Interval size measure: Difference between revisions

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**Interval size measure** means 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]] (¢), [[1200edo|1\1200 octave]], 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 [[Armodue theory|eka]], [[16edo|1\16 octave]], [[Normal diesis]]: [[31edo|1\31 octave]]; the [[Méride]]: [[43edo|1\43 octave]]; the [[Holdrian comma]]: [[53edo|1\53 octave]]; the [[Morion]]: [[72edo|1\72 octave]]; the [[Farab]]: [[144edo|1\144 octave]]; the [[Mem]]: [[205edo|1\205 octave]] (used by [[http://www.h-pi.com/theory/measurement3.html|Hi-pi Instruments]]); the [[Tredek]]: [[270edo|1\270 octave]]; the [[Eptaméride]] or [[Savart]]: [[301edo|1\301 of an octave]]; the [[Gene]]: [[31edo|1\311 octave]]; the [[Dröbisch Angle]]: [[360edo|1\360 octave]]; the [[Squb]]: [[494edo|1\494 octave]]; the [[Iring]]: [[600edo|1\600 octave]]; the [[Skisma]]: [[612edo|1\612 octave]]; the [[Delfi]]: [[665edo|1\665 octave]]; the [[Woolhouse]]: [[730edo|1\730 octave]]; the [[millioctave]] (mO), [[1000edo|1\1000 octave]]; the [[Iota]]: [[1\1700 octave]]; the [[Harmos]]: [[1728edo|1\1728octave]]; the [[Mina]]: [[2460edo|1\2460 octave]]; the [[Tina]]: [[8539edo|1\8539 octave]]; the [[Purdal]]: [[9900edo|1\9900 octave]]; the [[Türk sent]]: [[10600edo|1\10600 octave]]; the [[Prima]]: [[12276edo|1\12276 octave]], the [[Jinn]]: [[16808edo|1\16808 octave]], the [[Jot]]: [[30103edo|1\30103 octave]]; the [[Imp]]: [[31920edo|1\31920 octave]]; the [[Flu]]: [[46032edo|1\46032 octave]]; and the [[MIDI Tuning Standard unit]]: [[196608edo|1\196608 octave]]. Not based on the octave are the [[Grad]]: 1/12 of a Pythagorean comma and the [[Hekt]]: 1/1300 part of 3, ie 3^(1/1300).

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.

see also: Kirnberger Atom http://arxiv.org/abs/0907.5249
==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 size measure</strong> means the <em>distance</em> between pitches. Intervals can be measured logarithmically or by frequancy ratios.<br />
<br />
<!-- ws:start:WikiTextHeadingRule:0:&lt;h2&gt; --><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:&lt;h3&gt; --><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 &quot;atonal&quot; 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:&lt;h3&gt; --><h3 id="toc2"><a name="x-Logarithmic-Fine"></a><!-- ws:end:WikiTextHeadingRule:4 -->Fine</h3>
 The <a class="wiki_link" href="/cent">cent</a> (¢), <a class="wiki_link" href="/1200edo">1\1200 octave</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="/Armodue%20theory">eka</a>, <a class="wiki_link" href="/16edo">1\16 octave</a>, <a class="wiki_link" href="/Normal%20diesis">Normal diesis</a>: <a class="wiki_link" href="/31edo">1\31 octave</a>; the <a class="wiki_link" href="/M%C3%A9ride">Méride</a>: <a class="wiki_link" href="/43edo">1\43 octave</a>; the <a class="wiki_link" href="/Holdrian%20comma">Holdrian comma</a>: <a class="wiki_link" href="/53edo">1\53 octave</a>; the <a class="wiki_link" href="/Morion">Morion</a>: <a class="wiki_link" href="/72edo">1\72 octave</a>; the <a class="wiki_link" href="/Farab">Farab</a>: <a class="wiki_link" href="/144edo">1\144 octave</a>; the <a class="wiki_link" href="/Mem">Mem</a>: <a class="wiki_link" href="/205edo">1\205 octave</a> (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="/Tredek">Tredek</a>: <a class="wiki_link" href="/270edo">1\270 octave</a>; the <a class="wiki_link" href="/Eptam%C3%A9ride">Eptaméride</a> or <a class="wiki_link" href="/Savart">Savart</a>: <a class="wiki_link" href="/301edo">1\301 of an octave</a>; the <a class="wiki_link" href="/Gene">Gene</a>: <a class="wiki_link" href="/31edo">1\311 octave</a>; the <a class="wiki_link" href="/Dr%C3%B6bisch%20Angle">Dröbisch Angle</a>: <a class="wiki_link" href="/360edo">1\360 octave</a>; the <a class="wiki_link" href="/Squb">Squb</a>: <a class="wiki_link" href="/494edo">1\494 octave</a>; the <a class="wiki_link" href="/Iring">Iring</a>: <a class="wiki_link" href="/600edo">1\600 octave</a>; the <a class="wiki_link" href="/Skisma">Skisma</a>: <a class="wiki_link" href="/612edo">1\612 octave</a>; the <a class="wiki_link" href="/Delfi">Delfi</a>: <a class="wiki_link" href="/665edo">1\665 octave</a>; the <a class="wiki_link" href="/Woolhouse">Woolhouse</a>: <a class="wiki_link" href="/730edo">1\730 octave</a>; the <a class="wiki_link" href="/millioctave">millioctave</a> (mO), <a class="wiki_link" href="/1000edo">1\1000 octave</a>; the <a class="wiki_link" href="/Iota">Iota</a>: <a class="wiki_link" href="/1%5C1700%20octave">1\1700 octave</a>; the <a class="wiki_link" href="/Harmos">Harmos</a>: <a class="wiki_link" href="/1728edo">1\1728octave</a>; the <a class="wiki_link" href="/Mina">Mina</a>: <a class="wiki_link" href="/2460edo">1\2460 octave</a>; the <a class="wiki_link" href="/Tina">Tina</a>: <a class="wiki_link" href="/8539edo">1\8539 octave</a>; the <a class="wiki_link" href="/Purdal">Purdal</a>: <a class="wiki_link" href="/9900edo">1\9900 octave</a>; the <a class="wiki_link" href="/T%C3%BCrk%20sent">Türk sent</a>: <a class="wiki_link" href="/10600edo">1\10600 octave</a>; the <a class="wiki_link" href="/Prima">Prima</a>: <a class="wiki_link" href="/12276edo">1\12276 octave</a>, the <a class="wiki_link" href="/Jinn">Jinn</a>: <a class="wiki_link" href="/16808edo">1\16808 octave</a>, the <a class="wiki_link" href="/Jot">Jot</a>: <a class="wiki_link" href="/30103edo">1\30103 octave</a>; the <a class="wiki_link" href="/Imp">Imp</a>: <a class="wiki_link" href="/31920edo">1\31920 octave</a>; the <a class="wiki_link" href="/Flu">Flu</a>: <a class="wiki_link" href="/46032edo">1\46032 octave</a>; and the <a class="wiki_link" href="/MIDI%20Tuning%20Standard%20unit">MIDI Tuning Standard unit</a>: <a class="wiki_link" href="/196608edo">1\196608 octave</a>. Not based on the octave are the <a class="wiki_link" href="/Grad">Grad</a>: 1/12 of a Pythagorean comma and the <a class="wiki_link" href="/Hekt">Hekt</a>: 1/1300 part of 3, ie 3^(1/1300).<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 />
see also: Kirnberger Atom <!-- ws:start:WikiTextUrlRule:105: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:105 --><br />
<!-- 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 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&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>

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 <h2>IMPORTED REVISION FROM WIKISPACES</h2>
 This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
-: This revision was by author [[User:hearneg|hearneg]] and made on <tt>2015-02-01 12:58:22 UTC</tt>.<br>
+: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2015-07-20 10:23:08 UTC</tt>.<br>
-: The original revision id was <tt>539255984</tt>.<br>
+: The original revision id was <tt>555521221</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>
@@ Line 17: / Line 17: @@
 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).
-For 1/16 octave (one step of [[16edo]]), the term [[eka]] has been coined (see [[Armodue theory]]).
