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