7-limit: Difference between revisions
Wikispaces>genewardsmith **Imported revision 452992818 - Original comment: ** |
Wikispaces>spt3125 **Imported revision 513549056 - 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: | : This revision was by author [[User:spt3125|spt3125]] and made on <tt>2014-06-10 22:16:51 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>513549056</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> | ||
<h4>Original Wikitext content:</h4> | <h4>Original Wikitext content:</h4> | ||
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">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]], [[ | <div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">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_27|35/27]], 54/35, 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]]. | "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]]. | ||
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=Music= | =Music= | ||
[[http://micro.soonlabel.com/0-praxis/audio/August/august_12_Ruckus.mp3|Ruckus From the Quiet Zone]] by Ralph Lewis | [[http://micro.soonlabel.com/0-praxis/audio/August/august_12_Ruckus.mp3|Ruckus From the Quiet Zone]] by Ralph Lewis | ||
[[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/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]] | |||
[[http://clones.soonlabel.com/public/classical-music/mars-7-limit-kontakt5.mp3| Mars in 7-Limit JI]] from [[@http://en.wikipedia.org/wiki/The_Planets|The Planets]] the orchestral suite by Gustav Holst arranged by [[@Chris Vaisvil]] (Blog entry: [[http://chrisvaisvil.com/gustav-holsts-mars-arranged-for-7-limit-ji-orchestra/|Gustav Holst’s Mars arranged for 7-limit JI Orchestra « Music & Techniques by Chris Vaisvil]]) | |||
[[http://micro.soonlabel.com/gene_ward_smith/Others/Kite/Consolation%20%233%20by%20Ken%20Stillwell%20retuned.mp3|Liszt Consolation #3]] Ken Stillwell performance, retuned by Kite Giedraitis to the [[kite33]] 7-limit JI scale | [[http://micro.soonlabel.com/gene_ward_smith/Others/Kite/Consolation%20%233%20by%20Ken%20Stillwell%20retuned.mp3|Liszt Consolation #3]] Ken Stillwell performance, retuned by Kite Giedraitis to the [[kite33]] 7-limit JI scale | ||
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[[media type="custom" key="23473462"]]</pre></div> | [[media type="custom" key="23473462"]]</pre></div> | ||
<h4>Original HTML content:</h4> | <h4>Original HTML content:</h4> | ||
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>7-limit</title></head><body>The <em>7-limit</em> or &quot;7 prime-limit&quot; 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="/ | <div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>7-limit</title></head><body>The <em>7-limit</em> or &quot;7 prime-limit&quot; 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_27">35/27</a>, 54/35, 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.<br /> | ||
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&quot;7 odd-limit&quot; 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 /> | &quot;7 odd-limit&quot; 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 /> | ||