Interval system: Difference between revisions
Wikispaces>genewardsmith **Imported revision 143330515 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 143334889 - 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>2010-05-19 20: | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2010-05-19 20:27:37 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>143334889</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> | ||
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<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">By //musical interval system// is meant a range of notes or musical intervals theoretically available to a composer. The qualification "theoretically" is important, as such systems usually include notes or intervals which are not actually audible by human beings. The most basic of distinctions among such systems is between the open and closed systems, where a closed system has a finite set of possible musical intervals, whereas an open system has an infinite set. An example of a closed system would be all 2097151 notes of the [[http://en.wikipedia.org/wiki/MIDI_Tuning_Standard|MIDI tuning standard]]. An example of an open system is 12EDO, which puts no limit on how high or low the range of tones extends. From a practical point of view MTS is vastly more capable of representing musical intervals than 12EDO, and in fact includes it. From a theoretical point of view, 12EDO has an infinite set of available intervals, even though you can't hear or even physically produce most of them. | <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">By //musical interval system// is meant a range of notes or musical intervals theoretically available to a composer. The qualification "theoretically" is important, as such systems usually include notes or intervals which are not actually audible by human beings. The most basic of distinctions among such systems is between the open and closed systems, where a closed system has a finite set of possible musical intervals, whereas an open system has an infinite set. An example of a closed system would be all 2097151 notes of the [[http://en.wikipedia.org/wiki/MIDI_Tuning_Standard|MIDI tuning standard]]. An example of an open system is 12EDO, which puts no limit on how high or low the range of tones extends. From a practical point of view MTS is vastly more capable of representing musical intervals than 12EDO, and in fact includes it. From a theoretical point of view, 12EDO has an infinite set of available intervals, even though you can't hear or even physically produce most of them. | ||
Among open systems, the most important | Among open systems, the most important kinds are [[Periodic scale|periodic scales]] and group systems. The latter refers to "groups" in the mathematical sense of [[http://en.wikipedia.org/wiki/Abelian_group|abelian groups]], and means that you are always allowed to invert intervals, and that given any two intervals, you may combine them. | ||
Examples of group systems are all positive real numbers under multiplication, regarded as frequencies in hertz, all real numbers under addition, regarded as | Examples of group systems are all positive real numbers under multiplication, regarded as frequencies in hertz, all real numbers under addition, regarded as intervals in cents, all positive rational numbers, regarded as intervals from a chosen 1/1, all rational numbers in a given [[Harmonic Limit|harmonic limit]], all intervals in a [[Just intonation subgroups|just intonation subgroup]], and all intervals in a [[Regular Temperaments|regular temperament]].</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>Musical Interval Systems</title></head><body>By <em>musical interval system</em> is meant a range of notes or musical intervals theoretically available to a composer. The qualification &quot;theoretically&quot; is important, as such systems usually include notes or intervals which are not actually audible by human beings. The most basic of distinctions among such systems is between the open and closed systems, where a closed system has a finite set of possible musical intervals, whereas an open system has an infinite set. An example of a closed system would be all 2097151 notes of the <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/MIDI_Tuning_Standard" rel="nofollow">MIDI tuning standard</a>. An example of an open system is 12EDO, which puts no limit on how high or low the range of tones extends. From a practical point of view MTS is vastly more capable of representing musical intervals than 12EDO, and in fact includes it. From a theoretical point of view, 12EDO has an infinite set of available intervals, even though you can't hear or even physically produce most of them.<br /> | <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>Musical Interval Systems</title></head><body>By <em>musical interval system</em> is meant a range of notes or musical intervals theoretically available to a composer. The qualification &quot;theoretically&quot; is important, as such systems usually include notes or intervals which are not actually audible by human beings. The most basic of distinctions among such systems is between the open and closed systems, where a closed system has a finite set of possible musical intervals, whereas an open system has an infinite set. An example of a closed system would be all 2097151 notes of the <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/MIDI_Tuning_Standard" rel="nofollow">MIDI tuning standard</a>. An example of an open system is 12EDO, which puts no limit on how high or low the range of tones extends. From a practical point of view MTS is vastly more capable of representing musical intervals than 12EDO, and in fact includes it. From a theoretical point of view, 12EDO has an infinite set of available intervals, even though you can't hear or even physically produce most of them.<br /> | ||
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Among open systems, the most important | Among open systems, the most important kinds are <a class="wiki_link" href="/Periodic%20scale">periodic scales</a> and group systems. The latter refers to &quot;groups&quot; in the mathematical sense of <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Abelian_group" rel="nofollow">abelian groups</a>, and means that you are always allowed to invert intervals, and that given any two intervals, you may combine them. <br /> | ||
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Examples of group systems are all positive real numbers under multiplication, regarded as frequencies in hertz, all real numbers under addition, regarded as | Examples of group systems are all positive real numbers under multiplication, regarded as frequencies in hertz, all real numbers under addition, regarded as intervals in cents, all positive rational numbers, regarded as intervals from a chosen 1/1, all rational numbers in a given <a class="wiki_link" href="/Harmonic%20Limit">harmonic limit</a>, all intervals in a <a class="wiki_link" href="/Just%20intonation%20subgroups">just intonation subgroup</a>, and all intervals in a <a class="wiki_link" href="/Regular%20Temperaments">regular temperament</a>.</body></html></pre></div> | ||