Equal-step tuning: Difference between revisions

Revision as of 03:30, 1 August 2008

IMPORTED REVISION FROM WIKISPACES

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

This revision was by author xenwolf and made on 2008-08-01 03:30:24 UTC.

The original revision id was 29133487.

The revision comment was: subsets of 12edo can be taken as "macrotonal tunings"

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... [[72edo]] [[76edo]] [[88edo]] [[96edo]]

The equal temperaments formatted in //italic// build subsets of //[[12edo]]// and can be taken as "[[macrotonal tuning]]s".

===...of the Tritave (3/1)=== 
[[12edt| 12]]
[[BP|13 (Bohlen-Pierce)]]
[[19 (Bernhard Stopper)]]

===...of the Perfect Fifth (3/2)=== 
[[4edf|4]]
[[6edf|6]]
[[88cET|8 (88-cET)]]
[[Carlos Alpha|9 (Carlos Alpha)]]
[[Carlos Beta|11 (Carlos Beta)]]
[[Carlos Gamma|20 (Carlos Gamma)]]

===...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><em><a class="wiki_link" href="/1edo">1edo</a></em><br />
</td>
        <td><em><a class="wiki_link" href="/2edo">2edo</a></em><br />
</td>
        <td><em><a class="wiki_link" href="/3edo">3edo</a></em><br />
</td>
        <td><em><a class="wiki_link" href="/4edo">4edo</a></em><br />
</td>
        <td><a class="wiki_link" href="/5edo">5edo</a><br />
</td>
        <td><em><a class="wiki_link" href="/6edo">6edo</a></em><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><em><a class="wiki_link" href="/12edo">12edo</a></em><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="/72edo">72edo</a> <a class="wiki_link" href="/76edo">76edo</a> <a class="wiki_link" href="/88edo">88edo</a> <a class="wiki_link" href="/96edo">96edo</a><br />
<br />
The equal temperaments formatted in <em>italic</em> build subsets of <em><a class="wiki_link" href="/12edo">12edo</a></em> and can be taken as &quot;<a class="wiki_link" href="/macrotonal%20tuning">macrotonal tuning</a>s&quot;.<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>
 <a class="wiki_link" href="/12edt"> 12</a><br />
<a class="wiki_link" href="/BP">13 (Bohlen-Pierce)</a><br />
<a class="wiki_link" href="/19%20%28Bernhard%20Stopper%29">19 (Bernhard Stopper)</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="/4edf">4</a><br />
<a class="wiki_link" href="/6edf">6</a><br />
<a class="wiki_link" href="/88cET">8 (88-cET)</a><br />
<a class="wiki_link" href="/Carlos%20Alpha">9 (Carlos Alpha)</a><br />
<a class="wiki_link" href="/Carlos%20Beta">11 (Carlos Beta)</a><br />
<a class="wiki_link" href="/Carlos%20Gamma">20 (Carlos Gamma)</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:hstraub|hstraub]] and made on <tt>2008-02-26 11:43:04 UTC</tt>.<br>
+: This revision was by author [[User:xenwolf|xenwolf]] and made on <tt>2008-08-01 03:30:24 UTC</tt>.<br>
-: The original revision id was <tt>17888045</tt>.<br>
+: The original revision id was <tt>29133487</tt>.<br>
-: The revision comment was: <tt>4edf</tt><br>
+: The revision comment was: <tt>subsets of 12edo can be taken as "macrotonal tunings"</tt><br>
 The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
 <h4>Original Wikitext content:</h4>
@@ Line 26: / Line 26: @@
 ===...of the Octave (2/1)===
 (wildly popular; [[edo|dedicated page]])
