MOS scale: Difference between revisions

Line 1:

<h2>IMPORTED REVISION FROM WIKISPACES</h2>

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

: This revision was by author [[User:~~keenanpepper~~|~~keenanpepper~~]] and made on <tt>2011-05-~~11 04~~:07:57 UTC</tt>.

: This revision was by author [[User:guest|guest]] and made on <tt>2011-07-22 18:07:14 UTC</tt>.

: The original revision id was <tt>~~227405616~~</tt>.

: The original revision id was <tt>242472483</tt>.

: The revision comment was: <tt></tt>

The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.

Line 19:

5. The unison or starting point of the scale is then allowed to be transferred to any scale degree--all the modes of a MOS are legal.

Condition Four is [[http://en.wikipedia.org/wiki/Myhill%27s_property|Myhill's ~~propery~~]] where, as a [[periodic scale]], the scale has every generic interval aside from the initial unison interval and intervals some number of periods from it having exactly two specific intervals. Another characterization of when a generated scale is a MOS is that the number of scale steps is the denominator of a [[http://en.wikipedia.org/wiki/Continued_fraction|convergent or semiconvergent]] of the ratio g/P of the generator and the period.

Condition Four is [[http://en.wikipedia.org/wiki/Myhill%27s_property|Myhill's property]] where, as a [[periodic scale]], the scale has every generic interval aside from the initial unison interval and intervals some number of periods from it having exactly two specific intervals. Another characterization of when a generated scale is a MOS is that the number of scale steps is the denominator of a [[http://en.wikipedia.org/wiki/Continued_fraction|convergent or semiconvergent]] of the ratio g/P of the generator and the period.

These conditions entail that the generated scale has exactly two sizes of steps when sorted into ascending order of size, and usually that latter condition suffices to define a MOS. However, when the generator is a rational fraction of the period and the number of steps is more than half of the total possible, a generated scale can have only two sizes of steps and the pseudo-Myhill property, meaning that not all non-unison classes have only two specific intervals.

Line 320:

5. The unison or starting point of the scale is then allowed to be transferred to any scale degree--all the modes of a MOS are legal.

Condition Four is <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Myhill%27s_property" rel="nofollow">Myhill's ~~propery~~</a> where, as a <a class="wiki_link" href="/periodic%20scale">periodic scale</a>, the scale has every generic interval aside from the initial unison interval and intervals some number of periods from it having exactly two specific intervals. Another characterization of when a generated scale is a MOS is that the number of scale steps is the denominator of a <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Continued_fraction" rel="nofollow">convergent or semiconvergent</a> of the ratio g/P of the generator and the period.

Condition Four is <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Myhill%27s_property" rel="nofollow">Myhill's property</a> where, as a <a class="wiki_link" href="/periodic%20scale">periodic scale</a>, the scale has every generic interval aside from the initial unison interval and intervals some number of periods from it having exactly two specific intervals. Another characterization of when a generated scale is a MOS is that the number of scale steps is the denominator of a <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Continued_fraction" rel="nofollow">convergent or semiconvergent</a> of the ratio g/P of the generator and the period.

These conditions entail that the generated scale has exactly two sizes of steps when sorted into ascending order of size, and usually that latter condition suffices to define a MOS. However, when the generator is a rational fraction of the period and the number of steps is more than half of the total possible, a generated scale can have only two sizes of steps and the pseudo-Myhill property, meaning that not all non-unison classes have only two specific intervals.

@@ Line 1: / Line 1: @@
 <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:keenanpepper|keenanpepper]] and made on <tt>2011-05-11 04:07:57 UTC</tt>.<br>
+: This revision was by author [[User:guest|guest]] and made on <tt>2011-07-22 18:07:14 UTC</tt>.<br>
-: The original revision id was <tt>227405616</tt>.<br>
+: The original revision id was <tt>242472483</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 19: / Line 19: @@
 . The unison or starting point of the scale is then allowed to be transferred to any scale degree--all the modes of a MOS are legal.
-Condition Four is [[http://en.wikipedia.org/wiki/Myhill%27s_property|Myhill's propery]] where, as a [[periodic scale]], the scale has every generic interval aside from the initial unison interval and intervals some number of periods from it having exactly two specific intervals. Another characterization of when a generated scale is a MOS is that the number of scale steps is the denominator of a [[http://en.wikipedia.org/wiki/Continued_fraction|convergent or semiconvergent]] of the ratio g/P of the generator and the period.
+Condition Four is [[http://en.wikipedia.org/wiki/Myhill%27s_property|Myhill's property]] where, as a [[periodic scale]], the scale has every generic interval aside from the initial unison interval and intervals some number of periods from it having exactly two specific intervals. Another characterization of when a generated scale is a MOS is that the number of scale steps is the denominator of a [[http://en.wikipedia.org/wiki/Continued_fraction|convergent or semiconvergent]] of the ratio g/P of the generator and the period.
 These conditions entail that the generated scale has exactly two sizes of steps when sorted into ascending order of size, and usually that latter condition suffices to define a MOS. However, when the generator is a rational fraction of the period and the number of steps is more than half of the total possible, a generated scale can have only two sizes of steps and the pseudo-Myhill property, meaning that not all non-unison classes have only two specific intervals.
@@ Line 320: / Line 320: @@
 . The unison or starting point of the scale is then allowed to be transferred to any scale degree--all the modes of a MOS are legal.&lt;br /&gt;
 &lt;br /&gt;
-Condition Four is &lt;a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Myhill%27s_property" rel="nofollow"&gt;Myhill's propery&lt;/a&gt; where, as a &lt;a class="wiki_link" href="/periodic%20scale"&gt;periodic scale&lt;/a&gt;, the scale has every generic interval aside from the initial unison interval and intervals some number of periods from it having exactly two specific intervals. Another characterization of when a generated scale is a MOS is that the number of scale steps is the denominator of a &lt;a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Continued_fraction" rel="nofollow"&gt;convergent or semiconvergent&lt;/a&gt; of the ratio g/P of the generator and the period. &lt;br /&gt;
+Condition Four is &lt;a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Myhill%27s_property" rel="nofollow"&gt;Myhill's property&lt;/a&gt; where, as a &lt;a class="wiki_link" href="/periodic%20scale"&gt;periodic scale&lt;/a&gt;, the scale has every generic interval aside from the initial unison interval and intervals some number of periods from it having exactly two specific intervals. Another characterization of when a generated scale is a MOS is that the number of scale steps is the denominator of a &lt;a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Continued_fraction" rel="nofollow"&gt;convergent or semiconvergent&lt;/a&gt; of the ratio g/P of the generator and the period.&lt;br /&gt;
 &lt;br /&gt;
 These conditions entail that the generated scale has exactly two sizes of steps when sorted into ascending order of size, and usually that latter condition suffices to define a MOS. However, when the generator is a rational fraction of the period and the number of steps is more than half of the total possible, a generated scale can have only two sizes of steps and the pseudo-Myhill property, meaning that not all non-unison classes have only two specific intervals.&lt;br /&gt;