22edo: Difference between revisions

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<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>2007-06-25 09:20:24 UTC</tt>.<br>

: This revision was by author [[User:hstraub|hstraub]] and made on <tt>2007-06-25 09:27:09 UTC</tt>.<br>

: The original revision id was <tt>~~5478321~~</tt>.<br>

: The original revision id was <tt>5478453</tt>.<br>

: The revision comment was: <tt>~~Temperament links~~</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>

<h4>Original Wikitext content:</h4>

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In music, '''22 equal temperament''', called 22-tet, 22-edo, or 22-et, is the scale derived by dividing the octave into 22 equally large steps. Each step represents a frequency ratio of twenty-second root of 2, or 54.55 cents.

The idea of dividing the octave into 22 steps of equal size seems to have originated with nineteenth century music theorist RHM Bosanquet. Inspired by the division of the octave into 22 unequal parts in the music theory of India, Bosenquet noted that such an equal division was capable of representing 5-limit music with tolerable accuracy. In this he was followed in the twentieth century by theorist José Würschmidt, who noted it as a possible next step after [[19 equal temperament]], and J. Murray Barbour in his classic survey of tuning history, ''Tuning and Temperament''.

The idea of dividing the octave into 22 steps of equal size seems to have originated with nineteenth century music theorist RHM Bosanquet. Inspired by the division of the octave into 22 unequal parts in the music theory of India, Bosenquet noted that such an equal division was capable of representing 5-limit music with tolerable accuracy. In this he was followed in the twentieth century by theorist José Würschmidt, who noted it as a possible next step after [[19edo|19 equal temperament]], and J. Murray Barbour in his classic survey of tuning history, ''Tuning and Temperament''.

The 22-et system is in fact the third equal division, after 12 and 19, which is capable of tolerably dealing with 5-limit music. However, there is more to it than that; unlike 12 or 19 it is able to do rough justice to the 7- and 11-limits. While [[31 equal temperament]] does much better, 22-et at least allows the use of these higher-limit harmonies. Moreover, 22-et, unlike 12 and [[19edo|19]], is not a [[Regular Temperaments#meantone|meantone]] system. The net effect is that 22 allows, and to some extent even forces, the exploration of less familiar musical territory, yet is small enough that it can be used in live performances with suitably designed instruments, such as 22-tone guitars and the like.

The 22-et system is in fact the third equal division, after 12 and 19, which is capable of tolerably dealing with 5-limit music. However, there is more to it than that; unlike 12 or 19 it is able to do rough justice to the 7- and 11-limits. While [[31edo|31 equal temperament]] does much better, 22-et at least allows the use of these higher-limit harmonies. Moreover, 22-et, unlike 12 and [[19edo|19]], is not a [[Regular Temperaments#meantone|meantone]] system. The net effect is that 22 allows, and to some extent even forces, the exploration of less familiar musical territory, yet is small enough that it can be used in live performances with suitably designed instruments, such as 22-tone guitars and the like.

==Properties of 22 equal temperament==

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In music, '''22 equal temperament''', called 22-tet, 22-edo, or 22-et, is the scale derived by dividing the octave into 22 equally large steps. Each step represents a frequency ratio of twenty-second root of 2, or 54.55 cents.<br />

<br />

The idea of dividing the octave into 22 steps of equal size seems to have originated with nineteenth century music theorist RHM Bosanquet. Inspired by the division of the octave into 22 unequal parts in the music theory of India, Bosenquet noted that such an equal division was capable of representing 5-limit music with tolerable accuracy. In this he was followed in the twentieth century by theorist José Würschmidt, who noted it as a possible next step after <a class="wiki_link" href="/~~19%20equal%20temperament~~">19 equal temperament</a>, and J. Murray Barbour in his classic survey of tuning history, ''Tuning and Temperament''.<br />

The idea of dividing the octave into 22 steps of equal size seems to have originated with nineteenth century music theorist RHM Bosanquet. Inspired by the division of the octave into 22 unequal parts in the music theory of India, Bosenquet noted that such an equal division was capable of representing 5-limit music with tolerable accuracy. In this he was followed in the twentieth century by theorist José Würschmidt, who noted it as a possible next step after <a class="wiki_link" href="/19edo">19 equal temperament</a>, and J. Murray Barbour in his classic survey of tuning history, ''Tuning and Temperament''.<br />

