7-limit
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The //7-limit// or "7 prime-limit" refers to a constraint on rational intervals such that 7 is the highest allowable [[prime number]], so that every such interval may be written as a ratio of integers which are products of 2, 3, 5 and 7. This is an infinite set and still infinite even if we restrict consideration to a single octave. Some examples within the octave include [[9_7|9/7]], [[14_9|14/9]], [[15_14|15/14]], [[28_15|28/15]], [[21_16|21/16]], [[32_21|32/21]], [[25_14|25/14]], [[28_25|28/25]], [[25_21|25/21]], [[42_25|42/25]], [[28_27|28/27]], [[27_14|27/14]], [[35_28|35/28]], [[56_35|56/35]], 45/28, 56/45, 49/32, 64/49, 49/36, 72/49, 49/30, 60/49, 49/25, 50/49, 49/27, 54/49, 49/35, 70/49, 49/45, 90/49. "7 odd-limit" refers to a constraint on the selection of [[JustIntonation|just]] [[Interval class|intervals]] for a scale or composition such that 7 is the highest allowable odd number, either for the intervals of the scale, or the ratios between successive or simultaneously sounding notes of the composition. The complete list of 7 odd-limit intervals within the octave is [[1_1|1/1]], [[8_7|8/7]], [[7_6|7/6]], [[6_5|6/5]], [[5_4|5/4]], [[4_3|4/3]], [[7_5|7/5]], [[10_7|10/7]], [[3_2|3/2]], [[8_5|8/5]], [[5_3|5/3]], [[12_7|12/7]], [[7_4|7/4]], [[2_1|2/1]], which is known as the 7-limit [[http://en.wikipedia.org/wiki/Tonality_diamond|tonality diamond]]. 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. 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. see [[Harmonic Limit]] =Music= [[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://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Prelude%20%231%20for%207-limit%20JI.mp3|Prelude #1 in 7-limit JI]] by [[Ivor Darreg]] <-- are there any notations for it? [[http://www.archive.org/details/ClintonVariations|Clinton Variations]] [[http://www.archive.org/download/ClintonVariations/clinton.mp3|play]] by [[Gene Ward Smith]] [[http://www.youtube.com/watch?v=HzQmaxDIxnc&feature=channel_video_title|Pachelbel's Canon in D in 7-limit JI]] [[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Meneghin/Pachelbel_s%20Canon%20in%20D%20-%20Relaxing%20music,%20with%20mountain%20views.mp3|play]]
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<html><head><title>7-limit</title></head><body>The <em>7-limit</em> or "7 prime-limit" refers to a constraint on rational intervals such that 7 is the highest allowable <a class="wiki_link" href="/prime%20number">prime number</a>, so that every such interval may be written as a ratio of integers which are products of 2, 3, 5 and 7. This is an infinite set and still infinite even if we restrict consideration to a single octave. Some examples within the octave include <a class="wiki_link" href="/9_7">9/7</a>, <a class="wiki_link" href="/14_9">14/9</a>, <a class="wiki_link" href="/15_14">15/14</a>, <a class="wiki_link" href="/28_15">28/15</a>, <a class="wiki_link" href="/21_16">21/16</a>, <a class="wiki_link" href="/32_21">32/21</a>, <a class="wiki_link" href="/25_14">25/14</a>, <a class="wiki_link" href="/28_25">28/25</a>, <a class="wiki_link" href="/25_21">25/21</a>, <a class="wiki_link" href="/42_25">42/25</a>, <a class="wiki_link" href="/28_27">28/27</a>, <a class="wiki_link" href="/27_14">27/14</a>, <a class="wiki_link" href="/35_28">35/28</a>, <a class="wiki_link" href="/56_35">56/35</a>, 45/28, 56/45, 49/32, 64/49, 49/36, 72/49, 49/30, 60/49, 49/25, 50/49, 49/27, 54/49, 49/35, 70/49, 49/45, 90/49.