Interval size measure: Difference between revisions
Wikispaces>genewardsmith **Imported revision 236641334 - Original comment: ** |
Wikispaces>xenwolf **Imported revision 236657726 - Original comment: added examples for calculating with ratios** |
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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:xenwolf|xenwolf]] and made on <tt>2011-06-14 16:18:56 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>236657726</tt>.<br> | ||
: The revision comment was: <tt></tt><br> | : The revision comment was: <tt>added examples for calculating with ratios</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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For "atonal" music it was replaced by the number of 12edo-semitones. | For "atonal" music it was replaced by the number of 12edo-semitones. | ||
Proposal: The **relative interval measure** is the number of steps between two pitches of an [[equal]] tuning. | Proposal: The **relative interval measure** is the number of steps between two pitches of an [[equal]] tuning, sometimes called [[degree]]s (of an edo). For generators, the backslash notation is used d\edo, but it is also a ratio (of a logarithmic measure). | ||
=== Fine === | === Fine === | ||
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== 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 | 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 oder divide: | ||
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. | |||
Another notation for ratios is a vector of prime factor exponents, often called a [[monzo]], such as |-4 4 -1> (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. </pre></div> | Another notation for ratios is a vector of prime factor exponents, often called a [[monzo]], such as |-4 4 -1> (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. </pre></div> | ||
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For &quot;atonal&quot; music it was replaced by the number of 12edo-semitones.<br /> | For &quot;atonal&quot; music it was replaced by the number of 12edo-semitones.<br /> | ||
<br /> | <br /> | ||
Proposal: The <strong>relative interval measure</strong> is the number of steps between two pitches of an <a class="wiki_link" href="/equal">equal</a> tuning.<br /> | Proposal: The <strong>relative interval measure</strong> is the number of steps between two pitches of an <a class="wiki_link" href="/equal">equal</a> tuning, sometimes called <a class="wiki_link" href="/degree">degree</a>s (of an edo). For generators, the backslash notation is used d\edo, but it is also a ratio (of a logarithmic measure).<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:4:&lt;h3&gt; --><h3 id="toc2"><a name="x-Logarithmic-Fine"></a><!-- ws:end:WikiTextHeadingRule:4 --> Fine </h3> | <!-- ws:start:WikiTextHeadingRule:4:&lt;h3&gt; --><h3 id="toc2"><a name="x-Logarithmic-Fine"></a><!-- ws:end:WikiTextHeadingRule:4 --> Fine </h3> | ||
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<br /> | <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 | 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 /> | ||
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 /> | |||
<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> | ||