Interval size measure: Difference between revisions
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Wikispaces>xenwolf **Imported revision 236657726 - Original comment: added examples for calculating with ratios** |
Wikispaces>genewardsmith **Imported revision 236679424 - 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>2011-06-14 18:01:09 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>236679424</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]] (¢) 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]] (¢) 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 1/1000 of an octave, or 1.2 cents; the eptaméride or savart, 1/301 octave, the jot, 1/30103 octave, the morion, 1/72 octave, the farab, 1/144 octave, the flu, 1/46032 octave, the grad, 1/12 Pythagorean comma, the [[mina]], 1/2460 octave, the skisma, 1/612 octave, and the woolhouse, 1/730 octave. | Other measures include the [[millioctave]] (mO), which is 1/1000 of an octave, or 1.2 cents; the eptaméride or savart, 1/301 octave, the jot, 1/30103 octave, the morion, 1/72 octave, the farab, 1/144 octave, the flu, 1/46032 octave, the grad, 1/12 Pythagorean comma, the [[mina]], 1/2460 octave, the mem, 1/205 octaves (used by [[http://www.h-pi.com/theory/measurement3.html|Hi-pi Instruments]], the skisma, 1/612 octave, and the woolhouse, 1/730 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> (¢) 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> (¢) 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 /> | ||
<br /> | <br /> | ||
Other measures include the <a class="wiki_link" href="/millioctave">millioctave</a> (mO), which is 1/1000 of an octave, or 1.2 cents; the eptaméride or savart, 1/301 octave, the jot, 1/30103 octave, the morion, 1/72 octave, the farab, 1/144 octave, the flu, 1/46032 octave, the grad, 1/12 Pythagorean comma, the <a class="wiki_link" href="/mina">mina</a>, 1/2460 octave, the skisma, 1/612 octave, and the woolhouse, 1/730 octave.<br /> | Other measures include the <a class="wiki_link" href="/millioctave">millioctave</a> (mO), which is 1/1000 of an octave, or 1.2 cents; the eptaméride or savart, 1/301 octave, the jot, 1/30103 octave, the morion, 1/72 octave, the farab, 1/144 octave, the flu, 1/46032 octave, the grad, 1/12 Pythagorean comma, the <a class="wiki_link" href="/mina">mina</a>, 1/2460 octave, the mem, 1/205 octaves (used by <a class="wiki_link_ext" href="http://www.h-pi.com/theory/measurement3.html" rel="nofollow">Hi-pi Instruments</a>, the skisma, 1/612 octave, and the woolhouse, 1/730 octave.<br /> | ||
<br /> | <br /> | ||
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 /> | ||
Revision as of 18:01, 14 June 2011
IMPORTED REVISION FROM WIKISPACES
This is an imported revision from Wikispaces. The revision metadata is included below for reference:
- This revision was by author genewardsmith and made on 2011-06-14 18:01:09 UTC.
- The original revision id was 236679424.
- The revision comment was:
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.
Original Wikitext content:
**Interval measure** is the //distance// between pitches. Intervals can be measured logarithmically or by frequancy ratios. == Logarithmic == All logarithmic measures can be combined by adding and subtracting them. === Gross === Intervals are somtetimes expressed in the number of scale steps between them. These steps can be of different size, compare for example the names of the major scale in the classic music. 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, 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 === The [[cent]] (¢) 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 1/1000 of an octave, or 1.2 cents; the eptaméride or savart, 1/301 octave, the jot, 1/30103 octave, the morion, 1/72 octave, the farab, 1/144 octave, the flu, 1/46032 octave, the grad, 1/12 Pythagorean comma, the [[mina]], 1/2460 octave, the mem, 1/205 octaves (used by [[http://www.h-pi.com/theory/measurement3.html|Hi-pi Instruments]], the skisma, 1/612 octave, and the woolhouse, 1/730 octave. See [[http://www.huygens-fokker.org/docs/measures.html|Logarithmic Interval Measures]] Within a given [[equal]]-stepped tonal system, the [[Relative cent|relative cent]] (rct, r¢) can be used to describe properties of pitches (for instance the approximation of [[JI]] intervals). It is defined as on 100th (or 1 percent) of the interval between two neigbouring pitches in the used equal tuning. == 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 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.
Original HTML content:
<html><head><title>Interval size measure</title></head><body><strong>Interval measure</strong> is the <em>distance</em> between pitches. Intervals can be measured logarithmically or by frequancy ratios.<br /> <br /> <!-- ws:start:WikiTextHeadingRule:0:<h2> --><h2 id="toc0"><a name="x-Logarithmic"></a><!-- ws:end:WikiTextHeadingRule:0 --> Logarithmic </h2> All logarithmic measures can be combined by adding and subtracting them.<br /> <br /> <!-- ws:start:WikiTextHeadingRule:2:<h3> --><h3 id="toc1"><a name="x-Logarithmic-Gross"></a><!-- ws:end:WikiTextHeadingRule:2 --> Gross </h3> Intervals are somtetimes expressed in the number of scale steps between them. These steps can be of different size, compare for example the names of the major scale in the classic music.<br /> <br /> For "atonal" music it was replaced by the number of 12edo-semitones.<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, 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 /> <!-- ws:start:WikiTextHeadingRule:4:<h3> --><h3 id="toc2"><a name="x-Logarithmic-Fine"></a><!-- ws:end:WikiTextHeadingRule:4 --> Fine </h3> The <a class="wiki_link" href="/cent">cent</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 /> <br /> Other measures include the <a class="wiki_link" href="/millioctave">millioctave</a> (mO), which is 1/1000 of an octave, or 1.2 cents; the eptaméride or savart, 1/301 octave, the jot, 1/30103 octave, the morion, 1/72 octave, the farab, 1/144 octave, the flu, 1/46032 octave, the grad, 1/12 Pythagorean comma, the <a class="wiki_link" href="/mina">mina</a>, 1/2460 octave, the mem, 1/205 octaves (used by <a class="wiki_link_ext" href="http://www.h-pi.com/theory/measurement3.html" rel="nofollow">Hi-pi Instruments</a>, the skisma, 1/612 octave, and the woolhouse, 1/730 octave.<br /> <br /> See <a class="wiki_link_ext" href="http://www.huygens-fokker.org/docs/measures.html" rel="nofollow">Logarithmic Interval Measures</a><br /> <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 /> <br /> <!-- ws:start:WikiTextHeadingRule:6:<h2> --><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 /> 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 /> 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> (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>