Low harmonic entropy linear temperaments: Difference between revisions

Wikispaces>keenanpepper
**Imported revision 246374033 - Original comment: **
Wikispaces>keenanpepper
**Imported revision 246375261 - Original comment: **
Line 1: Line 1:
<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>2011-08-16 21:01:24 UTC</tt>.<br>
: This revision was by author [[User:keenanpepper|keenanpepper]] and made on <tt>2011-08-16 21:08:24 UTC</tt>.<br>
: The original revision id was <tt>246374033</tt>.<br>
: The original revision id was <tt>246375261</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>
Line 13: Line 13:
* [[5edo]] (coarse)
* [[5edo]] (coarse)
* [[7edo]] (coarse)
* [[7edo]] (coarse)
* [[12edo]] (coarse-medium)
* [[12edo]] (coarse/medium)
Temperaments where 4/3 has complexity 1 all have the same structure:
Temperaments where 4/3 has complexity 1 all have the same structure:
* [[Meantone]] (all-around)
* [[Meantone]] (all-around)
Line 29: Line 29:
Temperaments where 4/3 has higher complexity:
Temperaments where 4/3 has higher complexity:
* [[Magic family#Magic|Magic]] (5, fine)
* [[Magic family#Magic|Magic]] (5, fine)
* [[Orwell]] (7, fine)
* [[Orwell]] (7, extra fine)
* [[Starling temperaments#Myna temperament|Myna]] (10, fine)
* [[Starling temperaments#Myna temperament|Myna]] (10, extra fine)
* [[Hanson]]/[[Kleismic family#Catakleismic|catakleismic]] (6, extra fine)
* [[Hanson]]/[[Kleismic family#Catakleismic|catakleismic]] (6, extra fine)
* [[Gamelismic clan#Miracle|Miracle]] (6 extra fine)
* [[Gamelismic clan#Miracle|Miracle]] (6, super duper fine)
* [[Valentine]] (9, super duper fine)


Finally, a temperament in which 3 has two different mappings:
Finally, a temperament in which 3 has two different mappings:
Line 47: Line 48:
&lt;br /&gt;
&lt;br /&gt;
First of all, some small EDOs appear:&lt;br /&gt;
First of all, some small EDOs appear:&lt;br /&gt;
&lt;ul&gt;&lt;li&gt;&lt;a class="wiki_link" href="/5edo"&gt;5edo&lt;/a&gt; (coarse)&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link" href="/7edo"&gt;7edo&lt;/a&gt; (coarse)&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link" href="/12edo"&gt;12edo&lt;/a&gt; (coarse-medium)&lt;/li&gt;&lt;/ul&gt;Temperaments where 4/3 has complexity 1 all have the same structure:&lt;br /&gt;
&lt;ul&gt;&lt;li&gt;&lt;a class="wiki_link" href="/5edo"&gt;5edo&lt;/a&gt; (coarse)&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link" href="/7edo"&gt;7edo&lt;/a&gt; (coarse)&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link" href="/12edo"&gt;12edo&lt;/a&gt; (coarse/medium)&lt;/li&gt;&lt;/ul&gt;Temperaments where 4/3 has complexity 1 all have the same structure:&lt;br /&gt;
&lt;ul&gt;&lt;li&gt;&lt;a class="wiki_link" href="/Meantone"&gt;Meantone&lt;/a&gt; (all-around)&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link" href="/Archytas%20clan#Superpyth"&gt;Superpyth&lt;/a&gt; (all-around)&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link" href="/Mavila"&gt;Mavila&lt;/a&gt; (coarse)&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link" href="/Helmholtz"&gt;Helmholtz&lt;/a&gt;/&lt;a class="wiki_link" href="/Schismatic%20family#Garibaldi"&gt;garibaldi&lt;/a&gt; (fine)&lt;/li&gt;&lt;/ul&gt;Temperaments where 4/3 has complexity 2:&lt;br /&gt;
&lt;ul&gt;&lt;li&gt;&lt;a class="wiki_link" href="/Meantone"&gt;Meantone&lt;/a&gt; (all-around)&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link" href="/Archytas%20clan#Superpyth"&gt;Superpyth&lt;/a&gt; (all-around)&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link" href="/Mavila"&gt;Mavila&lt;/a&gt; (coarse)&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link" href="/Helmholtz"&gt;Helmholtz&lt;/a&gt;/&lt;a class="wiki_link" href="/Schismatic%20family#Garibaldi"&gt;garibaldi&lt;/a&gt; (fine)&lt;/li&gt;&lt;/ul&gt;Temperaments where 4/3 has complexity 2:&lt;br /&gt;
&lt;ul&gt;&lt;li&gt;&lt;a class="wiki_link" href="/Semaphore"&gt;Semaphore&lt;/a&gt; (both &lt;a class="wiki_link" href="/Meantone%20family#Godzilla"&gt;godzilla&lt;/a&gt; and no-5's semaphore, all-around)&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link" href="/Meantone%20family#Mohajira"&gt;Mohajira&lt;/a&gt; (both mohajira proper and no-5's mohajira, all-around)&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link" href="/Srutal"&gt;Srutal&lt;/a&gt;/&lt;a class="wiki_link" href="/Diaschismic%20family#Pajara"&gt;pajara&lt;/a&gt; (all-around)&lt;/li&gt;&lt;/ul&gt;Temperaments where 4/3 has complexity 3:&lt;br /&gt;
