7-limit: Difference between revisions

Wikispaces>xenwolf
**Imported revision 239308589 - Original comment: **
Wikispaces>Andrew_Heathwaite
**Imported revision 262979100 - 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:xenwolf|xenwolf]] and made on <tt>2011-06-29 09:13:58 UTC</tt>.<br>
: This revision was by author [[User:Andrew_Heathwaite|Andrew_Heathwaite]] and made on <tt>2011-10-09 12:07:09 UTC</tt>.<br>
: The original revision id was <tt>239308589</tt>.<br>
: The original revision id was <tt>262979100</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>
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The phrase "7-limit just intonation" usually refers to the 7 prime-limit and includes primes 2, 3, 5, and 7. When octave equivalence is assumed, an interval can be taken as a pitch class representing that interval in every possible octave. This leaves primes 3, 5, and 7, which can be represented in [[The Seven Limit Symmetrical Lattices|3-dimensional lattice diagrams]], each prime represented by a different dimension. Lattices describing scales beyond the 7-limit require more than three dimensions, and in the 7-limit, such lattices have unique features which simplify the relations between 7-limit chords.
The phrase "7-limit just intonation" usually refers to the 7 prime-limit and includes primes 2, 3, 5, and 7. When octave equivalence is assumed, an interval can be taken as a pitch class representing that interval in every possible octave. This leaves primes 3, 5, and 7, which can be represented in [[The Seven Limit Symmetrical Lattices|3-dimensional lattice diagrams]], each prime represented by a different dimension. Lattices describing scales beyond the 7-limit require more than three dimensions, and in the 7-limit, such lattices have unique features which simplify the relations between 7-limit chords.


For a variety of reasons, common-practice music has been somewhat stuck at the 5-limit for centuries, though 7-limit intervals have a characteristic jazzy sound which is at least partially familiar. Music in the 7-limit thus represents a large step forward, although not as much as 11- or 13-limit, which usually sound much more exotic.
For a variety of reasons, common-practice music has been somewhat stuck at the 5-limit for centuries, though 7-limit intervals have a characteristic jazzy sound which is at least partially familiar. Music in the 7-limit thus represents a large step forward, although not as much as [[11-limit|11-]] or [[13-limit]], which usually sound much more exotic.


Relative to their size, the equal divisions [[12edo]], [[19edo]], [[31edo]], [[99edo]] and [[171edo]] provide good approximations to the 7-limit, with [[15edo]], [[22edo]], [[27edo]], [[41edo]], [[46edo]], [[53edo]], [[58edo]], [[68edo]], [[72edo]], [[118edo]], [[130edo]], [[140edo]] and [[152edo]] among the others worthy of notice.
Relative to their size, the equal divisions [[12edo]], [[19edo]], [[31edo]], [[99edo]] and [[171edo]] provide good approximations to the 7-limit, with [[15edo]], [[22edo]], [[27edo]], [[41edo]], [[46edo]], [[53edo]], [[58edo]], [[68edo]], [[72edo]], [[118edo]], [[130edo]], [[140edo]] and [[152edo]] among the others worthy of notice.
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see [[Harmonic Limit]]
see [[Harmonic Limit]]


=Music=
=Music=  
[[http://micro.soonlabel.com/blue-tuning/blue-ji-excluded-by-peers.mp3|Excluded by Peers]] by [[Chris Vaisvil]]
[[http://micro.soonlabel.com/blue-tuning/blue-ji-excluded-by-peers.mp3|Excluded by Peers]] by [[Chris Vaisvil]]
[[http://micro.soonlabel.com/centaur_tuning/Prelude_For_Centaur_Tuned_Piano.mp3|Prelude for Centaur Tuned Piano]] by Chris Vaisvil
[[http://micro.soonlabel.com/centaur_tuning/Prelude_For_Centaur_Tuned_Piano.mp3|Prelude for Centaur Tuned Piano]] by Chris Vaisvil
