Interval size measure: Difference between revisions
Wikispaces>guest **Imported revision 317851032 - Original comment: found on [tuning]** |
Wikispaces>genewardsmith **Imported revision 492364314 - 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:genewardsmith|genewardsmith]] and made on <tt>2014-02-27 03:50:48 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>492364314</tt>.<br> | ||
: The revision comment was: <tt> | : 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> | ||
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The [[cent]] (¢), [[1200edo|1/1200 octave]], is the classic measure for intervals when more precision than 12edo is requied. Some people object to it on the grounds that it is too closely related to 12 equal. | The [[cent]] (¢), [[1200edo|1/1200 octave]], is the classic measure for intervals when more precision than 12edo is requied. Some people object to it on the grounds that it is too closely related to 12 equal. | ||
Other measures include the [[millioctave]] (mO), which is the [[1000edo|1000th part]] of an octave, or 1.2 cents; the [[Eptaméride]] or [[Savart]]: [[301edo|1 | Other measures include the [[millioctave]] (mO), which is the [[1000edo|1000th part]] of an octave, or 1.2 cents; the [[Eptaméride]] or [[Savart]]: [[301edo|1\301 of an octave]]; the [[Jot]]: [[30103edo|1\30103 octave]]; the [[Morion]]: [[72edo|1\72 octave]]; the [[Farab]]: [[144edo|1\144 octave]]; the [[Flu]]: [[46032edo|1\46032 octave]]; the [[Purdal]]: [[9900edo|1\9900 octave]]; the [[Grad]]: 1/12 of a Pythagorean comma; the [[Mina]]: [[2460edo|1\2460 octave]]; the [[Mem]]: [[205edo|1\205 octave]] (used by [[http://www.h-pi.com/theory/measurement3.html|Hi-pi Instruments]]); the [[Skisma]]: [[612edo|1\612 octave]]; the [[Woolhouse]]: [[730edo|1\730 octave]]; the [[Tredek]]: [[270edo|1\270 octave]]; and the [[Tina]]: [[8539edo|1\8539th octave]]. | ||
See [[http://www.huygens-fokker.org/docs/measures.html|Logarithmic Interval Measures]] | See [[http://www.huygens-fokker.org/docs/measures.html|Logarithmic Interval Measures]] | ||
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The <a class="wiki_link" href="/cent">cent</a> (¢), <a class="wiki_link" href="/1200edo">1/1200 octave</a>, is the classic measure for intervals when more precision than 12edo is requied. Some people object to it on the grounds that it is too closely related to 12 equal.<br /> | The <a class="wiki_link" href="/cent">cent</a> (¢), <a class="wiki_link" href="/1200edo">1/1200 octave</a>, is the classic measure for intervals when more precision than 12edo is requied. Some people object to it on the grounds that it is too closely related to 12 equal.<br /> | ||
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Other measures include the <a class="wiki_link" href="/millioctave">millioctave</a> (mO), which is the <a class="wiki_link" href="/1000edo">1000th part</a> of an octave, or 1.2 cents; the <a class="wiki_link" href="/Eptam%C3%A9ride">Eptaméride</a> or <a class="wiki_link" href="/Savart">Savart</a>: <a class="wiki_link" href="/301edo">1 | Other measures include the <a class="wiki_link" href="/millioctave">millioctave</a> (mO), which is the <a class="wiki_link" href="/1000edo">1000th part</a> of an octave, or 1.2 cents; the <a class="wiki_link" href="/Eptam%C3%A9ride">Eptaméride</a> or <a class="wiki_link" href="/Savart">Savart</a>: <a class="wiki_link" href="/301edo">1\301 of an octave</a>; the <a class="wiki_link" href="/Jot">Jot</a>: <a class="wiki_link" href="/30103edo">1\30103 octave</a>; the <a class="wiki_link" href="/Morion">Morion</a>: <a class="wiki_link" href="/72edo">1\72 octave</a>; the <a class="wiki_link" href="/Farab">Farab</a>: <a