MOS scale: Difference between revisions
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Wikispaces>JosephRuhf **Imported revision 600944970 - 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:JosephRuhf|JosephRuhf]] and made on <tt>2016-11-29 15:08:41 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>600944970</tt>.<br> | ||
: The revision comment was: <tt></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> | The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br> | ||
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Sometimes, scales are defined with respect to a period and an additional "equivalence interval," considered to be the interval at which pitch classes repeat. MOS's in which the equivalence interval is a multiple of the period, and in which there is more than one period per equivalence interval, are sometimes called **Multi-MOS**'s. MOS's in which the equivalence interval is equal to the period are sometimes called **Strict MOS**'s. MOS's in which the equivalence interval and period are simply disjunct, with no rational relationship between them, are simply MOS and have no additional distinguishing label. | Sometimes, scales are defined with respect to a period and an additional "equivalence interval," considered to be the interval at which pitch classes repeat. MOS's in which the equivalence interval is a multiple of the period, and in which there is more than one period per equivalence interval, are sometimes called **Multi-MOS**'s. MOS's in which the equivalence interval is equal to the period are sometimes called **Strict MOS**'s. MOS's in which the equivalence interval and period are simply disjunct, with no rational relationship between them, are simply MOS and have no additional distinguishing label. | ||
With a few notable exceptions, Wilson generally focused his attention on MOS with period equal to the equivalence interval. Hence, some people prefer to use the term [[Distributional Evenness|distributionally even scale]], with acronym DE, for the more general class of scales which are MOS with respect to other intervals. MOS/DE scales are also sometimes known as //well-formed scales//, the term used in the 1989 paper by Norman Carey and David Clampitt. A great deal of interesting work has been done on scales in academic circles extending these ideas. The idea of MOS also includes | With a few notable exceptions, Wilson generally focused his attention on MOS with period equal to the equivalence interval. Hence, some people prefer to use the term [[Distributional Evenness|distributionally even scale]], with acronym DE, for the more general class of scales which are MOS with respect to other intervals. MOS/DE scales are also sometimes known as //well-formed scales//, the term used in the 1989 paper by Norman Carey and David Clampitt. A great deal of interesting work has been done on scales in academic circles extending these ideas. The idea of MOS also includes secondary or bi-level MOS scales which are actually the inspiration of Wilsons' concept. They are in a sense the MOS of MOS patterns. This is used to explain the pentatonics used in traditional Japanese music, where the 5 tone cycles are derieved from a 7 tone MOS, which are not found in the concept of DE. | ||
See [[Mathematics of MOS]] for a more formal definition and a discussion of their mathematical properties. | See [[Mathematics of MOS]] for a more formal definition and a discussion of their mathematical properties. | ||
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Sometimes, scales are defined with respect to a period and an additional &quot;equivalence interval,&quot; considered to be the interval at which pitch classes repeat. MOS's in which the equivalence interval is a multiple of the period, and in which there is more than one period per equivalence interval, are sometimes called <strong>Multi-MOS</strong>'s. MOS's in which the equivalence interval is equal to the period are sometimes called <strong>Strict MOS</strong>'s. MOS's in which the equivalence interval and period are simply disjunct, with no rational relationship between them, are simply MOS and have no additional distinguishing label.<br /> | Sometimes, scales are defined with respect to a period and an additional &quot;equivalence interval,&quot; considered to be the interval at which pitch classes repeat. MOS's in which the equivalence interval is a multiple of the period, and in which there is more than one period per equivalence interval, are sometimes called <strong>Multi-MOS</strong>'s. MOS's in which the equivalence interval is equal to the period are sometimes called <strong>Strict MOS</strong>'s. MOS's in which the equivalence interval and period are simply disjunct, with no rational relationship between them, are simply MOS and have no additional distinguishing label.<br /> | ||
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With a few notable exceptions, Wilson generally focused his attention on MOS with period equal to the equivalence interval. Hence, some people prefer to use the term <a class="wiki_link" href="/Distributional%20Evenness">distributionally even scale</a>, with acronym DE, for the more general class of scales which are MOS with respect to other intervals. MOS/DE scales are also sometimes known as <em>well-formed scales</em>, the term used in the 1989 paper by Norman Carey and David Clampitt. A great deal of interesting work has been done on scales in academic circles extending these ideas. The idea of MOS also includes | With a few notable exceptions, Wilson generally focused his attention on MOS with period equal to the equivalence interval. Hence, some people prefer to use the term <a class="wiki_link" href="/Distributional%20Evenness">distributionally even scale</a>, with acronym DE, for the more general class of scales which are MOS with respect to other intervals. MOS/DE scales are also sometimes known as <em>well-formed scales</em>, the term used in the 1989 paper by Norman Carey and David Clampitt. A great deal of interesting work has been done on scales in academic circles extending these ideas. The idea of MOS also includes secondary or bi-level MOS scales which are actually the inspiration of Wilsons' concept. They are in a sense the MOS of MOS patterns. This is used to explain the pentatonics used in traditional Japanese music, where the 5 tone cycles are derieved from a 7 tone MOS, which are not found in the concept of DE.<br /> | ||
<br /> | <br /> | ||
See <a class="wiki_link" href="/Mathematics%20of%20MOS">Mathematics of MOS</a> for a more formal definition and a discussion of their mathematical properties.<br /> | See <a class="wiki_link" href="/Mathematics%20of%20MOS">Mathematics of MOS</a> for a more formal definition and a discussion of their mathematical properties.<br /> | ||
Revision as of 15:08, 29 November 2016
IMPORTED REVISION FROM WIKISPACES
This is an imported revision from Wikispaces. The revision metadata is included below for reference:
- This revision was by author JosephRuhf and made on 2016-11-29 15:08:41 UTC.
