Periodic 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:

: This revision was by author [[User:~~hstraub~~|~~hstraub~~]] and made on <tt>2010-10-~~12 10~~:33:08 UTC</tt>.

: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2010-12-22 11:24:25 UTC</tt>.

: The original revision id was <tt>~~169778165~~</tt>.

: The original revision id was <tt>189730622</tt>.

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

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(2) s[i + P] = s[i] + O

Scales written in the widely used [[http://www.huygens-fokker.org/scala/scl_format.html|Scala format]] are implicitly assumed to be periodic, with the repetition interval equal to the last scale entry, and the period equal to the number of notes (on the second line) of the scale. Neither Scala nor the above definition assumes that the scales are [[http://en.wikipedia.org/wiki/Monotonic_function|~~monotonicaally~~ strictly increasing]], but this condition, giving a **monotone periodic scale**, is often important to add:

Scales written in the widely used [[http://www.huygens-fokker.org/scala/scl_format.html|Scala format]] are implicitly assumed to be periodic, with the repetition interval equal to the last scale entry, and the period equal to the number of notes (on the second line) of the scale. Neither Scala nor the above definition assumes that the scales are [[http://en.wikipedia.org/wiki/Monotonic_function|monotonically strictly increasing]], but this condition, giving a **monotone periodic scale**, is often important to add:

(3) i < j implies s[i] < s[j]

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(2) s[i + P] = s[i] + O

Scales written in the widely used <a class="wiki_link_ext" href="http://www.huygens-fokker.org/scala/scl_format.html" rel="nofollow">Scala format</a> are implicitly assumed to be periodic, with the repetition interval equal to the last scale entry, and the period equal to the number of notes (on the second line) of the scale. Neither Scala nor the above definition assumes that the scales are <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Monotonic_function" rel="nofollow">~~monotonicaally~~ strictly increasing</a>, but this condition, giving a monotone periodic scale, is often important to add:

Scales written in the widely used <a class="wiki_link_ext" href="http://www.huygens-fokker.org/scala/scl_format.html" rel="nofollow">Scala format</a> are implicitly assumed to be periodic, with the repetition interval equal to the last scale entry, and the period equal to the number of notes (on the second line) of the scale. Neither Scala nor the above definition assumes that the scales are <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Monotonic_function" rel="nofollow">monotonically strictly increasing</a>, but this condition, giving a monotone periodic scale, is often important to add:

(3) i &lt; j implies s[i] &lt; s[j]

@@ 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:hstraub|hstraub]] and made on <tt>2010-10-12 10:33:08 UTC</tt>.<br>
+: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2010-12-22 11:24:25 UTC</tt>.<br>
-: The original revision id was <tt>169778165</tt>.<br>
+: The original revision id was <tt>189730622</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 12: / Line 12: @@
 (2) s[i + P] = s[i] + O
-Scales written in the widely used [[http://www.huygens-fokker.org/scala/scl_format.html|Scala format]] are implicitly assumed to be periodic, with the repetition interval equal to the last scale entry, and the period equal to the number of notes (on the second line) of the scale. Neither Scala nor the above definition assumes that the scales are [[http://en.wikipedia.org/wiki/Monotonic_function|monotonicaally strictly increasing]], but this condition, giving a **monotone periodic scale**, is often important to add:
+Scales written in the widely used [[http://www.huygens-fokker.org/scala/scl_format.html|Scala format]] are implicitly assumed to be periodic, with the repetition interval equal to the last scale entry, and the period equal to the number of notes (on the second line) of the scale. Neither Scala nor the above definition assumes that the scales are [[http://en.wikipedia.org/wiki/Monotonic_function|monotonically strictly increasing]], but this condition, giving a **monotone periodic scale**, is often important to add:
 (3) i &lt; j implies s[i] &lt; s[j]
@@ Line 32: / Line 32: @@
 (2) s[i + P] = s[i] + O&lt;br /&gt;
 &lt;br /&gt;
-Scales written in the widely used &lt;a class="wiki_link_ext" href="http://www.huygens-fokker.org/scala/scl_format.html" rel="nofollow"&gt;Scala format&lt;/a&gt; are implicitly assumed to be periodic, with the repetition interval equal to the last scale entry, and the period equal to the number of notes (on the second line) of the scale. Neither Scala nor the above definition assumes that the scales are &lt;a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Monotonic_function" rel="nofollow"&gt;monotonicaally strictly increasing&lt;/a&gt;, but this condition, giving a &lt;strong&gt;monotone periodic scale&lt;/strong&gt;, is often important to add:&lt;br /&gt;
+Scales written in the widely used &lt;a class="wiki_link_ext" href="http://www.huygens-fokker.org/scala/scl_format.html" rel="nofollow"&gt;Scala format&lt;/a&gt; are implicitly assumed to be periodic, with the repetition interval equal to the last scale entry, and the period equal to the number of notes (on the second line) of the scale. Neither Scala nor the above definition assumes that the scales are &lt;a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Monotonic_function" rel="nofollow"&gt;monotonically strictly increasing&lt;/a&gt;, but this condition, giving a &lt;strong&gt;monotone periodic scale&lt;/strong&gt;, is often important to add:&lt;br /&gt;
 &lt;br /&gt;
 (3) i &amp;lt; j implies s[i] &amp;lt; s[j] &lt;br /&gt;