class="wiki_link" href="/144edo">1\144 octave</a>; the <a class="wiki_link" href="/Flu">Flu</a>: <a class="wiki_link" href="/46032edo">1\46032 octave</a>; the <a class="wiki_link" href="/Purdal">Purdal</a>: <a class="wiki_link" href="/9900edo">1\9900 octave</a>; the <a class="wiki_link" href="/Grad">Grad</a>: 1/12 of a Pythagorean comma; the <a class="wiki_link" href="/Mina">Mina</a>: <a class="wiki_link" href="/2460edo">1\2460 octave</a>; the <a class="wiki_link" href="/Mem">Mem</a>: <a class="wiki_link" href="/205edo">1\205 octave</a> (used by <a class="wiki_link_ext" href="http://www.h-pi.com/theory/measurement3.html" rel="nofollow">Hi-pi Instruments</a>); the <a class="wiki_link" href="/Skisma">Skisma</a>: <a class="wiki_link" href="/612edo">1\612 octave</a>; the <a class="wiki_link" href="/Woolhouse">Woolhouse</a>: <a class="wiki_link" href="/730edo">1\730 octave</a>; the <a class="wiki_link" href="/Tredek">Tredek</a>: <a class="wiki_link" href="/270edo">1\270 octave</a>; and the <a class="wiki_link" href="/Tina">Tina</a>: <a class="wiki_link" href="/8539edo">1\8539th octave</a>.<br /> | ||
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See <a class="wiki_link_ext" href="http://www.huygens-fokker.org/docs/measures.html" rel="nofollow">Logarithmic Interval Measures</a><br /> | See <a class="wiki_link_ext" href="http://www.huygens-fokker.org/docs/measures.html" rel="nofollow">Logarithmic Interval Measures</a><br /> | ||
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Within a given <a class="wiki_link" href="/equal">equal</a>-stepped tonal system, the <a class="wiki_link" href="/Relative%20cent">relative cent</a> (rct, r¢) can be used to describe properties of pitches (for instance the approximation of <a class="wiki_link" href="/JI">JI</a> intervals). It is defined as on 100th (or 1 percent) of the interval between two neigbouring pitches in the used equal tuning.<br /> | Within a given <a class="wiki_link" href="/equal">equal</a>-stepped tonal system, the <a class="wiki_link" href="/Relative%20cent">relative cent</a> (rct, r¢) can be used to describe properties of pitches (for instance the approximation of <a class="wiki_link" href="/JI">JI</a> intervals). It is defined as on 100th (or 1 percent) of the interval between two neigbouring pitches in the used equal tuning.<br /> | ||
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see also: Kirnberger Atom <!-- ws:start:WikiTextUrlRule: | see also: Kirnberger Atom <!-- ws:start:WikiTextUrlRule:77:http://arxiv.org/abs/0907.5249 --><a class="wiki_link_ext" href="http://arxiv.org/abs/0907.5249" rel="nofollow">http://arxiv.org/abs/0907.5249</a><!-- ws:end:WikiTextUrlRule:77 --><br /> | ||
<!-- ws:start:WikiTextHeadingRule:6:&lt;h2&gt; --><h2 id="toc3"><a name="x-Ratio"></a><!-- ws:end:WikiTextHeadingRule:6 -->Ratio</h2> | <!-- ws:start:WikiTextHeadingRule:6:&lt;h2&gt; --><h2 id="toc3"><a name="x-Ratio"></a><!-- ws:end:WikiTextHeadingRule:6 -->Ratio</h2> | ||
Intervals can be measured also giving their <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Interval_ratio" rel="nofollow">(frequency) ratio</a>. For instance the major third as <a class="wiki_link" href="/5_4">5/4</a> or the pure fifth <a class="wiki_link" href="/3_2">3/2</a>. When combining sizes given in ratios, you have to multiply oder divide:<br /> | Intervals can be measured also giving their <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Interval_ratio" rel="nofollow">(frequency) ratio</a>. For instance the major third as <a class="wiki_link" href="/5_4">5/4</a> or the pure fifth <a class="wiki_link" href="/3_2">3/2</a>. When combining sizes given in ratios, you have to multiply oder divide:<br /> | ||