-|| [[1edo]] || [[2edo]] || [[3edo]] || [[4edo]] || [[5edo]] || [[6edo]] || [[7edo]] || [[8edo]] || [[9edo]] || [[10edo]] || [[11edo]] || [[12edo]] ||
+|| //[[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]] ||
@@ Line 32: / Line 32: @@
 || [[49edo]] || [[50edo]] || [[51edo]] || [[52edo]] || [[53edo]] || [[54edo]] || [[55edo]] || [[56edo]] || [[57edo]] || [[58edo]] || [[59edo]] || [[60edo]] ||
 and so on to less popular areas... [[72edo]] [[76edo]] [[88edo]] [[96edo]]
+The equal temperaments formatted in //italic// build subsets of //[[12edo]]// and can be taken as "[[macrotonal tuning]]s".
 ===...of the Tritave (3/1)===
@@ Line 76: / Line 78: @@
 &lt;table class="wiki_table"&gt;
      &lt;tr&gt;
-         &lt;td&gt;&lt;a class="wiki_link" href="/1edo"&gt;1edo&lt;/a&gt;&lt;br /&gt;
+         &lt;td&gt;&lt;em&gt;&lt;a class="wiki_link" href="/1edo"&gt;1edo&lt;/a&gt;&lt;/em&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;a class="wiki_link" href="/2edo"&gt;2edo&lt;/a&gt;&lt;br /&gt;
+         &lt;td&gt;&lt;em&gt;&lt;a class="wiki_link" href="/2edo"&gt;2edo&lt;/a&gt;&lt;/em&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;a class="wiki_link" href="/3edo"&gt;3edo&lt;/a&gt;&lt;br /&gt;
+         &lt;td&gt;&lt;em&gt;&lt;a class="wiki_link" href="/3edo"&gt;3edo&lt;/a&gt;&lt;/em&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;a class="wiki_link" href="/4edo"&gt;4edo&lt;/a&gt;&lt;br /&gt;
+         &lt;td&gt;&lt;em&gt;&lt;a class="wiki_link" href="/4edo"&gt;4edo&lt;/a&gt;&lt;/em&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;a class="wiki_link" href="/5edo"&gt;5edo&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;a class="wiki_link" href="/6edo"&gt;6edo&lt;/a&gt;&lt;br /&gt;
+         &lt;td&gt;&lt;em&gt;&lt;a class="wiki_link" href="/6edo"&gt;6edo&lt;/a&gt;&lt;/em&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;a class="wiki_link" href="/7edo"&gt;7edo&lt;/a&gt;&lt;br /&gt;
@@ Line 98: / Line 100: @@
          &lt;td&gt;&lt;a class="wiki_link" href="/11edo"&gt;11edo&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;a class="wiki_link" href="/12edo"&gt;12edo&lt;/a&gt;&lt;br /&gt;
+         &lt;td&gt;&lt;em&gt;&lt;a class="wiki_link" href="/12edo"&gt;12edo&lt;/a&gt;&lt;/em&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 208: / Line 210: @@
 and so on to less popular areas... &lt;a class="wiki_link" href="/72edo"&gt;72edo&lt;/a&gt; &lt;a class="wiki_link" href="/76edo"&gt;76edo&lt;/a&gt; &lt;a class="wiki_link" href="/88edo"&gt;88edo&lt;/a&gt; &lt;a class="wiki_link" href="/96edo"&gt;96edo&lt;/a&gt;&lt;br /&gt;
+&lt;br /&gt;
+The equal temperaments formatted in &lt;em&gt;italic&lt;/em&gt; build subsets of &lt;em&gt;&lt;a class="wiki_link" href="/12edo"&gt;12edo&lt;/a&gt;&lt;/em&gt; and can be taken as &amp;quot;&lt;a class="wiki_link" href="/macrotonal%20tuning"&gt;macrotonal tuning&lt;/a&gt;s&amp;quot;.&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 Tritave (3/1)"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:10 --&gt;...of the Tritave (3/1)&lt;/h3&gt;

Equal-step tuning: Difference between revisions

Revision as of 03:30, 1 August 2008

IMPORTED REVISION FROM WIKISPACES

Original Wikitext content:

Original HTML content:

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