Magic family: Difference between revisions
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<h2>IMPORTED REVISION FROM WIKISPACES</h2> | <h2>IMPORTED REVISION FROM WIKISPACES</h2> | ||
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: 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 08:14:49 UTC</tt>.<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+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]]. 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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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 /> | |||
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.<br /> | |||
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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>. See <a class="wiki_link_ext" href="http://x31eq.com/cgi-bin/uv.cgi?uvs=245:243" rel="nofollow">temperament finder</a>.) <br /> | |||
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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 /> | ||