7-limit
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- This revision was by author Andrew_Heathwaite and made on 2011-05-26 13:32:10 UTC.
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Original Wikitext content:
"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. The complete list of 7 Odd-Limit intervals within the octave is [[7_4|7/4]], [[8_7|8/7]], [[7_6|7/6]], [[12_7|12/7]], [[7_5|7/5]], and [[10_7|10/7]]. Intervals with odd numbers smaller than 7, such as [[5_3|5/3]], are generally considered allowable as well within the 7 Odd-Limit. "7 Prime-Limit" refers to a constraint such that 7 is the highest allowable prime number, while higher odd numbers are allowable. This is an infinite set which includes all of the 7 Odd-Limit intervals, plus many more. 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. 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, can be represented in 3-dimensional lattice diagrams, each prime represented by a different dimension. Lattices describing scales beyond the 7-limit require more than three dimensions. For a variety of reasons, common-practice music has been stuck at the 5-limit (and its approximations in meantone, various well-temperaments, and equal temperament) for centuries. Music in the 7-limit thus represents a large step forward, although not as much as 11- or 13-limit. see [[Harmonic Limit]] <span style="display: block; height: 1px; left: -10000px; overflow: hidden; position: absolute; top: 298px; width: 1px;"> For a variety of reasons, common-practice music has been stuck at the 5-limit (and its approximations in meantone, various well-temperaments, and equal temperament) for centuries. Music in the 7-limit thus represents a large step forward, although not as much as 11- or 13-limit.</span>
Original HTML content:
<html><head><title>7-limit</title></head><body>"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. The complete list of 7 Odd-Limit intervals within the octave is <a class="wiki_link" href="/7_4">7/4</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="/12_7">12/7</a>, <a class="wiki_link" href="/7_5">7/5</a>, and <a class="wiki_link" href="/10_7">10/7</a>. Intervals with odd numbers smaller than 7, such as <a class="wiki_link" href="/5_3">5/3</a>, are generally considered allowable as well within the 7 Odd-Limit.<br /> <br /> "7 Prime-Limit" refers to a constraint such that 7 is the highest allowable prime number, while higher odd numbers are allowable. This is an infinite set which includes all of the 7 Odd-Limit intervals, plus many more. 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 /> 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, can be represented in 3-dimensional lattice diagrams, each prime represented by a different dimension. Lattices describing scales beyond the 7-limit require more than three dimensions.<br /> <br /> For a variety of reasons, common-practice music has been stuck at the 5-limit (and its approximations in meantone, various well-temperaments, and equal temperament) for centuries. Music in the 7-limit thus represents a large step forward, although not as much as 11- or 13-limit.<br /> <br /> see <a class="wiki_link" href="/Harmonic%20Limit">Harmonic Limit</a><br /> <span style="display: block; height: 1px; left: -10000px; overflow: hidden; position: absolute; top: 298px; width: 1px;"><br /> For a variety of reasons, common-practice music has been stuck at the 5-limit (and its approximations in meantone, various well-temperaments, and equal temperament) for centuries. Music in the 7-limit thus represents a large step forward, although not as much as 11- or 13-limit.</span></body></html>