7-limit: Difference between revisions
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Wikispaces>xenwolf **Imported revision 231980972 - Original comment: ** |
Wikispaces>Andrew_Heathwaite **Imported revision 232144752 - 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:Andrew_Heathwaite|Andrew_Heathwaite]] and made on <tt>2011-05-26 13:32:10 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>232144752</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"> | <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">"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. | ||
see [[Harmonic Limit]]</pre></div> | "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></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> | <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>&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. 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 /> | |||
&quot;7 Prime-Limit&quot; 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 &quot;7-limit just intonation&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, 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 /> | <br /> | ||
see <a class="wiki_link" href="/Harmonic%20Limit">Harmonic Limit</a></body></html></pre></div> | 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></pre></div> | |||
Revision as of 13:32, 26 May 2011
IMPORTED REVISION FROM WIKISPACES
This is an imported revision from Wikispaces. The revision metadata is included below for reference:
- This revision was by author Andrew_Heathwaite and made on 2011-05-26 13:32:10 UTC.
- The original revision id was 232144752.
- The revision comment was:
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.
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>