- The original revision id was 600944970.
- 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:
<span style="display: block; text-align: right;">Other languages: [[xenharmonie/MOS-Skalen|Deutsch]] </span> [[toc|flat]] ---- =Definition= An **MOS** or **Moment Of Symmetry** is a scale in which every interval except for the period comes in two sizes. The term "MOS," and the method of scale construction it entails, were invented by [[Erv Wilson]] in 1975. His original paper can be found at [[http://anaphoria.com/mos.PDF]]. There is also an introduction at [[http://anaphoria.com/wilsonintroMOS.html]]. Sometimes, scales are defined with respect to a period and an additional "equivalence interval," considered to be the interval at which pitch classes repeat. MOS's in which the equivalence interval is a multiple of the period, and in which there is more than one period per equivalence interval, are sometimes called **Multi-MOS**'s. MOS's in which the equivalence interval is equal to the period are sometimes called **Strict MOS**'s. MOS's in which the equivalence interval and period are simply disjunct, with no rational relationship between them, are simply MOS and have no additional distinguishing label. With a few notable exceptions, Wilson generally focused his attention on MOS with period equal to the equivalence interval. Hence, some people prefer to use the term [[Distributional Evenness|distributionally even scale]], with acronym DE, for the more general class of scales which are MOS with respect to other intervals. MOS/DE scales are also sometimes known as //well-formed scales//, the term used in the 1989 paper by Norman Carey and David Clampitt. A great deal of interesting work has been done on scales in academic circles extending these ideas. The idea of MOS also includes secondary or bi-level MOS scales which are actually the inspiration of Wilsons' concept. They are in a sense the MOS of MOS patterns. This is used to explain the pentatonics used in traditional Japanese music, where the 5 tone cycles are derieved from a 7 tone MOS, which are not found in the concept of DE. See [[Mathematics of MOS]] for a more formal definition and a discussion of their mathematical properties. =Names for MOS= Since numbers tend to be dry, Graham Breed has proposed a [[MOSNamingScheme|naming scheme for MOS scales]]. See the [[Catalog of MOS]] for a listing of MOS in the more usual Ls scheme. ==[[MOSDiagrams]]== =Variations on MOS Scales= # [[MODMOS Scales]] are derived from chromatic alterations of one or more tones of an MOS scale, typically by the interval of L-s, the "chroma". # [[Muddle|Muddles]] are subsets of MOS parent scales with the general shape of a smaller (and possibly unrelated) MOS scale. # [[MOS Cradle]] is a technique of embedding MOS-like structures inside MOS scales and may or may not produce subsets of MOS scales. =MOS As Applied To Rhythms= David Canright was the first to suggest Fibonacci Rhythms in 1/1. This lead to Kraig Grady to be the first to apply MOS patterns to rhythms. Two papers on the subject can be found here [[http://anaphoria.com/hora.PDF]] and[[http://%20http://anaphoria.com/horo2.pdf| http://anaphoria.com/horo2.pdf]] MOS structures and thinking can be applied to the design of rhythms as well. See [[MOS Rhythm Tutorial]]
Original HTML content:
<html><head><title>MOSScales</title></head><body><span style="display: block; text-align: right;">Other languages: <a class="wiki_link" href="http://xenharmonie.wikispaces.com/MOS-Skalen">Deutsch</a><br /> </span><br /> <!-- ws:start:WikiTextTocRule:10:<img id="wikitext@@toc@@flat" class="WikiMedia WikiMediaTocFlat" title="Table of Contents" src="/site/embedthumbnail/toc/flat?w=100&h=16"/> --><!-- ws:end:WikiTextTocRule:10 --><!-- ws:start:WikiTextTocRule:11: --><a href="#Definition">Definition</a><!-- ws:end:WikiTextTocRule:11 --><!-- ws:start:WikiTextTocRule:12: --> | <a href="#Names for MOS">Names for MOS</a><!-- ws:end:WikiTextTocRule:12 --><!-- ws:start:WikiTextTocRule:13: --><!-- ws:end:WikiTextTocRule:13 --><!-- ws:start:WikiTextTocRule:14: --> | <a href="#Variations on MOS Scales">Variations on MOS Scales</a><!-- ws:end:WikiTextTocRule:14 --><!-- ws:start:WikiTextTocRule:15: --> | <a href="#MOS As Applied To Rhythms">MOS As Applied To Rhythms</a><!-- ws:end:WikiTextTocRule:15 --><!-- ws:start:WikiTextTocRule:16: --> <!-- ws:end:WikiTextTocRule:16 --><hr /> <br /> <!-- ws:start:WikiTextHeadingRule:0:<h1> --><h1 id="toc0"><a name="Definition"></a><!