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7-limit: Difference between revisions

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**Imported revision 239308589 - 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:genewardsmith|genewardsmith]] and made on <tt>2011-06-12 00:34:18 UTC</tt>.<br>
: This revision was by author [[User:xenwolf|xenwolf]] and made on <tt>2011-06-29 09:13:58 UTC</tt>.<br>
: The original revision id was <tt>236007722</tt>.<br>
: The original revision id was <tt>239308589</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]], [[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.
<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_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]].
"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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[[http://www.youtube.com/watch?v=HzQmaxDIxnc&amp;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]]</pre></div>
[[http://www.youtube.com/watch?v=HzQmaxDIxnc&amp;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]]</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">&lt;html&gt;&lt;head&gt;&lt;title&gt;7-limit&lt;/title&gt;&lt;/head&gt;&lt;body&gt;The &lt;em&gt;7-limit&lt;/em&gt; or &amp;quot;7 prime-limit&amp;quot; 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 &lt;a class="wiki_link" href="/9_7"&gt;9/7&lt;/a&gt;, &lt;a class="wiki_link" href="/14_9"&gt;14/9&lt;/a&gt;, &lt;a class="wiki_link" href="/15_14"&gt;15/14&lt;/a&gt;, &lt;a class="wiki_link" href="/28_15"&gt;28/15&lt;/a&gt;, &lt;a class="wiki_link" href="/21_16"&gt;21/16&lt;/a&gt;, &lt;a class="wiki_link" href="/32_21"&gt;32/21&lt;/a&gt;, &lt;a class="wiki_link" href="/25_14"&gt;25/14&lt;/a&gt;, &lt;a class="wiki_link" href="/28_25"&gt;28/25&lt;/a&gt;, &lt;a class="wiki_link" href="/25_21"&gt;25/21&lt;/a&gt;, &lt;a class="wiki_link" href="/42_25"&gt;42/25&lt;/a&gt;, &lt;a class="wiki_link" href="/28_27"&gt;28/27&lt;/a&gt;, &lt;a class="wiki_link" href="/27_14"&gt;27/14&lt;/a&gt;, &lt;a class="wiki_link" href="/35_28"&gt;35/28&lt;/a&gt;, &lt;a class="wiki_link" href="/56_35"&gt;56/35&lt;/a&gt;, 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.&lt;br /&gt;
<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">&lt;html&gt;&lt;head&gt;&lt;title&gt;7-limit&lt;/title&gt;&lt;/head&gt;&lt;body&gt;The &lt;em&gt;7-limit&lt;/em&gt; or &amp;quot;7 prime-limit&amp;quot; refers to a constraint on rational intervals such that 7 is the highest allowable &lt;a class="wiki_link" href="/prime%20number"&gt;prime number&lt;/a&gt;, 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 &lt;a class="wiki_link" href="/9_7"&gt;9/7&lt;/a&gt;, &lt;a class="wiki_link" href="/14_9"&gt;14/9&lt;/a&gt;, &lt;a class="wiki_link" href="/15_14"&gt;15/14&lt;/a&gt;, &lt;a class="wiki_link" href="/28_15"&gt;28/15&lt;/a&gt;, &lt;a class="wiki_link" href="/21_16"&gt;21/16&lt;/a&gt;, &lt;a class="wiki_link" href="/32_21"&gt;32/21&lt;/a&gt;, &lt;a class="wiki_link" href="/25_14"&gt;25/14&lt;/a&gt;, &lt;a class="wiki_link" href="/28_25"&gt;28/25&lt;/a&gt;, &lt;a class="wiki_link" href="/25_21"&gt;25/21&lt;/a&gt;, &lt;a class="wiki_link" href="/42_25"&gt;42/25&lt;/a&gt;, &lt;a class="wiki_link" href="/28_27"&gt;28/27&lt;/a&gt;, &lt;a class="wiki_link" href="/27_14"&gt;27/14&lt;/a&gt;, &lt;a class="wiki_link" href="/35_28"&gt;35/28&lt;/a&gt;, &lt;a class="wiki_link" href="/56_35"&gt;56/35&lt;/a&gt;, 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.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&amp;quot;7 odd-limit&amp;quot; refers to a constraint on the selection of &lt;a class="wiki_link" href="/JustIntonation"&gt;just&lt;/a&gt; &lt;a class="wiki_link" href="/Interval%20class"&gt;intervals&lt;/a&gt; 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 &lt;a class="wiki_link" href="/1_1"&gt;1/1&lt;/a&gt;, &lt;a class="wiki_link" href="/8_7"&gt;8/7&lt;/a&gt;, &lt;a class="wiki_link" href="/7_6"&gt;7/6&lt;/a&gt;, &lt;a class="wiki_link" href="/6_5"&gt;6/5&lt;/a&gt;, &lt;a class="wiki_link" href="/5_4"&gt;5/4&lt;/a&gt;, &lt;a class="wiki_link" href="/4_3"&gt;4/3&lt;/a&gt;, &lt;a class="wiki_link" href="/7_5"&gt;7/5&lt;/a&gt;, &lt;a class="wiki_link" href="/10_7"&gt;10/7&lt;/a&gt;, &lt;a class="wiki_link" href="/3_2"&gt;3/2&lt;/a&gt;, &lt;a class="wiki_link" href="/8_5"&gt;8/5&lt;/a&gt;, &lt;a class="wiki_link" href="/5_3"&gt;5/3&lt;/a&gt;, &lt;a class="wiki_link" href="/12_7"&gt;12/7&lt;/a&gt;, &lt;a class="wiki_link" href="/7_4"&gt;7/4&lt;/a&gt;, &lt;a class="wiki_link" href="/2_1"&gt;2/1&lt;/a&gt;, which is known as the 7-limit &lt;a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Tonality_diamond" rel="nofollow"&gt;tonality diamond&lt;/a&gt;.&lt;br /&gt;
&amp;quot;7 odd-limit&amp;quot; refers to a constraint on the selection of &lt;a class="wiki_link" href="/JustIntonation"&gt;just&lt;/a&gt; &lt;a class="wiki_link" href="/Interval%20class"&gt;intervals&lt;/a&gt; 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 &lt;a class="wiki_link" href="/1_1"&gt;1/1&lt;/a&gt;, &lt;a class="wiki_link" href="/8_7"&gt;8/7&lt;/a&gt;, &lt;a class="wiki_link" href="/7_6"&gt;7/6&lt;/a&gt;, &lt;a class="wiki_link" href="/6_5"&gt;6/5&lt;/a&gt;, &lt;a class="wiki_link" href="/5_4"&gt;5/4&lt;/a&gt;, &lt;a class="wiki_link" href="/4_3"&gt;4/3&lt;/a&gt;, &lt;a class="wiki_link" href="/7_5"&gt;7/5&lt;/a&gt;, &lt;a class="wiki_link" href="/10_7"&gt;10/7&lt;/a&gt;, &lt;a class="wiki_link" href="/3_2"&gt;3/2&lt;/a&gt;, &lt;a class="wiki_link" href="/8_5"&gt;8/5&lt;/a&gt;, &lt;a class="wiki_link" href="/5_3"&gt;5/3&lt;/a&gt;, &lt;a class="wiki_link" href="/12_7"&gt;12/7&lt;/a&gt;, &lt;a class="wiki_link" href="/7_4"&gt;7/4&lt;/a&gt;, &lt;a class="wiki_link" href="/2_1"&gt;2/1&lt;/a&gt;, which is known as the 7-limit &lt;a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Tonality_diamond" rel="nofollow"&gt;tonality diamond&lt;/a&gt;.&lt;br /&gt;
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