<br />

The 22-et system is in fact the third equal division, after 12 and 19, which is capable of tolerably dealing with 5-limit music. However, there is more to it than that; unlike 12 or 19 it is able to do rough justice to the 7- and 11-limits. While <a class="wiki_link" href="/~~31%20equal%20temperament~~">31 equal temperament</a> does much better, 22-et at least allows the use of these higher-limit harmonies. Moreover, 22-et, unlike 12 and <a class="wiki_link" href="/19edo">19</a>, is not a <a class="wiki_link" href="/Regular%20Temperaments#meantone">meantone</a> system. The net effect is that 22 allows, and to some extent even forces, the exploration of less familiar musical territory, yet is small enough that it can be used in live performances with suitably designed instruments, such as 22-tone guitars and the like.<br />

The 22-et system is in fact the third equal division, after 12 and 19, which is capable of tolerably dealing with 5-limit music. However, there is more to it than that; unlike 12 or 19 it is able to do rough justice to the 7- and 11-limits. While <a class="wiki_link" href="/31edo">31 equal temperament</a> does much better, 22-et at least allows the use of these higher-limit harmonies. Moreover, 22-et, unlike 12 and <a class="wiki_link" href="/19edo">19</a>, is not a <a class="wiki_link" href="/Regular%20Temperaments#meantone">meantone</a> system. The net effect is that 22 allows, and to some extent even forces, the exploration of less familiar musical territory, yet is small enough that it can be used in live performances with suitably designed instruments, such as 22-tone guitars and the like.<br />

<br />

<h2 id="toc1"><a name="x22 tone equal temperament-Properties of 22 equal temperament"></a>Properties of 22 equal temperament</h2>

