Magic family: Difference between revisions

: The original revision id was <tt>519360540</tt>.<br>

&lt;span style="display: block; text-align: right;"&gt;Other languages: [[xenharmonie/Magische Temperaturen|Deutsch]]

&lt;/span&gt;

The most prominent deficiency of magic temperaments is that they lack [[Rothenberg propriety|proper]] or nearly-proper MOS scales in the 5 to 10 note "diatonic" region.

The 5-limit parent comma for the magic family is 3125/3072, the small diesis or magic comma. Its monzo is |-10 -1 5&gt;, and flipping that yields &lt;&lt;5 1 -10|| for the wedgie. This tells us the generator is a major third, and that to get to the interval class of fifths will require five of these. In fact, (5/4)^5 = 3 * 3125/3072. 13\41 is a highly recommendable generator, though 19\60, the optimal patent val generator, also makes a lot of sense and using [[19edo]] or [[22edo]] is always possible.

[[Comma]]: [[3125_3072|3125/3072]]

Algebraic generator: Terzbirat, the positive root of 9x^2-8x-4 = (4+2√13)/9; approximately 380.3175 [[Cent|cents]].

==Seven limit children==  

The second comma of the [[Normal lists|normal comma list]] defines which 7-limit family member we are looking at. 875/864, the keemic comma, gives magic, and 525/512, Avicenna's enharmonic diesis, gives his annoying brother muggles. Both use the major third as a generator.

=Magic=  

(See also [[Magic]].)

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 &lt;&lt;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. 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, &lt;&lt;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.

[[POTE tuning|POTE generator]]: 380.352

[[Generator|Generators]]: 2, 5/4

==11-limit==  

See also [[Chords of magic]]

[[POTE tuning|POTE generator]]: 380.696

==13-limit==  

===Sorcery===  

===Necromancy===  

==Telepathy==  

===13-limit telepathy===  

==Horcrux==  

=Divination=  

==13-limit==  

=Soothsaying=  

=Witchcraft=  

==13-limit==  

=Muggles=  

Aside from 3125/3072 and 525/512 muggles also tempers out 126/125 and 1323/1280. A good muggles tuning is [[19edo]], in which tuning it's the same thing as magic. Muggles works better for small scales than magic in the sense that 7 or 10 note MOS are reasonable choices. The muggles wedgie is &lt;&lt;5 1 -7 -10 -25 -19||.

[[POTE tuning|POTE generator]]: ~5/4 = 378.479

==11-limit==  

[[POTE tuning|POTE generator]]: ~5/4 = 377.724

==13-limit==  

[[POTE tuning|POTE generator]]: ~5/4 = 377.724

=Astrology=  

==11-limit==  

==13-limit==  

[[http://micro.soonlabel.com/gene_ward_smith/Others/Taylor/AstrologyPercQuintet1_c.mp3|Astrology Percussion Quintet No 1]] by [[https://soundcloud.com/joelgranttaylor/astrology-percussion-quintet|Joel Taylor]]

==Horoscope==  

=Spell=  

==11-limit==  

==13-limit==  

==Cantrip==  

=Hocum=  

=Hocus=  

==13-limit==  

=Trismegistus=  

==11-limit==  

==13-limit==  

=Quadrimage=  

==11-limit==  

==13-limit==  

Badness: 0.0440</pre></div>

[&amp;lt;1 0 0|, &amp;lt;0 1 0|, &amp;lt;2 1/5 0|]&lt;br /&gt;

Map: [&amp;lt;1 0 2|, &amp;lt;0 5 1|]&lt;br /&gt;

&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc1"&gt;&lt;a name="Five limit magic-Seven limit children"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;Seven limit children&lt;/h2&gt;

The second comma of the &lt;a class="wiki_link" href="/Normal%20lists"&gt;normal comma list&lt;/a&gt; defines which 7-limit family member we are looking at. 875/864, the keemic comma, gives magic, and 525/512, Avicenna's enharmonic diesis, gives his annoying brother muggles. Both use the major third as a generator.&lt;br /&gt;

valid range: [378.947, 381.818] (19 to 22)&lt;br /&gt;

nice range: [378.910, 386.314]&lt;br /&gt;

strict range: [378.947, 381.818]&lt;br /&gt;

Map: [&amp;lt;1 0 2 -1|, &amp;lt;0 5 1 12|]&lt;br /&gt;

&lt;a class="wiki_link" href="/Generator"&gt;Generators&lt;/a&gt;: 2, 5/4&lt;br /&gt;

See also &lt;a class="wiki_link" href="/Chords%20of%20magic"&gt;Chords of magic&lt;/a&gt;&lt;br /&gt;

nice range: [378.910, 386.314]&lt;br /&gt;

strict range: [378.947, 381.818]&lt;br /&gt;

Map: [&amp;lt;1 0 2 -1 6|, &amp;lt;0 5 1 12 -8|]&lt;br /&gt;

valid range: [378.947, 381.818] (19 to 22f)&lt;br /&gt;

nice range: [378.617, 386.314]&lt;br /&gt;

strict range: [378.947, 381.818]&lt;br /&gt;

Map: [&amp;lt;1 0 2 -1 6 -2|, &amp;lt;0 5 1 12 -8 18|]&lt;br /&gt;

nice range: [359.472, 386.314]&lt;br /&gt;

Map: [&amp;lt;1 0 2 -1 6 4|, &amp;lt;0 5 1 12 -8 -1|]&lt;br /&gt;

Map: [&amp;lt;1 0 2 -1 -1|, &amp;lt;0 5 1 12 14|]&lt;br /&gt;