MOS scale: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>

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: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2010-05-18 22:34:37 UTC</tt>.

: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2010-05-18 22:37:16 UTC</tt>.

: The original revision id was <tt>~~143046049~~</tt>.

: The original revision id was <tt>143046639</tt>.

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

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The two systems are equivalent; in the Algorithms section you will find code for routines starting from the mediant and going to the Ls pair (the "Ls" routine) and for starting from an Ls pair and going to the mediant (the "medi" routine.) The Ls routine uses [[http://en.wikipedia.org/wiki/Modular_multiplicative_inverse|modular inverses]], whereas the medi routine uses continued fractions.

If the period is assumed to be 2^(1/n) for some integer n, we can give instead the total number of large and small steps in the octave, instead of just the period, and this is commonly done.

If the period is assumed to be 2^(1/n) for some integer n, we can give instead the total number of large and small steps in the octave, instead of just the period, and this is commonly done. In this case, GCD(L, s) gives the number of periods in an octave.

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

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The two systems are equivalent; in the Algorithms section you will find code for routines starting from the mediant and going to the Ls pair (the &quot;Ls&quot; routine) and for starting from an Ls pair and going to the mediant (the &quot;medi&quot; routine.) The Ls routine uses <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Modular_multiplicative_inverse" rel="nofollow">modular inverses</a>, whereas the medi routine uses continued fractions.

If the period is assumed to be 2^(1/n) for some integer n, we can give instead the total number of large and small steps in the octave, instead of just the period, and this is commonly done.

If the period is assumed to be 2^(1/n) for some integer n, we can give instead the total number of large and small steps in the octave, instead of just the period, and this is commonly done. In this case, GCD(L, s) gives the number of periods in an octave.

Since numbers tend to be dry, Graham Breed has proposed a <a class="wiki_link" href="/MOSNamingScheme">naming scheme for MOS scales</a>.

@@ 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:genewardsmith|genewardsmith]] and made on <tt>2010-05-18 22:34:37 UTC</tt>.<br>
+: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2010-05-18 22:37:16 UTC</tt>.<br>
-: The original revision id was <tt>143046049</tt>.<br>
+: The original revision id was <tt>143046639</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 26: / Line 26: @@
 The two systems are equivalent; in the Algorithms section you will find code for routines starting from the mediant and going to the Ls pair (the "Ls" routine) and for starting from an Ls pair and going to the mediant (the "medi" routine.) The Ls routine uses [[http://en.wikipedia.org/wiki/Modular_multiplicative_inverse|modular inverses]], whereas the medi routine uses continued fractions.
-If the period is assumed to be 2^(1/n) for some integer n, we can give instead the total number of large and small steps in the octave, instead of just the period, and this is commonly done.
+If the period is assumed to be 2^(1/n) for some integer n, we can give instead the total number of large and small steps in the octave, instead of just the period, and this is commonly done. In this case, GCD(L, s) gives the number of periods in an octave.
 Since numbers tend to be dry, Graham Breed has proposed a [[MOSNamingScheme|naming scheme for MOS scales]].
@@ Line 163: / Line 163: @@
 The two systems are equivalent; in the Algorithms section you will find code for routines starting from the mediant and going to the Ls pair (the &amp;quot;Ls&amp;quot; routine) and for starting from an Ls pair and going to the mediant (the &amp;quot;medi&amp;quot; routine.) The Ls routine uses &lt;a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Modular_multiplicative_inverse" rel="nofollow"&gt;modular inverses&lt;/a&gt;, whereas the medi routine uses continued fractions.&lt;br /&gt;
 &lt;br /&gt;
-If the period is assumed to be 2^(1/n) for some integer n, we can give instead the total number of large and small steps in the octave, instead of just the period, and this is commonly done. &lt;br /&gt;
+If the period is assumed to be 2^(1/n) for some integer n, we can give instead the total number of large and small steps in the octave, instead of just the period, and this is commonly done. In this case, GCD(L, s) gives the number of periods in an octave.&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;