@@ 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>2007-06-25 09:20:24 UTC</tt>.<br>
+: This revision was by author [[User:hstraub|hstraub]] and made on <tt>2007-06-25 09:27:09 UTC</tt>.<br>
-: The original revision id was <tt>5478321</tt>.<br>
+: The original revision id was <tt>5478453</tt>.<br>
-: The revision comment was: <tt>Temperament links</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>
 <h4>Original Wikitext content:</h4>
@@ Line 10: / Line 10: @@
 In music, '''22 equal temperament''', called 22-tet, 22-edo, or 22-et, is the scale derived by dividing the octave into 22 equally large steps. Each step represents a frequency ratio of twenty-second root of 2, or 54.55 cents.
-The idea of dividing the octave into 22 steps of equal size seems to have originated with nineteenth century music theorist RHM Bosanquet. Inspired by the division of the octave into 22 unequal parts in the music theory of India, Bosenquet noted that such an equal division was capable of representing 5-limit music with tolerable accuracy. In this he was followed in the twentieth century by theorist José Würschmidt, who noted it as a possible next step after [[19 equal temperament]], and J. Murray Barbour in his classic survey of tuning history, ''Tuning and Temperament''.
+The idea of dividing the octave into 22 steps of equal size seems to have originated with nineteenth century music theorist RHM Bosanquet. Inspired by the division of the octave into 22 unequal parts in the music theory of India, Bosenquet noted that such an equal division was capable of representing 5-limit music with tolerable accuracy. In this he was followed in the twentieth century by theorist José Würschmidt, who noted it as a possible next step after [[19edo|19 equal temperament]], and J. Murray Barbour in his classic survey of tuning history, ''Tuning and Temperament''.
-The 22-et system is in fact the third equal division, after 12 and 19, which is capable of tolerably dealing with 5-limit music. However, there is more to it than that; unlike 12 or 19 it is able to do rough justice to the 7- and 11-limits. While [[31 equal temperament]] does much better, 22-et at least allows the use of these higher-limit harmonies. Moreover, 22-et, unlike 12 and [[19edo|19]], is not a [[Regular Temperaments#meantone|meantone]] system. The net effect is that 22 allows, and to some extent even forces, the exploration of less familiar musical territory, yet is small enough that it can be used in live performances with suitably designed instruments, such as 22-tone guitars and the like.
+The 22-et system is in fact the third equal division, after 12 and 19, which is capable of tolerably dealing with 5-limit music. However, there is more to it than that; unlike 12 or 19 it is able to do rough justice to the 7- and 11-limits. While [[31edo|31 equal temperament]] does much better, 22-et at least allows the use of these higher-limit harmonies. Moreover, 22-et, unlike 12 and [[19edo|19]], is not a [[Regular Temperaments#meantone|meantone]] system. The net effect is that 22 allows, and to some extent even forces, the exploration of less familiar musical territory, yet is small enough that it can be used in live performances with suitably designed instruments, such as 22-tone guitars and the like.
 ==Properties of 22 equal temperament==
@@ Line 35: / Line 35: @@
 In music, '''22 equal temperament''', called 22-tet, 22-edo, or 22-et, is the scale derived by dividing the octave into 22 equally large steps. Each step represents a frequency ratio of twenty-second root of 2, or 54.55 cents.&lt;br /&gt;
 &lt;br /&gt;
-The idea of dividing the octave into 22 steps of equal size seems to have originated with nineteenth century music theorist RHM Bosanquet. Inspired by the division of the octave into 22 unequal parts in the music theory of India, Bosenquet noted that such an equal division was capable of representing 5-limit music with tolerable accuracy. In this he was followed in the twentieth century by theorist José Würschmidt, who noted it as a possible next step after &lt;a class="wiki_link" href="/19%20equal%20temperament"&gt;19 equal temperament&lt;/a&gt;, and J. Murray Barbour in his classic survey of tuning history, ''Tuning and Temperament''.&lt;br /&gt;
+The idea of dividing the octave into 22 steps of equal size seems to have originated with nineteenth century music theorist RHM Bosanquet. Inspired by the division of the octave into 22 unequal parts in the music theory of India, Bosenquet noted that such an equal division was capable of representing 5-limit music with tolerable accuracy. In this he was followed in the twentieth century by theorist José Würschmidt, who noted it as a possible next step after &lt;a class="wiki_link" href="/19edo"&gt;19 equal temperament&lt;/a&gt;, and J. Murray Barbour in his classic survey of tuning history, ''Tuning and Temperament''.&lt;br /&gt;
 &lt;br /&gt;
-The 22-et system is in fact the third equal division, after 12 and 19, which is capable of tolerably dealing with 5-limit music. However, there is more to it than that; unlike 12 or 19 it is able to do rough justice to the 7- and 11-limits. While &lt;a class="wiki_link" href="/31%20equal%20temperament"&gt;31 equal temperament&lt;/a&gt; does much better, 22-et at least allows the use of these higher-limit harmonies. Moreover, 22-et, unlike 12 and &lt;a class="wiki_link" href="/19edo"&gt;19&lt;/a&gt;, is not a &lt;a class="wiki_link" href="/Regular%20Temperaments#meantone"&gt;meantone&lt;/a&gt; system. The net effect is that 22 allows, and to some extent even forces, the exploration of less familiar musical territory, yet is small enough that it can be used in live performances with suitably designed instruments, such as 22-tone guitars and the like.&lt;br /&gt;
+The 22-et system is in fact the third equal division, after 12 and 19, which is capable of tolerably dealing with 5-limit music. However, there is more to it than that; unlike 12 or 19 it is able to do rough justice to the 7- and 11-limits. While &lt;a class="wiki_link" href="/31edo"&gt;31 equal temperament&lt;/a&gt; does much better, 22-et at least allows the use of these higher-limit harmonies. Moreover, 22-et, unlike 12 and &lt;a class="wiki_link" href="/19edo"&gt;19&lt;/a&gt;, is not a &lt;a class="wiki_link" href="/Regular%20Temperaments#meantone"&gt;meantone&lt;/a&gt; system. The net effect is that 22 allows, and to some extent even forces, the exploration of less familiar musical territory, yet is small enough that it can be used in live performances with suitably designed instruments, such as 22-tone guitars and the like.&lt;br /&gt;
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc1"&gt;&lt;a name="x22 tone equal temperament-Properties of 22 equal temperament"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;Properties of 22 equal temperament&lt;/h2&gt;