 ===Fine===
 The [[cent]] (¢), [[1200edo|1\1200 octave]], 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 [[Normal diesis]]: [[31edo|1\31 octave]]; the [[Méride]]: [[43edo|1\43 octave]]; the [[Holdrian comma]]: [[53edo|1\53 octave]]; the [[Morion]]: [[72edo|1\72 octave]]; the [[Farab]]: [[144edo|1\144 octave]]; the [[Mem]]: [[205edo|1\205 octave]] (used by [[http://www.h-pi.com/theory/measurement3.html|Hi-pi Instruments]]); the [[Tredek]]: [[270edo|1\270 octave]]; the [[Eptaméride]] or [[Savart]]: [[301edo|1\301 of an octave]]; the [[Gene]]: [[31edo|1\311 octave]]; the [[Dröbisch Angle]]: [[360edo|1\360 octave]]; the [[Squb]]: [[494edo|1\494 octave]]; the [[Iring]]: [[600edo|1\600 octave]]; the [[Skisma]]: [[612edo|1\612 octave]]; the [[Delfi]]: [[665edo|1\665 octave]]; the [[Woolhouse]]: [[730edo|1\730 octave]]; the [[millioctave]] (mO), [[1000edo|1\1000 octave]]; the [[Iota]]: [[1\1700 octave]]; the [[Harmos]]: [[1728edo|1\1728octave]]; the [[Mina]]: [[2460edo|1\2460 octave]]; the [[Tina]]: [[8539edo|1\8539 octave]]; the [[Purdal]]: [[9900edo|1\9900 octave]]; the [[Türk sent]]: [[10600edo|1\10600 octave]]; the [[Prima]]: [[12276edo|1\12276 octave]], the [[Jinn]]: [[16808edo|1\16808 octave]], the [[Jot]]: [[30103edo|1\30103 octave]]; the [[Imp]]: [[31920edo|1\31920 octave]]; the [[Flu]]: [[46032edo|1\46032 octave]]; and the [[MIDI Tuning Standard unit]]: [[196608edo|1\196608 octave]]. Not based on the octave are the [[Grad]]: 1/12 of a Pythagorean comma and the [[Hekt]]: 1/1300 part of 3, ie 3^(1/1300).
+Other measures include the [[Armodue theory|eka]], [[16edo|1\16 octave]], [[Normal diesis]]: [[31edo|1\31 octave]]; the [[Méride]]: [[43edo|1\43 octave]]; the [[Holdrian comma]]: [[53edo|1\53 octave]]; the [[Morion]]: [[72edo|1\72 octave]]; the [[Farab]]: [[144edo|1\144 octave]]; the [[Mem]]: [[205edo|1\205 octave]] (used by [[http://www.h-pi.com/theory/measurement3.html|Hi-pi Instruments]]); the [[Tredek]]: [[270edo|1\270 octave]]; the [[Eptaméride]] or [[Savart]]: [[301edo|1\301 of an octave]]; the [[Gene]]: [[31edo|1\311 octave]]; the [[Dröbisch Angle]]: [[360edo|1\360 octave]]; the [[Squb]]: [[494edo|1\494 octave]]; the [[Iring]]: [[600edo|1\600 octave]]; the [[Skisma]]: [[612edo|1\612 octave]]; the [[Delfi]]: [[665edo|1\665 octave]]; the [[Woolhouse]]: [[730edo|1\730 octave]]; the [[millioctave]] (mO), [[1000edo|1\1000 octave]]; the [[Iota]]: [[1\1700 octave]]; the [[Harmos]]: [[1728edo|1\1728octave]]; the [[Mina]]: [[2460edo|1\2460 octave]]; the [[Tina]]: [[8539edo|1\8539 octave]]; the [[Purdal]]: [[9900edo|1\9900 octave]]; the [[Türk sent]]: [[10600edo|1\10600 octave]]; the [[Prima]]: [[12276edo|1\12276 octave]], the [[Jinn]]: [[16808edo|1\16808 octave]], the [[Jot]]: [[30103edo|1\30103 octave]]; the [[Imp]]: [[31920edo|1\31920 octave]]; the [[Flu]]: [[46032edo|1\46032 octave]]; and the [[MIDI Tuning Standard unit]]: [[196608edo|1\196608 octave]]. Not based on the octave are the [[Grad]]: 1/12 of a Pythagorean comma and the [[Hekt]]: 1/1300 part of 3, ie 3^(1/1300).