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The phrase &amp;quot;7-limit just intonation&amp;quot; usually refers to the 7 prime-limit and includes primes 2, 3, 5, and 7. When octave equivalence is assumed, an interval can be taken as a pitch class representing that interval in every possible octave. This leaves primes 3, 5, and 7, which can be represented in &lt;a class="wiki_link" href="/The%20Seven%20Limit%20Symmetrical%20Lattices"&gt;3-dimensional lattice diagrams&lt;/a&gt;, each prime represented by a different dimension. Lattices describing scales beyond the 7-limit require more than three dimensions, and in the 7-limit, such lattices have unique features which simplify the relations between 7-limit chords.&lt;br /&gt;
The phrase &amp;quot;7-limit just intonation&amp;quot; usually refers to the 7 prime-limit and includes primes 2, 3, 5, and 7. When octave equivalence is assumed, an interval can be taken as a pitch class representing that interval in every possible octave. This leaves primes 3, 5, and 7, which can be represented in &lt;a class="wiki_link" href="/The%20Seven%20Limit%20Symmetrical%20Lattices"&gt;3-dimensional lattice diagrams&lt;/a&gt;, each prime represented by a different dimension. Lattices describing scales beyond the 7-limit require more than three dimensions, and in the 7-limit, such lattices have unique features which simplify the relations between 7-limit chords.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
For a variety of reasons, common-practice music has been somewhat stuck at the 5-limit for centuries, though 7-limit intervals have a characteristic jazzy sound which is at least partially familiar. Music in the 7-limit thus represents a large step forward, although not as much as 11- or 13-limit, which usually sound much more exotic.&lt;br /&gt;
For a variety of reasons, common-practice music has been somewhat stuck at the 5-limit for centuries, though 7-limit intervals have a characteristic jazzy sound which is at least partially familiar. Music in the 7-limit thus represents a large step forward, although not as much as &lt;a class="wiki_link" href="/11-limit"&gt;11-&lt;/a&gt; or &lt;a class="wiki_link" href="/13-limit"&gt;13-limit&lt;/a&gt;, which usually sound much more exotic.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Relative to their size, the equal divisions &lt;a class="wiki_link" href="/12edo"&gt;12edo&lt;/a&gt;, &lt;a class="wiki_link" href="/19edo"&gt;19edo&lt;/a&gt;, &lt;a class="wiki_link" href="/31edo"&gt;31edo&lt;/a&gt;, &lt;a class="wiki_link" href="/99edo"&gt;99edo&lt;/a&gt; and &lt;a class="wiki_link" href="/171edo"&gt;171edo&lt;/a&gt; provide good approximations to the 7-limit, with &lt;a class="wiki_link" href="/15edo"&gt;15edo&lt;/a&gt;, &lt;a class="wiki_link" href="/22edo"&gt;22edo&lt;/a&gt;, &lt;a class="wiki_link" href="/27edo"&gt;27edo&lt;/a&gt;, &lt;a class="wiki_link" href="/41edo"&gt;41edo&lt;/a&gt;, &lt;a class="wiki_link" href="/46edo"&gt;46edo&lt;/a&gt;, &lt;a class="wiki_link" href="/53edo"&gt;53edo&lt;/a&gt;, &lt;a class="wiki_link" href="/58edo"&gt;58edo&lt;/a&gt;, &lt;a class="wiki_link" href="/68edo"&gt;68edo&lt;/a&gt;, &lt;a class="wiki_link" href="/72edo"&gt;72edo&lt;/a&gt;, &lt;a class="wiki_link" href="/118edo"&gt;118edo&lt;/a&gt;, &lt;a class="wiki_link" href="/130edo"&gt;130edo&lt;/a&gt;, &lt;a class="wiki_link" href="/140edo"&gt;140edo&lt;/a&gt; and &lt;a class="wiki_link" href="/152edo"&gt;152edo&lt;/a&gt; among the others worthy of notice.&lt;br /&gt;
