divisions of 2/1, the octave,&amp;quot; but it also implies a mindset of &lt;a class="wiki_link" href="/Regular%20Temperaments"&gt;temperament&lt;/a&gt;—that is, of a harmony-centric, JI-approximation-based understanding of the scale.&lt;br /&gt;
 &lt;br /&gt;
-The less loaded term &lt;em&gt;EDO&lt;/em&gt;, meaning &amp;quot;equal divisions of the octave,&amp;quot; is helpful for leaving comparison to JI completely out of the picture.&lt;br /&gt;
+The less loaded term &lt;em&gt;EDO&lt;/em&gt;, meaning &amp;quot;equal divisions of the octave,&amp;quot; is helpful for leaving comparison to JI completely out of the picture. (There are other less standard terms, many in the &lt;a class="wiki_link_ext" href="http://www.tonalsoft.com/enc/encyclopedia.aspx" rel="nofollow"&gt;Tonalsoft Encyclopedia&lt;/a&gt;.)&lt;br /&gt;
 &lt;br /&gt;
-There are other less standard terms, many in the &lt;a class="wiki_link_ext" href="http://www.tonalsoft.com/enc/encyclopedia.aspx" rel="nofollow"&gt;Tonalsoft Encyclopedia&lt;/a&gt;.&lt;br /&gt;
+&lt;strong&gt;As there are infinite intervals, there are infinite equal scales.&lt;/strong&gt; Barring technicalities there are large quantities of perceivably different equal scales. Seeing such a diverse menagerie at their disposal, some composers choose to combine multiple equal tunings &lt;a class="wiki_link" href="/ET%20surveys"&gt;sequentially&lt;/a&gt; or &lt;a class="wiki_link" href="/Polymicrotonality"&gt;simultaneously&lt;/a&gt;.&lt;br /&gt;
 &lt;br /&gt;
 &lt;hr /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc1"&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt; &lt;/h2&gt;
-  &lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc2"&gt;&lt;a name="Equal-Equal divisions..."&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;Equal divisions...&lt;/h2&gt;
+  &lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc2"&gt;&lt;a name="Scale gallery"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;Scale gallery&lt;/h1&gt;
-  &lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc3"&gt;&lt;a name="Equal-Equal divisions...-...of the Octave (2/1)"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;...of the Octave (2/1)&lt;/h3&gt;
+ &lt;br /&gt;
-  &lt;a class="wiki_link" href="/edo"&gt;(wildly popular; dedicated page on e.d.o.)&lt;/a&gt;&lt;br /&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc3"&gt;&lt;a name="Scale gallery-Equal divisions..."&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;Equal divisions...&lt;/h2&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 Octave (2/1)"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;...of the Octave (2/1)&lt;/h3&gt;
+  (wildly popular; &lt;a class="wiki_link" href="/edo"&gt;dedicated page&lt;/a&gt;)&lt;br /&gt;
@@ Line 210: / Line 203: @@
 and so on to less popular areas... &lt;a class="wiki_link" href="/76edo"&gt;76edo&lt;/a&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="Equal-Equal divisions...-...of the Tritave (3/1)"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;...of the Tritave (3/1)&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 Tritave (3/1)"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:10 --&gt;...of the Tritave (3/1)&lt;/h3&gt;
 &lt;br /&gt;
 &lt;a class="wiki_link" href="/BohlenPierce"&gt;13 (Bohlen-Pierce)&lt;/a&gt;&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="Equal-Equal divisions...-...of the Perfect Fifth (3/2)"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:10 --&gt;...of the Perfect Fifth (3/2)&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 Fifth (3/2)"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:12 --&gt;...of the Perfect Fifth (3/2)&lt;/h3&gt;
   &lt;a class="wiki_link" href="/88cET"&gt;8 (88-cET)&lt;/a&gt;&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="Equal-Equal divisions...-...of the Just Major 17th (5/1)"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:12 --&gt;...of the Just Major 17th (5/1)&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;...of the Just Major 17th (5/1)&lt;/h3&gt;
 (Stockhausen, McLaren)&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:14:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc7"&gt;&lt;a name="Equal-Equal multiplications"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:14 --&gt;Equal multiplications&lt;/h2&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:16:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc8"&gt;&lt;a name="Scale gallery-Equal multiplications?"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:16 --&gt;Equal multiplications?&lt;/h2&gt;
--cET, Alpha, Beta, Gamma&lt;br /&gt;
+-cET, Alpha, Beta, Gamma&lt;/body&gt;&lt;/html&gt;</pre></div>
-&lt;br /&gt;
-&lt;br /&gt;
-&lt;hr /&gt;
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-&lt;!-- ws:start:WikiTextHeadingRule:16:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc8"&gt;&lt;a name="Equal temperament surveys"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:16 --&gt;Equal temperament surveys&lt;/h1&gt;
- A rather strange emerging genre. Some curious composers, wishing to test the Darregian notion that each equal temperament, to a certain extent, possesses a certain quality or mood to it, endeavor to compose entire series of pieces which sample the field, often sequentially. Easley Blackwood's rather neoclassical &lt;em&gt;Microtonal Etudes&lt;/em&gt; (1980-1), in EDO's 13 through 24, was one of the first such surveys. &lt;a class="wiki_link" href="/McLaren"&gt;Brian McLaren&lt;/a&gt;'s idiosyncratic &lt;em&gt;240 Piano Pieces&lt;/em&gt; from the 90's, with 5 pieces in each tuning from 5/oct to 53/oct (excepting 12!), might be the most extensive, so much that each set of 5 pieces might be thought of as a whole. &lt;a class="wiki_link" href="/Warren%20Burt"&gt;Warren Burt&lt;/a&gt;'s &lt;em&gt;39 Dissonant Etudes&lt;/em&gt; (1992-8) (5/oct to 43/oct) all use the same type of technique to generate &amp;quot;dissonance.&amp;quot;&lt;br /&gt;
-&lt;br /&gt;
-Daniel Wolf has a series of etudes from ET's 8 through 23, excepting 10, 12, and 20, written between 1994 and 2004. Jacob Barton's &lt;em&gt;Moods&lt;/em&gt; and &lt;em&gt;Xenharmonic Variations on a Theme by Mozart&lt;/em&gt; from 2004 progress sequentially in sections (ET's 1-13 and 12-19). Igliashon Jones is currently at work on an album of electronic pop songs in EDOs 10-23 in which the time signature matches the tuning(!), an idea from Hans Straub, who has written such works in 5- and 17-EDO.&lt;br /&gt;
-&lt;br /&gt;
-In addition to the proper surveys, many individuals have made forays into a wide range of EDOs that don't necessarily constitute suites or &amp;quot;thorough&amp;quot; surveys. Ivor Darreg, Marc Jones, Gene Ward Smith, X. J. Scott, Andrew Heathwaite, and Aaron Hunt come to mind, as well as more music by Brian McLaren and Warren Burt.&lt;br /&gt;
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-&lt;!-- ws:start:WikiTextHeadingRule:18:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc9"&gt;&lt;a name="Polymicrotonality with equal temperaments"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:18 --&gt;&lt;a class="wiki_link" href="/Polymicrotonality"&gt;Polymicrotonality&lt;/a&gt; with equal temperaments&lt;/h1&gt;
- You are invited to share your experiences with combining equal temperaments with each other and with unequal temperaments.&lt;/body&gt;&lt;/html&gt;</pre></div>

Equal-step tuning: Difference between revisions

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