<br /> <br /> "7 odd-limit" refers to a constraint on the selection of <a class="wiki_link" href="/JustIntonation">just</a> <a class="wiki_link" href="/Interval%20class">intervals</a> for a scale or composition such that 7 is the highest allowable odd number, either for the intervals of the scale, or the ratios between successive or simultaneously sounding notes of the composition. The complete list of 7 odd-limit intervals within the octave is <a class="wiki_link" href="/1_1">1/1</a>, <a class="wiki_link" href="/8_7">8/7</a>, <a class="wiki_link" href="/7_6">7/6</a>, <a class="wiki_link" href="/6_5">6/5</a>, <a class="wiki_link" href="/5_4">5/4</a>, <a class="wiki_link" href="/4_3">4/3</a>, <a class="wiki_link" href="/7_5">7/5</a>, <a class="wiki_link" href="/10_7">10/7</a>, <a class="wiki_link" href="/3_2">3/2</a>, <a class="wiki_link" href="/8_5">8/5</a>, <a class="wiki_link" href="/5_3">5/3</a>, <a class="wiki_link" href="/12_7">12/7</a>, <a class="wiki_link" href="/7_4">7/4</a>, <a class="wiki_link" href="/2_1">2/1</a>, which is known as the 7-limit <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Tonality_diamond" rel="nofollow">tonality diamond</a>.<br /> <br /> 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 <a class="wiki_link" href="/The%20Seven%20Limit%20Symmetrical%20Lattices">3-dimensional lattice diagrams</a>, 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.<br /> <br /> 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.<br /> <br /> Relative to their size, the equal divisions <a class="wiki_link" href="/12edo">12edo</a>, <a class="wiki_link" href="/19edo">19edo</a>, <a class="wiki_link" href="/31edo">31edo</a>, <a class="wiki_link" href="/99edo">99edo</a> and <a class="wiki_link" href="/171edo">171edo</a> provide good approximations to the 7-limit, with <a class="wiki_link" href="/15edo">15edo</a>, <a class="wiki_link" href="/22edo">22edo</a>, <a class="wiki_link" href="/27edo">27edo</a>, <a class="wiki_link" href="/41edo">41edo</a>, <a class="wiki_link" href="/46edo">46edo</a>, <a class="wiki_link" href="/53edo">53edo</a>, <a class="wiki_link" href="/58edo">58edo</a>, <a class="wiki_link" href="/68edo">68edo</a>, <a class="wiki_link" href="/72edo">72edo</a>, <a class="wiki_link" href="/118edo">118edo</a>, <a class="wiki_link" href="/130edo">130edo</a>, <a class="wiki_link" href="/140edo">140edo</a> and <a class="wiki_link" href="/152edo">152edo</a> among the others worthy of notice.<br /> <br /> see <a class="wiki_link" href="/Harmonic%20Limit">Harmonic Limit</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:0:<h1> --><h1 id="toc0"><a name="Music"></a><!-- ws:end:WikiTextHeadingRule:0 -->Music</h1> <a class="wiki_link_ext" href="http://micro.soonlabel.com/blue-tuning/blue-ji-excluded-by-peers.mp3" rel="nofollow">Excluded by Peers</a> by <a class="wiki_link" href="/Chris%20Vaisvil">Chris Vaisvil</a><br /> <a class="wiki_link_ext" href="http://micro.soonlabel.com/centaur_tuning/Prelude_For_Centaur_Tuned_Piano.mp3" rel="nofollow">Prelude for Centaur Tuned Piano</a> by Chris Vaisvil<br /> <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">Prelude #1 in 7-limit JI</a> by <a class="wiki_link" href="/Ivor%20Darreg">Ivor Darreg</a> <-- are there any notations for it?<br /> <a class="wiki_link_ext" href="http://www.archive.org/details/ClintonVariations" rel="nofollow">Clinton Variations</a> <a class="wiki_link_ext" href="http://www.archive.org/download/ClintonVariations/clinton.mp3" rel="nofollow">play</a> by <a class="wiki_link" href="/Gene%20Ward%20Smith">Gene Ward Smith</a><br /> <a class="wiki_link_ext" href="http://www.youtube.com/watch?v=HzQmaxDIxnc&feature=channel_video_title" rel="nofollow">Pachelbel's Canon in D in 7-limit JI</a> <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">play</a></body></html>