Equal-step tuning: Difference between revisions

Line 1:

<h2>IMPORTED REVISION FROM WIKISPACES</h2>

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

: This revision was by author [[User:igliashon|igliashon]] and made on <tt>2011-07-~~15 09~~:55:23 UTC</tt>.

: This revision was by author [[User:igliashon|igliashon]] and made on <tt>2011-07-16 19:37:28 UTC</tt>.

: The original revision id was <tt>~~241474831~~</tt>.

: The original revision id was <tt>241612589</tt>.

: The revision comment was: <tt></tt>

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

Line 14:

When a tuning is called "n-tone equal temperament" (abbreviated n-tET or n-ET), this usually means "n divisions of 2/1, the octave, or some approximation thereof" 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 theory-laden term //EDO// (occasionally written ED2), meaning "equal divisions of the octave" (or "equal divisions of 2/1"), leaves comparison to JI out of the picture, aside from the octave itself. (There are other less standard terms, many in the [[http://www.tonalsoft.com/enc/encyclopedia.aspx|Tonalsoft Encyclopedia]].) More generally, the term //EDn// can be used, where n is any harmonic of the harmonic series. For example, the equal-tempered Bohlen-Pierce scale may also be referred to as 13-ED3, for 13 equal divisions of 3/1 (the 3rd harmonic).

There are many reasons why one might choose to not consider JI approximations when dealing with equal tunings, and thus not treat equal tunings as temperaments. In such case, the less theory-laden term //EDO//(occasionally written ED2), meaning "equal divisions of the octave" (or "equal divisions of 2/1"), leaves comparison to JI out of the picture, aside from the octave itself (which is assumed to be Just). There are other less standard terms, many in the [[http://www.tonalsoft.com/enc/encyclopedia.aspx|Tonalsoft Encyclopedia]]. More generally, the term //EDn// can be used, where n is any harmonic of the harmonic series. For example, the equal-tempered Bohlen-Pierce scale may also be referred to as 13-ED3, for 13 equal divisions of 3/1 (the 3rd harmonic).

**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]].

Line 71:

When a tuning is called &quot;n-tone equal temperament&quot; (abbreviated n-tET or n-ET), this usually means &quot;n divisions of 2/1, the octave, or some approximation thereof&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.

~~The~~ less theory-laden term EDO (occasionally written ED2), meaning &quot;equal divisions of the octave&quot; (or &quot;equal divisions of 2/1&quot;), leaves comparison to JI out of the picture, aside from the octave itself. (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>.) More generally, the term EDn can be used, where n is any harmonic of the harmonic series. For example, the equal-tempered Bohlen-Pierce scale may also be referred to as 13-ED3, for 13 equal divisions of 3/1 (the 3rd harmonic).

There are many reasons why one might choose to not consider JI approximations when dealing with equal tunings, and thus not treat equal tunings as temperaments. In such case, the less theory-laden term EDO(occasionally written ED2), meaning &quot;equal divisions of the octave&quot; (or &quot;equal divisions of 2/1&quot;), leaves comparison to JI out of the picture, aside from the octave itself (which is assumed to be Just). 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>. More generally, the term EDn can be used, where n is any harmonic of the harmonic series. For example, the equal-tempered Bohlen-Pierce scale may also be referred to as 13-ED3, for 13 equal divisions of 3/1 (the 3rd harmonic).

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 <a class="wiki_link" href="/ET%20surveys">sequentially</a> or <a class="wiki_link" href="/Polymicrotonality">simultaneously</a>.

@@ 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:igliashon|igliashon]] and made on <tt>2011-07-15 09:55:23 UTC</tt>.<br>
+: This revision was by author [[User:igliashon|igliashon]] and made on <tt>2011-07-16 19:37:28 UTC</tt>.<br>
-: The original revision id was <tt>241474831</tt>.<br>
+: The original revision id was <tt>241612589</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 14: / Line 14: @@
 When a tuning is called "n-tone equal temperament" (abbreviated n-tET or n-ET), this usually means "n divisions of 2/1, the octave, or some approximation thereof" 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 theory-laden term //EDO// (occasionally written ED2), meaning "equal divisions of the octave" (or "equal divisions of 2/1"), leaves comparison to JI out of the picture, aside from the octave itself. (There are other less standard terms, many in the [[http://www.tonalsoft.com/enc/encyclopedia.aspx|Tonalsoft Encyclopedia]].) More generally, the term //EDn// can be used, where n is any harmonic of the harmonic series. For example, the equal-tempered Bohlen-Pierce scale may also be referred to as 13-ED3, for 13 equal divisions of 3/1 (the 3rd harmonic).
+There are many reasons why one might choose to not consider JI approximations when dealing with equal tunings, and thus not treat equal tunings as temperaments. In such case, the less theory-laden term //EDO//(occasionally written ED2), meaning "equal divisions of the octave" (or "equal divisions of 2/1"), leaves comparison to JI out of the picture, aside from the octave itself (which is assumed to be Just). There are other less standard terms, many in the [[http://www.tonalsoft.com/enc/encyclopedia.aspx|Tonalsoft Encyclopedia]]. More generally, the term //EDn// can be used, where n is any harmonic of the harmonic series. For example, the equal-tempered Bohlen-Pierce scale may also be referred to as 13-ED3, for 13 equal divisions of 3/1 (the 3rd harmonic).
 **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]].
@@ Line 71: / Line 71: @@
 When a tuning is called &amp;quot;n-tone equal temperament&amp;quot; (abbreviated n-tET or n-ET), this usually means &amp;quot;n divisions of 2/1, the octave, or some approximation thereof&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 theory-laden term &lt;em&gt;EDO&lt;/em&gt; (occasionally written ED2), meaning &amp;quot;equal divisions of the octave&amp;quot; (or &amp;quot;equal divisions of 2/1&amp;quot;), leaves comparison to JI out of the picture, aside from the octave itself. (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;.) More generally, the term &lt;em&gt;EDn&lt;/em&gt; can be used, where n is any harmonic of the harmonic series. For example, the equal-tempered Bohlen-Pierce scale may also be referred to as 13-ED3, for 13 equal divisions of 3/1 (the 3rd harmonic).&lt;br /&gt;
+There are many reasons why one might choose to not consider JI approximations when dealing with equal tunings, and thus not treat equal tunings as temperaments. In such case, the less theory-laden term &lt;em&gt;EDO&lt;/em&gt;(occasionally written ED2), meaning &amp;quot;equal divisions of the octave&amp;quot; (or &amp;quot;equal divisions of 2/1&amp;quot;), leaves comparison to JI out of the picture, aside from the octave itself (which is assumed to be Just). 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;. More generally, the term &lt;em&gt;EDn&lt;/em&gt; can be used, where n is any harmonic of the harmonic series. For example, the equal-tempered Bohlen-Pierce scale may also be referred to as 13-ED3, for 13 equal divisions of 3/1 (the 3rd harmonic).&lt;br /&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;