MODMOS scale: Difference between revisions

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<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>2011-03-14 21:51:11 UTC</tt>.<br>

: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-03-14 21:53:41 UTC</tt>.<br>

: The original revision id was <tt>~~210514932~~</tt>.<br>

: The original revision id was <tt>210515536</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>

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A MOS scale is constructed by iterating a generator g inside of a period R. That is, for non-negative integers n, we take n*g and reduce it modulo the period R to the range 0 <= i < R. We stop only at points when there are exactly two sizes of intervals in the scale, the large interval L and the small interval s. If the period R is 1/P octave for some integer P, we obtain an octave-repeating [[periodic scale]] by conjoining P copies of the MOS scale inside R so as to produce a MOS scale for the whole octave.

If we continue by adding another interval, it will either fall short of R, or exceed it, but either way we will now have an interval c = L-s, which has been called the "chroma". A MODMOS is in essence, a chromatically altered MOS; that is, a MOS altered by chromas. If we take a MOS scale, and adjust its notes up or down by a chroma consistently, so that octave periodicity is respected, and do not obtain another MOS, then we obtain a MODMOS. We can restrict this definition by requiring that no more than a certain percentage of the notes may be adjusted, or ~~require~~ that the monotonic ascending ordering of the notes by size be retained, or ~~relax~~ the condition that notes are adjusted by a single chroma so that they can be adjusted by any number of them, but we will take this as the basic definition of a MODMOS. The name comes from the fact that if the period is an octave and the number of notes in the MOS scale is N, then a chroma moves a note along the chain of generators by +-N, so that a MODMOS, reduced modulo N on the generator chain, becomes a MOS.

If we continue by adding another interval, it will either fall short of R, or exceed it, but either way we will now have an interval c = L-s, which has been called the "chroma". A MODMOS is in essence, a chromatically altered MOS; that is, a MOS altered by chromas. If we take a MOS scale, and adjust its notes up or down by a chroma consistently, so that octave periodicity is respected, and do not obtain another MOS, then we obtain a MODMOS. We can restrict this definition by requiring that no more than a certain percentage of the notes may be adjusted, or requiring that the monotonic ascending ordering of the notes by size be retained, or relaxing the condition that notes are adjusted by a single chroma so that they can be adjusted by any number of them, but we will take this as the basic definition of a MODMOS. The name comes from the fact that if the period is an octave and the number of notes in the MOS scale is N, then a chroma moves a note along the chain of generators by +-N, so that a MODMOS, reduced modulo N on the generator chain, becomes a MOS.

=Examples=

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A MOS scale is constructed by iterating a generator g inside of a period R. That is, for non-negative integers n, we take n*g and reduce it modulo the period R to the range 0 &lt;= i &lt; R. We stop only at points when there are exactly two sizes of intervals in the scale, the large interval L and the small interval s. If the period R is 1/P octave for some integer P, we obtain an octave-repeating <a class="wiki_link" href="/periodic%20scale">periodic scale</a> by conjoining P copies of the MOS scale inside R so as to produce a MOS scale for the whole octave.<br />

<br />

If we continue by adding another interval, it will either fall short of R, or exceed it, but either way we will now have an interval c = L-s, which has been called the &quot;chroma&quot;. A MODMOS is in essence, a chromatically altered MOS; that is, a MOS altered by chromas. If we take a MOS scale, and adjust its notes up or down by a chroma consistently, so that octave periodicity is respected, and do not obtain another MOS, then we obtain a MODMOS. We can restrict this definition by requiring that no more than a certain percentage of the notes may be adjusted, or ~~require~~ that the monotonic ascending ordering of the notes by size be retained, or ~~relax~~ the condition that notes are adjusted by a single chroma so that they can be adjusted by any number of them, but we will take this as the basic definition of a MODMOS. The name comes from the fact that if the period is an octave and the number of notes in the MOS scale is N, then a chroma moves a note along the chain of generators by +-N, so that a MODMOS, reduced modulo N on the generator chain, becomes a MOS.<br />

If we continue by adding another interval, it will either fall short of R, or exceed it, but either way we will now have an interval c = L-s, which has been called the &quot;chroma&quot;. A MODMOS is in essence, a chromatically altered MOS; that is, a MOS altered by chromas. If we take a MOS scale, and adjust its notes up or down by a chroma consistently, so that octave periodicity is respected, and do not obtain another MOS, then we obtain a MODMOS. We can restrict this definition by requiring that no more than a certain percentage of the notes may be adjusted, or requiring that the monotonic ascending ordering of the notes by size be retained, or relaxing the condition that notes are adjusted by a single chroma so that they can be adjusted by any number of them, but we will take this as the basic definition of a MODMOS. The name comes from the fact that if the period is an octave and the number of notes in the MOS scale is N, then a chroma moves a note along the chain of generators by +-N, so that a MODMOS, reduced modulo N on the generator chain, becomes a MOS.<br />