 See [[http://www.huygens-fokker.org/docs/measures.html|Logarithmic Interval Measures]]
@@ Line 48: / Line 46: @@
 &lt;br /&gt;
 Proposal: The &lt;strong&gt;relative interval measure&lt;/strong&gt; is the number of steps between two pitches of an &lt;a class="wiki_link" href="/equal"&gt;equal&lt;/a&gt; tuning, sometimes called &lt;a class="wiki_link" href="/degree"&gt;degree&lt;/a&gt;s (of an edo). For generators, the backslash notation is used d\edo, but it is also a ratio (of a logarithmic measure).&lt;br /&gt;
-&lt;br /&gt;
-For 1/16 octave (one step of &lt;a class="wiki_link" href="/16edo"&gt;16edo&lt;/a&gt;), the term &lt;a class="wiki_link" href="/eka"&gt;eka&lt;/a&gt; has been coined (see &lt;a class="wiki_link" href="/Armodue%20theory"&gt;Armodue theory&lt;/a&gt;).&lt;br /&gt;
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc2"&gt;&lt;a name="x-Logarithmic-Fine"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;Fine&lt;/h3&gt;
   The &lt;a class="wiki_link" href="/cent"&gt;cent&lt;/a&gt; (¢), &lt;a class="wiki_link" href="/1200edo"&gt;1\1200 octave&lt;/a&gt;, 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.&lt;br /&gt;
 &lt;br /&gt;
-Other measures include the &lt;a class="wiki_link" href="/Normal%20diesis"&gt;Normal diesis&lt;/a&gt;: &lt;a class="wiki_link" href="/31edo"&gt;1\31 octave&lt;/a&gt;; the &lt;a class="wiki_link" href="/M%C3%A9ride"&gt;Méride&lt;/a&gt;: &lt;a class="wiki_link" href="/43edo"&gt;1\43 octave&lt;/a&gt;; the &lt;a class="wiki_link" href="/Holdrian%20comma"&gt;Holdrian comma&lt;/a&gt;: &lt;a class="wiki_link" href="/53edo"&gt;1\53 octave&lt;/a&gt;; the &lt;a class="wiki_link" href="/Morion"&gt;Morion&lt;/a&gt;: &lt;a class="wiki_link" href="/72edo"&gt;1\72 octave&lt;/a&gt;; the &lt;a class="wiki_link" href="/Farab"&gt;Farab&lt;/a&gt;: &lt;a class="wiki_link" href="/144edo"&gt;1\144 octave&lt;/a&gt;; the &lt;a class="wiki_link" href="/Mem"&gt;Mem&lt;/a&gt;: &lt;a class="wiki_link" href="/205edo"&gt;1\205 octave&lt;/a&gt; (used by &lt;a class="wiki_link_ext" href="http://www.h-pi.com/theory/measurement3.html" rel="nofollow"&gt;Hi-pi Instruments&lt;/a&gt;); the &lt;a class="wiki_link" href="/Tredek"&gt;Tredek&lt;/a&gt;: &lt;a class="wiki_link" href="/270edo"&gt;1\270 octave&lt;/a&gt;; the &lt;a class="wiki_link" href="/Eptam%C3%A9ride"&gt;Eptaméride&lt;/a&gt; or &lt;a class="wiki_link" href="/Savart"&gt;Savart&lt;/a&gt;: &lt;a class="wiki_link" href="/301edo"&gt;1\301 of an octave&lt;/a&gt;; the &lt;a class="wiki_link" href="/Gene"&gt;Gene&lt;/a&gt;: &lt;a class="wiki_link" href="/31edo"&gt;1\311 octave&lt;/a&gt;; the &lt;a class="wiki_link" href="/Dr%C3%B6bisch%20Angle"&gt;Dröbisch Angle&lt;/a&gt;: &lt;a class="wiki_link" href="/360edo"&gt;1\360 octave&lt;/a&gt;; the &lt;a class="wiki_link" href="/Squb"&gt;Squb&lt;/a&gt;: &lt;a class="wiki_link" href="/494edo"&gt;1\494 octave&lt;/a&gt;; the &lt;a