22edo: Difference between revisions
Wikispaces>keenanpepper **Imported revision 249240357 - Original comment: ** |
Wikispaces>keenanpepper **Imported revision 268023498 - Original comment: ** |
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<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:keenanpepper|keenanpepper]] and made on <tt>2011- | : This revision was by author [[User:keenanpepper|keenanpepper]] and made on <tt>2011-10-24 14:29:28 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>268023498</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> | ||
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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 [[Indian|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 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 [[Indian|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, and while not an integral or gap edo it at least qualifies as a [[The Riemann Zeta Function and Tuning#Zeta | 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, and while not an integral or gap edo it at least qualifies as a [[The Riemann Zeta Function and Tuning#Zeta%20EDO%20lists|zeta peak]]. Moreover, there is more to it than just the 5-limit; unlike 12 or 19 it is able to do rough justice to the [[7-limit|7-]] and [[11-limit]]s. While [[31edo|31 equal temperament]] does much better, 22-et at least allows the use of these higher-limit harmonies, and in fact 22 is the smallest equal division to represent the 11-limit[[consistent| consistent]]ly. Furthermore, 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. | ||
22-et can also be treated as adding harmonics 3 and 5 to 11-EDO's 2.7.9.11.15.17 subgroup, making it a (rather accurate) 2.3.5.7.11.17 subgroup temperament. | 22-et can also be treated as adding harmonics 3 and 5 to 11-EDO's 2.7.9.11.15.17 subgroup, making it a (rather accurate) 2.3.5.7.11.17 subgroup temperament. | ||
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|| 1 || 5\22 || [[Orson]]/[[orwell]] || | || 1 || 5\22 || [[Orson]]/[[orwell]] || | ||
|| 1 || 7\22 || [[Magic]] || | || 1 || 7\22 || [[Magic]] || | ||
|| 1 || 9\22 || [[Superpyth]] || | || 1 || 9\22 || [[Superpyth]]/[[suprapyth]] || | ||
|| 2 || 1\22 || [[Shrutar]] || | || 2 || 1\22 || [[Shrutar]] || | ||
|| 2 || 2\22 || [[Srutal]]/[[pajara]] || | || 2 || 2\22 || [[Srutal]]/[[pajara]] || | ||
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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 <a class="wiki_link" href="/Indian">music theory of India</a>, 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 /> | 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 <a class="wiki_link" href="/Indian">music theory of India</a>, 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 /> | <br /> | ||
The 22-et system is in fact the third equal division, after 12 and 19, which is capable of tolerably dealing with <a class="wiki_link" href="/5-limit">5-limit</a> music, and while not an integral or gap edo it at least qualifies as a <a class="wiki_link" href="/The%20Riemann%20Zeta%20Function%20and%20Tuning#Zeta | The 22-et system is in fact the third equal division, after 12 and 19, which is capable of tolerably dealing with <a class="wiki_link" href="/5-limit">5-limit</a> music, and while not an integral or gap edo it at least qualifies as a <a class="wiki_link" href="/The%20Riemann%20Zeta%20Function%20and%20Tuning#Zeta%20EDO%20lists">zeta peak</a>. Moreover, there is more to it than just the 5-limit; unlike 12 or 19 it is able to do rough justice to the <a class="wiki_link" href="/7-limit">7-</a> and <a class="wiki_link" href="/11-limit">11-limit</a>s. 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, and in fact 22 is the smallest equal division to represent the 11-limit<a class="wiki_link" href="/consistent"> consistent</a>ly. Furthermore, 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 /> | <br /> | ||
22-et can also be treated as adding harmonics 3 and 5 to 11-EDO's 2.7.9.11.15.17 subgroup, making it a (rather accurate) 2.3.5.7.11.17 subgroup temperament.<br /> | 22-et can also be treated as adding harmonics 3 and 5 to 11-EDO's 2.7.9.11.15.17 subgroup, making it a (rather accurate) 2.3.5.7.11.17 subgroup temperament.<br /> | ||
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<td>9\22<br /> | <td>9\22<br /> | ||
</td> | </td> | ||
<td><a class="wiki_link" href="/Superpyth">Superpyth</a><br /> | <td><a class="wiki_link" href="/Superpyth">Superpyth</a>/<a class="wiki_link" href="/suprapyth">suprapyth</a><br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||