<br />

<h1 id="toc1"><a name="Examples"></a>Examples</h1>

@@ 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>2011-03-14 21:51:11 UTC</tt>.<br>
+: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-03-14 21:53:41 UTC</tt>.<br>
-: The original revision id was <tt>210514932</tt>.<br>
+: The original revision id was <tt>210515536</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 10: / Line 10: @@
 A MOS scale is constructed by iterating a generator g inside of a period R. That is, for non-negative integers n, we take n*g and reduce it modulo the period R to the range 0 &lt;= i &lt; R. We stop only at points when there are exactly two sizes of intervals in the scale, the large interval L and the small interval s. If the period R is 1/P octave for some integer P, we obtain an octave-repeating [[periodic scale]] by conjoining P copies of the MOS scale inside R so as to produce a MOS scale for the whole octave.
-If we continue by adding another interval, it will either fall short of R, or exceed it, but either way we will now have an interval c = L-s, which has been called the "chroma". A MODMOS is in essence, a chromatically altered MOS; that is, a MOS altered by chromas. If we take a MOS scale, and adjust its notes up or down by a chroma consistently, so that octave periodicity is respected, and do not obtain another MOS, then we obtain a MODMOS. We can restrict this definition by requiring that no more than a certain percentage of the notes may be adjusted, or require that the monotonic ascending ordering of the notes by size be retained, or relax the condition that notes are adjusted by a single chroma so that they can be adjusted by any number of them, but we will take this as the basic definition of a MODMOS. The name comes from the fact that if the period is an octave and the number of notes in the MOS scale is N, then a chroma moves a note along the chain of generators by +-N, so that a MODMOS, reduced modulo N on the generator chain, becomes a MOS.
+If we continue by adding another interval, it will either fall short of R, or exceed it, but either way we will now have an interval c = L-s, which has been called the "chroma". A MODMOS is in essence, a chromatically altered MOS; that is, a MOS altered by chromas. If we take a MOS scale, and adjust its notes up or down by a chroma consistently, so that octave periodicity is respected, and do not obtain another MOS, then we obtain a MODMOS. We can restrict this definition by requiring that no more than a certain percentage of the notes may be adjusted, or requiring that the monotonic ascending ordering of the notes by size be retained, or relaxing the condition that notes are adjusted by a single chroma so that they can be adjusted by any number of them, but we will take this as the basic definition of a MODMOS. The name comes from the fact that if the period is an octave and the number of notes in the MOS scale is N, then a chroma moves a note along the chain of generators by +-N, so that a MODMOS, reduced modulo N on the generator chain, becomes a MOS.
 =Examples=
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   A MOS scale is constructed by iterating a generator g inside of a period R. That is, for non-negative integers n, we take n*g and reduce it modulo the period R to the range 0 &amp;lt;= i &amp;lt; R. We stop only at points when there are exactly two sizes of intervals in the scale, the large interval L and the small interval s. If the period R is 1/P octave for some integer P, we obtain an octave-repeating &lt;a class="wiki_link" href="/periodic%20scale"&gt;periodic scale&lt;/a&gt; by conjoining P copies of the MOS scale inside R so as to produce a MOS scale for the whole octave.&lt;br /&gt;
 &lt;br /&gt;
-If we continue by adding another interval, it will either fall short of R, or exceed it, but either way we will now have an interval c = L-s, which has been called the &amp;quot;chroma&amp;quot;. A MODMOS is in essence, a chromatically altered MOS; that is, a MOS altered by chromas. If we take a MOS scale, and adjust its notes up or down by a chroma consistently, so that octave periodicity is respected, and do not obtain another MOS, then we obtain a MODMOS. We can restrict this definition by requiring that no more than a certain percentage of the notes may be adjusted, or require that the monotonic ascending ordering of the notes by size be retained, or relax the condition that notes are adjusted by a single chroma so that they can be adjusted by any number of them, but we will take this as the basic definition of a MODMOS. The name comes from the fact that if the period is an octave and the number of notes in the MOS scale is N, then a chroma moves a note along the chain of generators by +-N, so that a MODMOS, reduced modulo N on the generator chain, becomes a MOS.&lt;br /&gt;
+If we continue by adding another interval, it will either fall short of R, or exceed it, but either way we will now have an interval c = L-s, which has been called the &amp;quot;chroma&amp;quot;. A MODMOS is in essence, a chromatically altered MOS; that is, a MOS altered by chromas. If we take a MOS scale, and adjust its notes up or down by a chroma consistently, so that octave periodicity is respected, and do not obtain another MOS, then we obtain a MODMOS. We can restrict this definition by requiring that no more than a certain percentage of the notes may be adjusted, or requiring that the monotonic ascending ordering of the notes by size be retained, or relaxing the condition that notes are adjusted by a single chroma so that they can be adjusted by any number of them, but we will take this as the basic definition of a MODMOS. The name comes from the fact that if the period is an octave and the number of notes in the MOS scale is N, then a chroma moves a note along the chain of generators by +-N, so that a MODMOS, reduced modulo N on the generator chain, becomes a MOS.&lt;br /&gt;
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc1"&gt;&lt;a name="Examples"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;Examples&lt;/h1&gt;