&lt;ul&gt;&lt;li&gt;&lt;a class="wiki_link" href="/Semaphore"&gt;Semaphore&lt;/a&gt; (both &lt;a class="wiki_link" href="/Meantone%20family#Godzilla"&gt;godzilla&lt;/a&gt; and no-5's semaphore, all-around)&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link" href="/Meantone%20family#Mohajira"&gt;Mohajira&lt;/a&gt; (both mohajira proper and no-5's mohajira, all-around)&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link" href="/Srutal"&gt;Srutal&lt;/a&gt;/&lt;a class="wiki_link" href="/Diaschismic%20family#Pajara"&gt;pajara&lt;/a&gt; (all-around)&lt;/li&gt;&lt;/ul&gt;Temperaments where 4/3 has complexity 3:&lt;br /&gt;
&lt;ul&gt;&lt;li&gt;&lt;a class="wiki_link" href="/Porcupine%20family#Porcupine"&gt;Porcupine&lt;/a&gt; (all-around)&lt;/li&gt;&lt;li&gt;1029/1024 2.3.7 temperament in the &lt;a class="wiki_link" href="/Gamelismic%20clan"&gt;gamelismic clan&lt;/a&gt; (medium/fine)&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link" href="/Meantone%20family#Liese"&gt;Liese&lt;/a&gt;/&lt;a class="wiki_link" href="/Marvel%20temperaments#Triton"&gt;triton&lt;/a&gt; (fine)&lt;/li&gt;&lt;/ul&gt;Temperaments where 4/3 has higher complexity:&lt;br /&gt;
&lt;ul&gt;&lt;li&gt;&lt;a class="wiki_link" href="/Porcupine%20family#Porcupine"&gt;Porcupine&lt;/a&gt; (all-around)&lt;/li&gt;&lt;li&gt;1029/1024 2.3.7 temperament in the &lt;a class="wiki_link" href="/Gamelismic%20clan"&gt;gamelismic clan&lt;/a&gt; (medium/fine)&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link" href="/Meantone%20family#Liese"&gt;Liese&lt;/a&gt;/&lt;a class="wiki_link" href="/Marvel%20temperaments#Triton"&gt;triton&lt;/a&gt; (fine)&lt;/li&gt;&lt;/ul&gt;Temperaments where 4/3 has higher complexity:&lt;br /&gt;
&lt;ul&gt;&lt;li&gt;&lt;a class="wiki_link" href="/Magic%20family#Magic"&gt;Magic&lt;/a&gt; (5, fine)&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link" href="/Orwell"&gt;Orwell&lt;/a&gt; (7, fine)&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link" href="/Starling%20temperaments#Myna temperament"&gt;Myna&lt;/a&gt; (10, fine)&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link" href="/Hanson"&gt;Hanson&lt;/a&gt;/&lt;a class="wiki_link" href="/Kleismic%20family#Catakleismic"&gt;catakleismic&lt;/a&gt; (6, extra fine)&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link" href="/Gamelismic%20clan#Miracle"&gt;Miracle&lt;/a&gt; (6 extra fine)&lt;/li&gt;&lt;/ul&gt;&lt;br /&gt;
&lt;ul&gt;&lt;li&gt;&lt;a class="wiki_link" href="/Magic%20family#Magic"&gt;Magic&lt;/a&gt; (5, fine)&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link" href="/Orwell"&gt;Orwell&lt;/a&gt; (7, extra fine)&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link" href="/Starling%20temperaments#Myna temperament"&gt;Myna&lt;/a&gt; (10, extra fine)&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link" href="/Hanson"&gt;Hanson&lt;/a&gt;/&lt;a class="wiki_link" href="/Kleismic%20family#Catakleismic"&gt;catakleismic&lt;/a&gt; (6, extra fine)&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link" href="/Gamelismic%20clan#Miracle"&gt;Miracle&lt;/a&gt; (6, super duper fine)&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link" href="/Valentine"&gt;Valentine&lt;/a&gt; (9, super duper fine)&lt;/li&gt;&lt;/ul&gt;&lt;br /&gt;
Finally, a temperament in which 3 has two different mappings:&lt;br /&gt;
Finally, a temperament in which 3 has two different mappings:&lt;br /&gt;
&lt;ul&gt;&lt;li&gt;&lt;a class="wiki_link" href="/Pseudo-semaphore"&gt;Pseudo-semaphore&lt;/a&gt; (medium)&lt;/li&gt;&lt;/ul&gt;&lt;br /&gt;
&lt;ul&gt;&lt;li&gt;&lt;a class="wiki_link" href="/Pseudo-semaphore"&gt;Pseudo-semaphore&lt;/a&gt; (medium)&lt;/li&gt;&lt;/ul&gt;&lt;br /&gt;
The following temperaments were not included in the list, because they don't stand out as good independent temperaments:&lt;br /&gt;
The following temperaments were not included in the list, because they don't stand out as good independent temperaments:&lt;br /&gt;
&lt;ul&gt;&lt;li&gt;Augmented (indistinguishable in practice from 12-EDO subsets)&lt;/li&gt;&lt;li&gt;Roulette (index-2 subtemperament of meantone)&lt;/li&gt;&lt;li&gt;Injera (pajara is simply better; injera just appears as a little shoulder on its side in a plot of average HE)&lt;/li&gt;&lt;/ul&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>
&lt;ul&gt;&lt;li&gt;Augmented (indistinguishable in practice from 12-EDO subsets)&lt;/li&gt;&lt;li&gt;Roulette (index-2 subtemperament of meantone)&lt;/li&gt;&lt;li&gt;Injera (pajara is simply better; injera just appears as a little shoulder on its side in a plot of average HE)&lt;/li&gt;&lt;/ul&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>