Magic family: Difference between revisions
Wikispaces>x31eq **Imported revision 401595338 - 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:x31eq|x31eq]] and made on <tt>2013-01-26 | : This revision was by author [[User:x31eq|x31eq]] and made on <tt>2013-01-26 10:35:07 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>401608738</tt>.<br> | ||
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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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Magic, with its accurate fifths, works well with 9-limit harmony. It's more accurate than [[Meantone family|meantone]] and simpler than [[Garibaldi temperament|garibaldi]]. It's a little tricky to work with because in it fifths are a relatively complex interval and it doesn't naturally work with scales of around seven notes to the octave. Its wedgie is <<5 1 12 -10 5 25||. | Magic, with its accurate fifths, works well with 9-limit harmony. It's more accurate than [[Meantone family|meantone]] and simpler than [[Garibaldi temperament|garibaldi]]. It's a little tricky to work with because in it fifths are a relatively complex interval and it doesn't naturally work with scales of around seven notes to the octave. Its wedgie is <<5 1 12 -10 5 25||. | ||
225/224 is the [[Marvel | 225/224 is the [[Marvel temperaments|marvel]] comma. Because the augmented triad is the simplest triad in magic temperaments, it is especially significant in magic temperament. | ||
243/242 leads to another essentially tempered 9-limit triad with two thirds approximating 9/7 and the other 6/5. (This "octarod comma" is shared with [[Sensi|sensi]], [[Semaphore and Godzilla|godzilla]], [[Superpyth|superpyth]], [[Tetracot family|octacot]], [[Gamelismic clan|rodan]], [[Shrutar|shrutar]], [[Porcupine family|hedgehog]], [[Clyde node|clyde]], and [[Sensamagic clan|bohpier]]. | 243/242 leads to another essentially tempered 9-limit triad with two thirds approximating 9/7 and the other 6/5. It also divides the approximate 3/2 into two steps of 7/6 and one of 10/9. (This "octarod comma" is shared with [[Sensi|sensi]], [[Semaphore and Godzilla|godzilla]], [[Superpyth|superpyth]], [[Tetracot family|octacot]], [[Gamelismic clan|rodan]], [[Shrutar|shrutar]], [[Porcupine family|hedgehog]], [[Clyde node|clyde]], and [[Sensamagic clan|bohpier]]. See [[http://x31eq.com/cgi-bin/uv.cgi?uvs=245:243|temperament finder]].) | ||
By adding 100/99 to the list of commas, magic can be extended to an 11-limit version, <<5 1 12 -8 ... ||. For this, [[104edo]] provides an excellent tuning, as it does also for the rank three temperaments tempering out 100/99 with 225/224, 245/243 or 875/864. Septimage (see below) is also an excellent 11-limit magic tuning. | By adding 100/99 to the list of commas, magic can be extended to an 11-limit version, <<5 1 12 -8 ... ||. For this, [[104edo]] provides an excellent tuning, as it does also for the rank three temperaments tempering out 100/99 with 225/224, 245/243 or 875/864. Septimage (see below) is also an excellent 11-limit magic tuning. | ||
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EDOs: 41, 142cd, 183cd, 224cd | EDOs: 41, 142cd, 183cd, 224cd | ||
==11-limit== | ==11-limit== | ||
Tempering 100/99 allows for a tritone substitution where the extended 5-limit tuning of a dominant seventh with a 9/5 above the root shares its tritone with an 8:10:11:12:16 chord rooted on the seventh of the original chord. (The tritone of the dominant seventh is (9/5)/(5/4)=36/25. (16/11)/(26/25)=100/99.) | |||
See also [[Chords of magic]] | |||
Commas: 225/224, 245/243, 100/99 | Commas: 225/224, 245/243, 100/99 | ||
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Magic, with its accurate fifths, works well with 9-limit harmony. It's more accurate than <a class="wiki_link" href="/Meantone%20family">meantone</a> and simpler than <a class="wiki_link" href="/Garibaldi%20temperament">garibaldi</a>. It's a little tricky to work with because in it fifths are a relatively complex interval and it doesn't naturally work with scales of around seven notes to the octave. Its wedgie is &lt;&lt;5 1 12 -10 5 25||.<br /> | Magic, with its accurate fifths, works well with 9-limit harmony. It's more accurate than <a class="wiki_link" href="/Meantone%20family">meantone</a> and simpler than <a class="wiki_link" href="/Garibaldi%20temperament">garibaldi</a>. It's a little tricky to work with because in it fifths are a relatively complex interval and it doesn't naturally work with scales of around seven notes to the octave. Its wedgie is &lt;&lt;5 1 12 -10 5 25||.<br /> | ||