class="wiki_link" href="/Iring"&gt;Iring&lt;/a&gt;: &lt;a class="wiki_link" href="/600edo"&gt;1\600 octave&lt;/a&gt;; the &lt;a class="wiki_link" href="/Skisma"&gt;Skisma&lt;/a&gt;: &lt;a class="wiki_link" href="/612edo"&gt;1\612 octave&lt;/a&gt;; the &lt;a class="wiki_link" href="/Delfi"&gt;Delfi&lt;/a&gt;: &lt;a class="wiki_link" href="/665edo"&gt;1\665 octave&lt;/a&gt;; the &lt;a class="wiki_link" href="/Woolhouse"&gt;Woolhouse&lt;/a&gt;: &lt;a class="wiki_link" href="/730edo"&gt;1\730 octave&lt;/a&gt;; the &lt;a class="wiki_link" href="/millioctave"&gt;millioctave&lt;/a&gt; (mO), &lt;a class="wiki_link" href="/1000edo"&gt;1\1000 octave&lt;/a&gt;; the &lt;a class="wiki_link" href="/Iota"&gt;Iota&lt;/a&gt;: &lt;a class="wiki_link" href="/1%5C1700%20octave"&gt;1\1700 octave&lt;/a&gt;; the &lt;a class="wiki_link" href="/Harmos"&gt;Harmos&lt;/a&gt;: &lt;a class="wiki_link" href="/1728edo"&gt;1\1728octave&lt;/a&gt;; the &lt;a class="wiki_link" href="/Mina"&gt;Mina&lt;/a&gt;: &lt;a class="wiki_link" href="/2460edo"&gt;1\2460 octave&lt;/a&gt;; the &lt;a class="wiki_link" href="/Tina"&gt;Tina&lt;/a&gt;: &lt;a class="wiki_link" href="/8539edo"&gt;1\8539 octave&lt;/a&gt;; the &lt;a class="wiki_link" href="/Purdal"&gt;Purdal&lt;/a&gt;: &lt;a class="wiki_link" href="/9900edo"&gt;1\9900 octave&lt;/a&gt;; the &lt;a class="wiki_link" href="/T%C3%BCrk%20sent"&gt;Türk sent&lt;/a&gt;: &lt;a class="wiki_link" href="/10600edo"&gt;1\10600 octave&lt;/a&gt;; the &lt;a class="wiki_link" href="/Prima"&gt;Prima&lt;/a&gt;: &lt;a class="wiki_link" href="/12276edo"&gt;1\12276 octave&lt;/a&gt;, the &lt;a class="wiki_link" href="/Jinn"&gt;Jinn&lt;/a&gt;: &lt;a class="wiki_link" href="/16808edo"&gt;1\16808 octave&lt;/a&gt;, the &lt;a class="wiki_link" href="/Jot"&gt;Jot&lt;/a&gt;: &lt;a class="wiki_link" href="/30103edo"&gt;1\30103 octave&lt;/a&gt;; the &lt;a class="wiki_link" href="/Imp"&gt;Imp&lt;/a&gt;: &lt;a class="wiki_link" href="/31920edo"&gt;1\31920 octave&lt;/a&gt;; the &lt;a class="wiki_link" href="/Flu"&gt;Flu&lt;/a&gt;: &lt;a class="wiki_link" href="/46032edo"&gt;1\46032 octave&lt;/a&gt;; and the &lt;a class="wiki_link" href="/MIDI%20Tuning%20Standard%20unit"&gt;MIDI Tuning Standard unit&lt;/a&gt;: &lt;a class="wiki_link" href="/196608edo"&gt;1\196608 octave&lt;/a&gt;. Not based on the octave are the &lt;a class="wiki_link" href="/Grad"&gt;Grad&lt;/a&gt;: 1/12 of a Pythagorean comma and the &lt;a class="wiki_link" href="/Hekt"&gt;Hekt&lt;/a&gt;: 1/1300 part of 3, ie 3^(1/1300).&lt;br /&gt;
