Interval size measure: Difference between revisions
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Wikispaces>xenwolf **Imported revision 236759538 - Original comment: Links to units for details about definition, history, advantages, disadvantages** |
Wikispaces>xenwolf **Imported revision 236821246 - 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:xenwolf|xenwolf]] and made on <tt>2011-06-15 | : This revision was by author [[User:xenwolf|xenwolf]] and made on <tt>2011-06-15 09:58:47 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>236821246</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 the Octave/1000 parts, or 1.2 cents; the Eptaméride or [[Savart]]: Octave/301 parts; the [[Jot]]: Octave/30103 parts; the [[Morion]]: Octave/72 parts; the [[Farab]]: Octave/144 parts; the [[Flu]]: Octave/46032 parts; the [[Purdal]]: Octave/9900 parts; the [[Grad]]: Octave/12 "Pythagorean comma"; the [[mina]]: Octave/2460 parts; the [[Mem]]: Octave/205 parts (used by [[http://www.h-pi.com/theory/measurement3.html|Hi-pi Instruments]]); the [[Skisma]]: Octave/612 parts | Other measures include the [[millioctave]] (mO), which is the Octave/1000 parts, or 1.2 cents; the Eptaméride or [[Savart]]: Octave/301 parts; the [[Jot]]: Octave/30103 parts; the [[Morion]]: Octave/72 parts; the [[Farab]]: Octave/144 parts; the [[Flu]]: Octave/46032 parts; the [[Purdal]]: Octave/9900 parts; the [[Grad]]: Octave/12 "Pythagorean comma"; the [[mina]]: Octave/2460 parts; the [[Mem]]: Octave/205 parts (used by [[http://www.h-pi.com/theory/measurement3.html|Hi-pi Instruments]]); the [[Skisma]]: Octave/612 parts; the [[Woolhouse]]: Octave/730 parts, and the [[Tina]]: [[8539edo|1/8539 of an 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 the Octave/1000 parts, or 1.2 cents; the Eptaméride or <a class="wiki_link" href="/Savart">Savart</a>: Octave/301 parts; the <a class="wiki_link" href="/Jot">Jot</a>: Octave/30103 parts; the <a class="wiki_link" href="/Morion">Morion</a>: Octave/72 parts; the <a class="wiki_link" href="/Farab">Farab</a>: Octave/144 parts; the <a class="wiki_link" href="/Flu">Flu</a>: Octave/46032 parts; the <a class="wiki_link" href="/Purdal">Purdal</a>: Octave/9900 parts; the <a class="wiki_link" href="/Grad">Grad</a>: Octave/12 &quot;Pythagorean comma&quot;; the <a class="wiki_link" href="/mina">mina</a>: Octave/2460 parts; the <a class="wiki_link" href="/Mem">Mem</a>: Octave/205 parts (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>: Octave/612 parts | Other measures include the <a class="wiki_link" href="/millioctave">millioctave</a> (mO), which is the Octave/1000 parts, or 1.2 cents; the Eptaméride or <a class="wiki_link" href="/Savart">Savart</a>: Octave/301 parts; the <a class="wiki_link" href="/Jot">Jot</a>: Octave/30103 parts; the <a class="wiki_link" href="/Morion">Morion</a>: Octave/72 parts; the <a class="wiki_link" href="/Farab">Farab</a>: Octave/144 parts; the <a class="wiki_link" href="/Flu">Flu</a>: Octave/46032 parts; the <a class="wiki_link" href="/Purdal">Purdal</a>: Octave/9900 parts; the <a class="wiki_link" href="/Grad">Grad</a>: Octave/12 &quot;Pythagorean comma&quot;; the <a class="wiki_link" href="/mina">mina</a>: Octave/2460 parts; the <a class="wiki_link" href="/Mem">Mem</a>: Octave/205 parts (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>: Octave/612 parts; the <a class="wiki_link" href="/Woolhouse">Woolhouse</a>: Octave/730 parts, and the <a class="wiki_link" href="/Tina">Tina</a>: <a class="wiki_link" href="/8539edo">1/8539 of an octave</a>.<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 09:58, 15 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 xenwolf and made on 2011-06-15 09:58:47 UTC.
- The original revision id was 236821246.
- 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 the Octave/1000 parts, or 1.2 cents; the Eptaméride or [[Savart]]: Octave/301 parts; the [[Jot]]: Octave/30103 parts; the [[Morion]]: Octave/72 parts; the [[Farab]]: Octave/144 parts; the [[Flu]]: Octave/46032 parts; the [[Purdal]]: Octave/9900 parts; the [[Grad]]: Octave/12 "Pythagorean comma"; the [[mina]]: Octave/2460 parts; the [[Mem]]: Octave/205 parts (used by [[http://www.h-pi.com/theory/measurement3.html|Hi-pi Instruments]]); the [[Skisma]]: Octave/612 parts; the [[Woolhouse]]: Octave/730 parts, and the [[Tina]]: [[8539edo|1/8539 of an 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 the Octave/1000 parts, or 1.2 cents; the Eptaméride or <a class="wiki_link" href="/Savart">Savart</a>: Octave/301 parts; the <a class="wiki_link" href="/Jot">Jot</a>: Octave/30103 parts; the <a class="wiki_link" href="/Morion">Morion</a>: Octave/72 parts; the <a class="wiki_link" href="/Farab">Farab</a>: Octave/144 parts; the <a class="wiki_link" href="/Flu">Flu</a>: Octave/46032 parts; the <a class="wiki_link" href="/Purdal">Purdal</a>: Octave/9900 parts; the <a class="wiki_link" href="/Grad">Grad</a>: Octave/12 "Pythagorean comma"; the <a class="wiki_link" href="/mina">mina</a>: Octave/2460 parts; the <a class="wiki_link" href="/Mem">Mem</a>: Octave/205 parts (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>: Octave/612 parts; the <a class="wiki_link" href="/Woolhouse">Woolhouse</a>: Octave/730 parts, and the <a class="wiki_link" href="/Tina">Tina</a>: <a class="wiki_link" href="/8539edo">1/8539 of an octave</a>.<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>