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| <h2>IMPORTED REVISION FROM WIKISPACES</h2>
| | {{Wikipedia|Interval class|Generic and specific intervals}} |
| This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
| | '''Interval class''' is used in the following ways: |
| : This revision was by author [[User:xenwolf|xenwolf]] and made on <tt>2011-06-29 07:57:00 UTC</tt>.<br>
| | # First, common in academic [[Wikipedia: Set theory (music)|set theory]], defines it as the [[Octave #Octave equivalence|octave-equivalent]] distance between two pitch classes, measured by the shortest distance. Thus C to G may be the interval of 7, but its interval class is 5. The largest interval class or "ic" – in [[12edo]] – is the tritone (6). This may be criticized on the grounds that it is less useful and less generalizable than the second definition. |
| : The original revision id was <tt>239300707</tt>.<br>
| | # The second definition, used for example by [[Scala]], defines the ''interval class'', or the '''''generic interval''''', as the set of all specific intervals ([[interval qualities]]) at a certain number of scale steps apart. More formally, an interval class is the set of all intervals that occur in the scale as ''k''-step intervals, or ''k''-steps, for a specific fixed integer ''k''. For example, the interval class of 2-steps in the diatonic scale ([[5L 2s]]) is the set {2L, L + s} = {major third, minor third}. |
| : The revision comment was: <tt></tt><br>
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| 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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| <h4>Original Wikitext content:</h4>
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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">//Interval class// is used in two different ways. One, common in academic "set theory", defines it as the distance between two pitch classes, measured by the shortest distance. Thus C to G may be the interval of 7, but its interval class is 5. The largest interval class or "ic"--in [[12edo]]--is the tritone (6). This may be criticized on two grounds: it's not a class in the vocabulary of mathematics, and it's less useful than the second definition.
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| The second definition, used for example by Scala, defines the interval class as the "generic interval" to which the specific intervals at a certain number of scale steps i apart belong. //see also [[interval size measure]], [[interval measure]]//
| | == See also == |
| | * [[Pitch class]] |
| | * [[Interval size measure]] |
| | * [[Interval region]] |
| | * [[Functional systems]] |
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| ==Links==
| | [[Category:Interval]] |
| * [[http://solomonsmusic.net/setheory.htm#Basic%20Definition]]
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| * [[http://en.wikipedia.org/wiki/Interval_class|Interval class]] </pre></div>
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| <h4>Original HTML content:</h4>
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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;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>Interval class</title></head><body><em>Interval class</em> is used in two different ways. One, common in academic &quot;set theory&quot;, defines it as the distance between two pitch classes, measured by the shortest distance. Thus C to G may be the interval of 7, but its interval class is 5. The largest interval class or &quot;ic&quot;--in <a class="wiki_link" href="/12edo">12edo</a>--is the tritone (6). This may be criticized on two grounds: it's not a class in the vocabulary of mathematics, and it's less useful than the second definition.<br />
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| The second definition, used for example by Scala, defines the interval class as the &quot;generic interval&quot; to which the specific intervals at a certain number of scale steps i apart belong. <em>see also <a class="wiki_link" href="/interval%20size%20measure">interval size measure</a>, <a class="wiki_link" href="/interval%20measure">interval measure</a></em><br />
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| <ul><li><a class="wiki_link_ext" href="http://solomonsmusic.net/setheory.htm#Basic%20Definition" rel="nofollow">http://solomonsmusic.net/setheory.htm#Basic%20Definition</a></li><li><a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Interval_class" rel="nofollow">Interval class</a></li></ul></body></html></pre></div>
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Interval class is used in the following ways:
- First, common in academic set theory, defines it as the octave-equivalent distance between two pitch classes, measured by the shortest distance. Thus C to G may be the interval of 7, but its interval class is 5. The largest interval class or "ic" – in 12edo – is the tritone (6). This may be criticized on the grounds that it is less useful and less generalizable than the second definition.
- The second definition, used for example by Scala, defines the interval class, or the generic interval, as the set of all specific intervals (interval qualities) at a certain number of scale steps apart. More formally, an interval class is the set of all intervals that occur in the scale as k-step intervals, or k-steps, for a specific fixed integer k. For example, the interval class of 2-steps in the diatonic scale (5L 2s) is the set {2L, L + s} = {major third, minor third}.
See also