Relative to their size, the equal divisions &lt;a class="wiki_link" href="/12edo"&gt;12edo&lt;/a&gt;, &lt;a class="wiki_link" href="/19edo"&gt;19edo&lt;/a&gt;, &lt;a class="wiki_link" href="/31edo"&gt;31edo&lt;/a&gt;, &lt;a class="wiki_link" href="/99edo"&gt;99edo&lt;/a&gt; and &lt;a class="wiki_link" href="/171edo"&gt;171edo&lt;/a&gt; provide good approximations to the 7-limit, with &lt;a class="wiki_link" href="/15edo"&gt;15edo&lt;/a&gt;, &lt;a class="wiki_link" href="/22edo"&gt;22edo&lt;/a&gt;, &lt;a class="wiki_link" href="/27edo"&gt;27edo&lt;/a&gt;, &lt;a class="wiki_link" href="/41edo"&gt;41edo&lt;/a&gt;, &lt;a class="wiki_link" href="/46edo"&gt;46edo&lt;/a&gt;, &lt;a class="wiki_link" href="/53edo"&gt;53edo&lt;/a&gt;, &lt;a class="wiki_link" href="/58edo"&gt;58edo&lt;/a&gt;, &lt;a class="wiki_link" href="/68edo"&gt;68edo&lt;/a&gt;, &lt;a class="wiki_link" href="/72edo"&gt;72edo&lt;/a&gt;, &lt;a class="wiki_link" href="/118edo"&gt;118edo&lt;/a&gt;, &lt;a class="wiki_link" href="/130edo"&gt;130edo&lt;/a&gt;, &lt;a class="wiki_link" href="/140edo"&gt;140edo&lt;/a&gt; and &lt;a class="wiki_link" href="/152edo"&gt;152edo&lt;/a&gt; among the others worthy of notice.&lt;br /&gt;
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&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="Music"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Music&lt;/h1&gt;
&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="Music"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Music&lt;/h1&gt;
&lt;a class="wiki_link_ext" href="http://micro.soonlabel.com/blue-tuning/blue-ji-excluded-by-peers.mp3" rel="nofollow"&gt;Excluded by Peers&lt;/a&gt; by &lt;a class="wiki_link" href="/Chris%20Vaisvil"&gt;Chris Vaisvil&lt;/a&gt;&lt;br /&gt;
&lt;a class="wiki_link_ext" href="http://micro.soonlabel.com/blue-tuning/blue-ji-excluded-by-peers.mp3" rel="nofollow"&gt;Excluded by Peers&lt;/a&gt; by &lt;a class="wiki_link" href="/Chris%20Vaisvil"&gt;Chris Vaisvil&lt;/a&gt;&lt;br /&gt;
&lt;a class="wiki_link_ext" href="http://micro.soonlabel.com/centaur_tuning/Prelude_For_Centaur_Tuned_Piano.mp3" rel="nofollow"&gt;Prelude for Centaur Tuned Piano&lt;/a&gt; by Chris Vaisvil&lt;br /&gt;
&lt;a class="wiki_link_ext" href="http://micro.soonlabel.com/centaur_tuning/Prelude_For_Centaur_Tuned_Piano.mp3" rel="nofollow"&gt;Prelude for Centaur Tuned Piano&lt;/a&gt; by Chris Vaisvil&lt;br /&gt;
&lt;a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Prelude%20%231%20for%207-limit%20JI.mp3" rel="nofollow"&gt;Prelude #1 in 7-limit JI&lt;/a&gt; by &lt;a class="wiki_link" href="/Ivor%20Darreg"&gt;Ivor Darreg&lt;/a&gt; &amp;lt;-- are there any notations for it?&lt;br /&gt;
&lt;a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Prelude%20%231%20for%207-limit%20JI.mp3" rel="nofollow"&gt;Prelude #1 in 7-limit JI&lt;/a&gt; by &lt;a class="wiki_link" href="/Ivor%20Darreg"&gt;Ivor Darreg&lt;/a&gt; &amp;lt;-- are there any notations for it?&lt;br /&gt;
&lt;a class="wiki_link_ext" href="http://www.archive.org/details/ClintonVariations" rel="nofollow"&gt;Clinton Variations&lt;/a&gt; &lt;a class="wiki_link_ext" href="http://www.archive.org/download/ClintonVariations/clinton.mp3" rel="nofollow"&gt;play&lt;/a&gt; by &lt;a class="wiki_link" href="/Gene%20Ward%20Smith"&gt;Gene Ward Smith&lt;/a&gt;&lt;br /&gt;
&lt;a class="wiki_link_ext" href="http://www.archive.org/details/ClintonVariations" rel="nofollow"&gt;Clinton Variations&lt;/a&gt; &lt;a class="wiki_link_ext" href="http://www.archive.org/download/ClintonVariations/clinton.mp3" rel="nofollow"&gt;play&lt;/a&gt; by &lt;a class="wiki_link" href="/Gene%20Ward%20Smith"&gt;Gene Ward Smith&lt;/a&gt;&lt;br /&gt;
&lt;a class="wiki_link_ext" href="http://www.youtube.com/watch?v=HzQmaxDIxnc&amp;amp;feature=channel_video_title" rel="nofollow"&gt;Pachelbel's Canon in D in 7-limit JI&lt;/a&gt; &lt;a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Meneghin/Pachelbel_s%20Canon%20in%20D%20-%20Relaxing%20music,%20with%20mountain%20views.mp3" rel="nofollow"&gt;play&lt;/a&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>
&lt;a class="wiki_link_ext" href="http://www.youtube.com/watch?v=HzQmaxDIxnc&amp;amp;feature=channel_video_title" rel="nofollow"&gt;Pachelbel's Canon in D in 7-limit JI&lt;/a&gt; &lt;a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Meneghin/Pachelbel_s%20Canon%20in%20D%20-%20Relaxing%20music,%20with%20mountain%20views.mp3" rel="nofollow"&gt;play&lt;/a&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>