<br /> | <br /> | ||
225/224 is the | 225/224 is the <a class="wiki_link" href="/Marvel%20temperaments">marvel</a> comma. Because the augmented triad is the simplest triad in magic temperaments, it is especially significant in magic temperament.<br /> | ||
<br /> | <br /> | ||
243/242 leads to another essentially tempered 9-limit triad with two thirds approximating 9/7 and the other 6/5. (This &quot;octarod comma&quot; is shared with <a class="wiki_link" href="/Sensi">sensi</a>, <a class="wiki_link" href="/Semaphore%20and%20Godzilla">godzilla</a>, <a class="wiki_link" href="/Superpyth">superpyth</a>, <a class="wiki_link" href="/Tetracot%20family">octacot</a>, <a class="wiki_link" href="/Gamelismic%20clan">rodan</a>, <a class="wiki_link" href="/Shrutar">shrutar</a>, <a class="wiki_link" href="/Porcupine%20family">hedgehog</a>, <a class="wiki_link" href="/Clyde%20node">clyde</a>, and <a class="wiki_link" href="/Sensamagic%20clan">bohpier</a>. | 243/242 leads to another essentially tempered 9-limit triad with two thirds approximating 9/7 and the other 6/5. It also divides the approximate 3/2 into two steps of 7/6 and one of 10/9. (This &quot;octarod comma&quot; is shared with <a class="wiki_link" href="/Sensi">sensi</a>, <a class="wiki_link" href="/Semaphore%20and%20Godzilla">godzilla</a>, <a class="wiki_link" href="/Superpyth">superpyth</a>, <a class="wiki_link" href="/Tetracot%20family">octacot</a>, <a class="wiki_link" href="/Gamelismic%20clan">rodan</a>, <a class="wiki_link" href="/Shrutar">shrutar</a>, <a class="wiki_link" href="/Porcupine%20family">hedgehog</a>, <a class="wiki_link" href="/Clyde%20node">clyde</a>, and <a class="wiki_link" href="/Sensamagic%20clan">bohpier</a>. See <a class="wiki_link_ext" href="http://x31eq.com/cgi-bin/uv.cgi?uvs=245:243" rel="nofollow">temperament finder</a>.)<br /> | ||
<br /> | <br /> | ||
By adding 100/99 to the list of commas, magic can be extended to an 11-limit version, &lt;&lt;5 1 12 -8 ... ||. For this, <a class="wiki_link" href="/104edo">104edo</a> provides an excellent tuning, as it does also for the rank three temperaments tempering out 100/99 with 225/224, 245/243 or 875/864. Septimage (see below) is also an excellent 11-limit magic tuning.<br /> | By adding 100/99 to the list of commas, magic can be extended to an 11-limit version, &lt;&lt;5 1 12 -8 ... ||. For this, <a class="wiki_link" href="/104edo">104edo</a> provides an excellent tuning, as it does also for the rank three temperaments tempering out 100/99 with 225/224, 245/243 or 875/864. Septimage (see below) is also an excellent 11-limit magic tuning.<br /> | ||
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<!-- ws:start:WikiTextHeadingRule:6:&lt;h2&gt; --><h2 id="toc3"><a name="Magic-11-limit"></a><!-- ws:end:WikiTextHeadingRule:6 -->11-limit</h2> | <!-- ws:start:WikiTextHeadingRule:6:&lt;h2&gt; --><h2 id="toc3"><a name="Magic-11-limit"></a><!-- ws:end:WikiTextHeadingRule:6 -->11-limit</h2> | ||
Commas: 225/224, 245/243, 100/99<br /> | <br /> | ||
Tempering 100/99 allows for a tritone substitution where the extended 5-limit tuning of a dominant seventh with a 9/5 above the root shares its tritone with an 8:10:11:12:16 chord rooted on the seventh of the original chord. (The tritone of the dominant seventh is (9/5)/(5/4)=36/25. (16/11)/(26/25)=100/99.)<br /> | |||
<br /> | |||
See also <a class="wiki_link" href="/Chords%20of%20magic">Chords of magic</a><br /> | |||
<br /> | |||
Commas: 225/224, 245/243, 100/99<br /> | |||
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<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 380.696<br /> | <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 380.696<br /> | ||