-- ws:end:WikiTextHeadingRule:0 -->Definition</h1> An <strong>MOS</strong> or <strong>Moment Of Symmetry</strong> is a scale in which every interval except for the period comes in two sizes. The term "MOS," and the method of scale construction it entails, were invented by <a class="wiki_link" href="/Erv%20Wilson">Erv Wilson</a> in 1975. His original paper can be found at <a class="wiki_link_ext" href="http://anaphoria.com/mos.PDF" rel="nofollow">http://anaphoria.com/mos.PDF</a>. There is also an introduction at <a class="wiki_link_ext" href="http://anaphoria.com/wilsonintroMOS.html" rel="nofollow">http://anaphoria.com/wilsonintroMOS.html</a>.<br /> <br /> Sometimes, scales are defined with respect to a period and an additional "equivalence interval," considered to be the interval at which pitch classes repeat. MOS's in which the equivalence interval is a multiple of the period, and in which there is more than one period per equivalence interval, are sometimes called <strong>Multi-MOS</strong>'s. MOS's in which the equivalence interval is equal to the period are sometimes called <strong>Strict MOS</strong>'s. MOS's in which the equivalence interval and period are simply disjunct, with no rational relationship between them, are simply MOS and have no additional distinguishing label.<br /> <br /> With a few notable exceptions, Wilson generally focused his attention on MOS with period equal to the equivalence interval. Hence, some people prefer to use the term <a class="wiki_link" href="/Distributional%20Evenness">distributionally even scale</a>, with acronym DE, for the more general class of scales which are MOS with respect to other intervals. MOS/DE scales are also sometimes known as <em>well-formed scales</em>, the term used in the 1989 paper by Norman Carey and David Clampitt. A great deal of interesting work has been done on scales in academic circles extending these ideas. The idea of MOS also includes secondary or bi-level MOS scales which are actually the inspiration of Wilsons' concept. They are in a sense the MOS of MOS patterns. This is used to explain the pentatonics used in traditional Japanese music, where the 5 tone cycles are derieved from a 7 tone MOS, which are not found in the concept of DE.<br /> <br /> See <a class="wiki_link" href="/Mathematics%20of%20MOS">Mathematics of MOS</a> for a more formal definition and a discussion of their mathematical properties.<br /> <br /> <!-- ws:start:WikiTextHeadingRule:2:<h1> --><h1 id="toc1"><a name="Names for MOS"></a><!-- ws:end:WikiTextHeadingRule:2 -->Names for MOS</h1> Since numbers tend to be dry, Graham Breed has proposed a <a class="wiki_link" href="/MOSNamingScheme">naming scheme for MOS scales</a>. See the <a class="wiki_link" href="/Catalog%20of%20MOS">Catalog of MOS</a> for a listing of MOS in the more usual Ls scheme.<br /> <br /> <!-- ws:start:WikiTextHeadingRule:4:<h2> --><h2 id="toc2"><a name="Names for MOS-MOSDiagrams"></a><!-- ws:end:WikiTextHeadingRule:4 --><a class="wiki_link" href="/MOSDiagrams">MOSDiagrams</a></h2> <br /> <!-- ws:start:WikiTextHeadingRule:6:<h1> --><h1 id="toc3"><a name="Variations on MOS Scales"></a><!-- ws:end:WikiTextHeadingRule:6 -->Variations on MOS Scales</h1> <ol><li><a class="wiki_link" href="/MODMOS%20Scales">MODMOS Scales</a> are derived from chromatic alterations of one or more tones of an MOS scale, typically by the interval of L-s, the "chroma".</li><li><a class="wiki_link" href="/Muddle">Muddles</a> are subsets of MOS parent scales with the general shape of a smaller (and possibly unrelated) MOS scale.</li><li><a class="wiki_link" href="/MOS%20Cradle">MOS Cradle</a> is a technique of embedding MOS-like structures inside MOS scales and may or may not produce subsets of MOS scales.</li></ol><br /> <!-- ws:start:WikiTextHeadingRule:8:<h1> --><h1 id="toc4"><a name="MOS As Applied To Rhythms"></a><!-- ws:end:WikiTextHeadingRule:8 -->MOS As Applied To Rhythms</h1> David Canright was the first to suggest Fibonacci Rhythms in 1/1. This lead to Kraig Grady to be the first to apply MOS patterns to rhythms. Two papers on the subject can be found here <a class="wiki_link_ext" href="http://anaphoria.com/hora.PDF" rel="nofollow">http://anaphoria.com/hora.PDF</a> and<a class="wiki_link_ext" href="http://%20http://anaphoria.com/horo2.pdf" rel="nofollow"> http://anaphoria.com/horo2.pdf</a><br /> MOS structures and thinking can be applied to the design of rhythms as well. See <a class="wiki_link" href="/MOS%20Rhythm%20Tutorial">MOS Rhythm Tutorial</a></body></html>