+Other measures include the &lt;a class="wiki_link" href="/Armodue%20theory"&gt;eka&lt;/a&gt;, &lt;a class="wiki_link" href="/16edo"&gt;1\16 octave&lt;/a&gt;, &lt;a class="wiki_link" href="/Normal%20diesis"&gt;Normal diesis&lt;/a&gt;: &lt;a class="wiki_link" href="/31edo"&gt;1\31 octave&lt;/a&gt;; the &lt;a class="wiki_link" href="/M%C3%A9ride"&gt;Méride&lt;/a&gt;: &lt;a class="wiki_link" href="/43edo"&gt;1\43 octave&lt;/a&gt;; the &lt;a class="wiki_link" href="/Holdrian%20comma"&gt;Holdrian comma&lt;/a&gt;: &lt;a class="wiki_link" href="/53edo"&gt;1\53 octave&lt;/a&gt;; the &lt;a class="wiki_link" href="/Morion"&gt;Morion&lt;/a&gt;: &lt;a class="wiki_link" href="/72edo"&gt;1\72 octave&lt;/a&gt;; the &lt;a class="wiki_link" href="/Farab"&gt;Farab&lt;/a&gt;: &lt;a class="wiki_link" href="/144edo"&gt;1\144 octave&lt;/a&gt;; the &lt;a class="wiki_link" href="/Mem"&gt;Mem&lt;/a&gt;: &lt;a class="wiki_link" href="/205edo"&gt;1\205 octave&lt;/a&gt; (used by &lt;a class="wiki_link_ext" href="http://www.h-pi.com/theory/measurement3.html" rel="nofollow"&gt;Hi-pi Instruments&lt;/a&gt;); the &lt;a class="wiki_link" href="/Tredek"&gt;Tredek&lt;/a&gt;: &lt;a class="wiki_link" href="/270edo"&gt;1\270 octave&lt;/a&gt;; the &lt;a class="wiki_link" href="/Eptam%C3%A9ride"&gt;Eptaméride&lt;/a&gt; or &lt;a class="wiki_link" href="/Savart"&gt;Savart&lt;/a&gt;: &lt;a class="wiki_link" href="/301edo"&gt;1\301 of an octave&lt;/a&gt;; the &lt;a class="wiki_link" href="/Gene"&gt;Gene&lt;/a&gt;: &lt;a class="wiki_link" href="/31edo"&gt;1\311 octave&lt;/a&gt;; the &lt;a class="wiki_link" href="/Dr%C3%B6bisch%20Angle"&gt;Dröbisch Angle&lt;/a&gt;: &lt;a class="wiki_link" href="/360edo"&gt;1\360 octave&lt;/a&gt;; the &lt;a class="wiki_link" href="/Squb"&gt;Squb&lt;/a&gt;: &lt;a class="wiki_link" href="/494edo"&gt;1\494 octave&lt;/a&gt;; the &lt;a class="wiki_link" href="/Iring"&gt;Iring&lt;/a&gt;: &lt;a class="wiki_link" href="/600edo"&gt;1\600 octave&lt;/a&gt;; the &lt;a class="wiki_link" href="/Skisma"&gt;Skisma&lt;/a&gt;: &lt;a class="wiki_link" href="/612edo"&gt;1\612 octave&lt;/a&gt;; the &lt;a class="wiki_link" href="/Delfi"&gt;Delfi&lt;/a&gt;: &lt;a class="wiki_link" href="/665edo"&gt;1\665 octave&lt;/a&gt;; the &lt;a class="wiki_link" href="/Woolhouse"&gt;Woolhouse&lt;/a&gt;: &lt;a class="wiki_link" href="/730edo"&gt;1\730 octave&lt;/a&gt;; the &lt;a class="wiki_link" href="/millioctave"&gt;millioctave&lt;/a&gt; (mO), &lt;a class="wiki_link" href="/1000edo"&gt;1\1000 octave&lt;/a&gt;; the &lt;a class="wiki_link" href="/Iota"&gt;Iota&lt;/a&gt;: &lt;a class="wiki_link" href="/1%5C1700%20octave"&gt;1\1700 octave&lt;/a&gt;; the &lt;a class="wiki_link" href="/Harmos"&gt;Harmos&lt;/a&gt;: &lt;a class="wiki_link" href="/1728edo"&gt;1\1728octave&lt;/a&gt;; the &lt;a class="wiki_link" href="/Mina"&gt;Mina&lt;/a&gt;: &lt;a class="wiki_link" href="/2460edo"&gt;1\2460 octave&lt;/a&gt;; the &lt;a class="wiki_link" href="/Tina"&gt;Tina&lt;/a&gt;: &lt;a class="wiki_link" href="/8539edo"&gt;1\8539 octave&lt;/a&gt;; the &lt;a class="wiki_link" href="/Purdal"&gt;Purdal&lt;/a&gt;: &lt;a class="wiki_link" href="/9900edo"&gt;1\9900 octave&lt;/a&gt;; the &lt;a class="wiki_link" href="/T%C3%BCrk%20sent"&gt;Türk sent&lt;/a&gt;: &lt;a class="wiki_link" href="/10600edo"&gt;1\10600 octave&lt;/a&gt;; the &lt;a