MOS scale: Difference between revisions

<h2>IMPORTED REVISION FROM WIKISPACES</h2>

This is an imported revision from Wikispaces. The revision metadata is included below for reference:<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>

<h4>Original Wikitext content:</h4>

An important class of scales are MOS scales (MOS "Moment of symmetry").

[[http://tonalsoft.com/enc/m/mos.aspx|Joe Monzo's encyclopedia of microtonal music theory]]

An obvious first rough classification of MOS scales is given by the number of elements of the scale - the number of large intervals (L) and the number of small intervals (s). E.g., the diatonic scale in 12-tone equal temperament could be described as 5L 2s (5 large steps and 2 small steps).

Since numbers tend to be dry, Graham Breed has proposed a [[MOSNamingScheme|naming scheme for MOS scales]].

In the special case of an equal temperament, more concrete things about MOS can be stated.

In an equal temparement, all intervals - and hence also the intervals L and s - are integer multiples of a smallest unit. (Example: in case of the diatonic scale in 12EDO, L would be 2 and s 1.)

<h4>Original HTML content:</h4>

<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html">&lt;html&gt;&lt;head&gt;&lt;title&gt;MOSScales&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="MOS scales"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;MOS scales&lt;/h1&gt;

An important class of scales are MOS scales (MOS &amp;quot;Moment of symmetry&amp;quot;).&lt;br /&gt;

An MOS scale is a scale whose basic steps come in 2 different sizes. This is an interesting property because two basic scales of classical music theory have it: the diatonic scale (whole tone and semitone) and the pentatonic scale (minor third and whole tone).&lt;br /&gt;

&lt;a class="wiki_link_ext" href="http://tonalsoft.com/enc/m/mos.aspx" rel="nofollow"&gt;Joe Monzo's encyclopedia of microtonal music theory&lt;/a&gt;&lt;br /&gt;

&lt;br /&gt;

Since numbers tend to be dry, Graham Breed has proposed a &lt;a class="wiki_link" href="/MOSNamingScheme"&gt;naming scheme for MOS scales&lt;/a&gt;.&lt;br /&gt;

&lt;br /&gt;

In an equal temparement, all intervals - and hence also the intervals L and s - are integer multiples of a smallest unit. (Example: in case of the diatonic scale in 12EDO, L would be 2 and s 1.)&lt;br /&gt;

If we have an arbitrary MOS scale in an n-tone equal temperament, with a steps of size L and b steps of size s, there holds&lt;br /&gt;