Interval size measure
IMPORTED REVISION FROM WIKISPACES
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- This revision was by author xenwolf and made on 2011-06-13 09:11:15 UTC.
- The original revision id was 236214326.
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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. === Fine === The [[Cent]] (¢) is the classic measure for intervals minor than the 12eod-semitone. In this concern it should be mentioned, that the Cent measure is somewhat xenophobe. The [[Millioctave]] (mO) is a more technical measure, more independend of the common twelve-step division of the octave. 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. Another notation for ratios is a vector of prime factors exponents |-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 substraction 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.<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 minor than the 12eod-semitone. In this concern it should be mentioned, that the Cent measure is somewhat xenophobe.<br /> <br /> The <a class="wiki_link" href="/Millioctave">Millioctave</a> (mO) is a more technical measure, more independend of the common twelve-step division of the octave.<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 /> <br /> Another notation for ratios is a vector of prime factors exponents |-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 substraction of their vectors.</body></html>