MOS scale: Difference between revisions
Wikispaces>Andrew_Heathwaite **Imported revision 246086881 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 275397570 - 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>2011-11-14 18:48:59 UTC</tt>.<br> | ||
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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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Note that an octave scale with a period a 1/N fraction of an octave will be a MOS if it is a MOS, identically, within each period. | Note that an octave scale with a period a 1/N fraction of an octave will be a MOS if it is a MOS, identically, within each period. | ||
The term MOS and the scale construction method were invented by Erv Wilson in 1975. His original paper can be found here [[http://anaphoria.com/mos.PDF]]. There is also an introduction [[http://anaphoria.com/wilsonintroMOS.html]]. | The term MOS and the scale construction method were invented by Erv Wilson in 1975. His original paper can be found here [[http://anaphoria.com/mos.PDF]]. There is also an introduction [[http://anaphoria.com/wilsonintroMOS.html]]. Wilson considered only MOS with period an octave, and hence some people prefer to use the term [[distributional evenness|distributionally even scale]], with acronym DE, for the more general concept. 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. | ||
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=Mathematical Properties of MOS= | =Mathematical Properties of MOS= | ||
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Note that an octave scale with a period a 1/N fraction of an octave will be a MOS if it is a MOS, identically, within each period.<br /> | Note that an octave scale with a period a 1/N fraction of an octave will be a MOS if it is a MOS, identically, within each period.<br /> | ||
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The term MOS and the scale construction method were invented by Erv Wilson in 1975. His original paper can be found here <a class="wiki_link_ext" href="http://anaphoria.com/mos.PDF" rel="nofollow">http://anaphoria.com/mos.PDF</a>. There is also an introduction <a class="wiki_link_ext" href="http://anaphoria.com/wilsonintroMOS.html" rel="nofollow">http://anaphoria.com/wilsonintroMOS.html</a>. | The term MOS and the scale construction method were invented by Erv Wilson in 1975. His original paper can be found here <a class="wiki_link_ext" href="http://anaphoria.com/mos.PDF" rel="nofollow">http://anaphoria.com/mos.PDF</a>. There is also an introduction <a class="wiki_link_ext" href="http://anaphoria.com/wilsonintroMOS.html" rel="nofollow">http://anaphoria.com/wilsonintroMOS.html</a>. Wilson considered only MOS with period an octave, and 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 concept. 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.<br /> | ||
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<!-- ws:start:WikiTextHeadingRule:4:&lt;h1&gt; --><h1 id="toc2"><a name="Mathematical Properties of MOS"></a><!-- ws:end:WikiTextHeadingRule:4 -->Mathematical Properties of MOS</h1> | <!-- ws:start:WikiTextHeadingRule:4:&lt;h1&gt; --><h1 id="toc2"><a name="Mathematical Properties of MOS"></a><!-- ws:end:WikiTextHeadingRule:4 -->Mathematical Properties of MOS</h1> | ||