Interval size measure: Difference between revisions
Wikispaces>JosephRuhf **Imported revision 597524720 - Original comment: ** |
Wikispaces>YahyaA **Imported revision 606514885 - 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:YahyaA|YahyaA]] and made on <tt>2017-02-17 09:32:18 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>606514885</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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see also: Kirnberger Atom http://arxiv.org/abs/0907.5249 | see also: Kirnberger Atom http://arxiv.org/abs/0907.5249 | ||
==Ratio== | ==Ratio== | ||
Intervals can be measured also giving their [[http://en.wikipedia.org/wiki/Interval_ratio|(frequency) ratio]]. For instance the major third as [[5_4|5/4]] or the pure fifth [[3_2|3/2]]. When combining sizes given in ratios, you have to multiply | Intervals can be measured also giving their [[http://en.wikipedia.org/wiki/Interval_ratio|(frequency) ratio]]. For instance the major third as [[5_4|5/4]] or the pure fifth [[3_2|3/2]]. When combining sizes given in ratios, you have to multiply or divide: | ||
a pure fifth increased by a major third gives the major seventh 3/2*5/4 = 15/8, | a pure fifth increased by a major third gives the major seventh 3/2*5/4 = 15/8, | ||
which is a diatonic semitone below an octave (2/1)/(15/8) = 2/1*8/15 = 16/15. | which is a diatonic semitone below an octave (2/1)/(15/8) = 2/1*8/15 = 16/15. | ||
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see also: Kirnberger Atom <!-- ws:start:WikiTextUrlRule:107: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:107 --><br /> | see also: Kirnberger Atom <!-- ws:start:WikiTextUrlRule:107: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:107 --><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 | 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 or divide:<br /> | ||
a pure fifth increased by a major third gives the major seventh 3/2*5/4 = 15/8,<br /> | a pure fifth increased by a major third gives the major seventh 3/2*5/4 = 15/8,<br /> | ||
which is a diatonic semitone below an octave (2/1)/(15/8) = 2/1*8/15 = 16/15.<br /> | which is a diatonic semitone below an octave (2/1)/(15/8) = 2/1*8/15 = 16/15.<br /> | ||
<br /> | <br /> | ||
Another notation for ratios is a vector of prime factor exponents, often called a <a class="wiki_link" href="/monzo">monzo</a>, such as |-4 4 -1&gt; (for the syntonic comma, 81/80 = 2^(-4) * 3^4 * 5^(-1)), which builds a bridge back to the logarithmic measure: intervals can be combined by component-wise addition or subtraction of their vectors.</body></html></pre></div> | Another notation for ratios is a vector of prime factor exponents, often called a <a class="wiki_link" href="/monzo">monzo</a>, such as |-4 4 -1&gt; (for the syntonic comma, 81/80 = 2^(-4) * 3^4 * 5^(-1)), which builds a bridge back to the logarithmic measure: intervals can be combined by component-wise addition or subtraction of their vectors.</body></html></pre></div> | ||