class="wiki_link" href="/Prima"&gt;Prima&lt;/a&gt;: &lt;a class="wiki_link" href="/12276edo"&gt;1\12276 octave&lt;/a&gt;, the &lt;a class="wiki_link" href="/Jinn"&gt;Jinn&lt;/a&gt;: &lt;a class="wiki_link" href="/16808edo"&gt;1\16808 octave&lt;/a&gt;, the &lt;a class="wiki_link" href="/Jot"&gt;Jot&lt;/a&gt;: &lt;a class="wiki_link" href="/30103edo"&gt;1\30103 octave&lt;/a&gt;; the &lt;a class="wiki_link" href="/Imp"&gt;Imp&lt;/a&gt;: &lt;a class="wiki_link" href="/31920edo"&gt;1\31920 octave&lt;/a&gt;; the &lt;a class="wiki_link" href="/Flu"&gt;Flu&lt;/a&gt;: &lt;a class="wiki_link" href="/46032edo"&gt;1\46032 octave&lt;/a&gt;; and the &lt;a class="wiki_link" href="/MIDI%20Tuning%20Standard%20unit"&gt;MIDI Tuning Standard unit&lt;/a&gt;: &lt;a class="wiki_link" href="/196608edo"&gt;1\196608 octave&lt;/a&gt;. Not based on the octave are the &lt;a class="wiki_link" href="/Grad"&gt;Grad&lt;/a&gt;: 1/12 of a Pythagorean comma and the &lt;a class="wiki_link" href="/Hekt"&gt;Hekt&lt;/a&gt;: 1/1300 part of 3, ie 3^(1/1300).&lt;br /&gt;
 &lt;br /&gt;
 See &lt;a class="wiki_link_ext" href="http://www.huygens-fokker.org/docs/measures.html" rel="nofollow"&gt;Logarithmic Interval Measures&lt;/a&gt;&lt;br /&gt;
@@ Line 60: / Line 56: @@
 Within a given &lt;a class="wiki_link" href="/equal"&gt;equal&lt;/a&gt;-stepped tonal system, the &lt;a class="wiki_link" href="/Relative%20cent"&gt;relative cent&lt;/a&gt; (rct, r¢) can be used to describe properties of pitches (for instance the approximation of &lt;a class="wiki_link" href="/JI"&gt;JI&lt;/a&gt; intervals). It is defined as on 100th (or 1 percent) of the interval between two neigbouring pitches in the used equal tuning.&lt;br /&gt;
 &lt;br /&gt;
-see also: Kirnberger Atom &lt;!-- ws:start:WikiTextUrlRule:108:http://arxiv.org/abs/0907.5249 --&gt;&lt;a class="wiki_link_ext" href="http://arxiv.org/abs/0907.5249" rel="nofollow"&gt;http://arxiv.org/abs/0907.5249&lt;/a&gt;&lt;!-- ws:end:WikiTextUrlRule:108 --&gt;&lt;br /&gt;
+see also: Kirnberger Atom &lt;!-- ws:start:WikiTextUrlRule:105:http://arxiv.org/abs/0907.5249 --&gt;&lt;a class="wiki_link_ext" href="http://arxiv.org/abs/0907.5249" rel="nofollow"&gt;http://arxiv.org/abs/0907.5249&lt;/a&gt;&lt;!-- ws:end:WikiTextUrlRule:105 --&gt;&lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc3"&gt;&lt;a name="x-Ratio"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;Ratio&lt;/h2&gt;
   Intervals can be measured also giving their &lt;a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Interval_ratio" rel="nofollow"&gt;(frequency) ratio&lt;/a&gt;. For instance the major third as &lt;a class="wiki_link" href="/5_4"&gt;5/4&lt;/a&gt; or the pure fifth &lt;a class="wiki_link" href="/3_2"&gt;3/2&lt;/a&gt;. When combining sizes given in ratios, you have to multiply oder divide:&lt;br /&gt;

Interval size measure: Difference between revisions

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