Glossary of scale properties: Difference between revisions

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**MOS/DE/Myhill's**

* **Distributional Evenness:** A scale is distributionally even (DE) if there are no more than two interval sizes for each generic interval class (e.g. major/minor thirds, perfect/augmented fourths, etc).

* **Myhill's Property:** A scale has Myhill's property if every generic interval class contains exactly two interval sizes (~~bar periods/~~octaves). The 12-tone diatonic scale has Myhill's property, and is also distributionally even.

* **Myhill's Property:** A scale has Myhill's property if every generic interval class contains exactly two interval sizes (except octaves or other equivalence intervals such as tritaves). The 12-tone diatonic scale has Myhill's property, and is also distributionally even.

** **Trivalence Property:** Same as Myhill's property, but replace "two interval sizes" with "three interval sizes." The scale formed from the notes of a dominant 7th chord (e.g. C-E-G-Bb-C) is an example of a trivalent scale.

* **Moment of Symmetry:** Both DE and Myhill's are essentially synonymous with [[MOS]]; Myhill's property is sometimes called "strict MOS".

An example of a scale which is MOS/DE but non-Myhill is the diminished scale, which is an MOS with a 1/4-octave period. Because there is only one interval size at the period, it does not have exactly two interval sizes per interval class.

An EDO is a kind of degenerate MOS, in that it is distributionally even. It does not have Myhill's property. In other words, it has no more than two interval sizes for each generic interval class, but does not have exactly two interval sizes.

**Convexity**

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MOS/DE/Myhill's

<ul><li>Distributional Evenness: A scale is distributionally even (DE) if there are no more than two interval sizes for each generic interval class (e.g. major/minor thirds, perfect/augmented fourths, etc).</li><li>Myhill's Property: A scale has Myhill's property if every generic interval class contains exactly two interval sizes (~~bar periods/~~octaves). The 12-tone diatonic scale has Myhill's property, and is also distributionally even.<ul><li>Trivalence Property: Same as Myhill's property, but replace &quot;two interval sizes&quot; with &quot;three interval sizes.&quot; The scale formed from the notes of a dominant 7th chord (e.g. C-E-G-Bb-C) is an example of a trivalent scale.</li></ul></li><li>Moment of Symmetry: Both DE and Myhill's are essentially synonymous with <a class="wiki_link" href="/MOS">MOS</a>; Myhill's property is sometimes called &quot;strict MOS&quot;.</li></ul>

<ul><li>Distributional Evenness: A scale is distributionally even (DE) if there are no more than two interval sizes for each generic interval class (e.g. major/minor thirds, perfect/augmented fourths, etc).</li><li>Myhill's Property: A scale has Myhill's property if every generic interval class contains exactly two interval sizes (except octaves or other equivalence intervals such as tritaves). The 12-tone diatonic scale has Myhill's property, and is also distributionally even.<ul><li>Trivalence Property: Same as Myhill's property, but replace &quot;two interval sizes&quot; with &quot;three interval sizes.&quot; The scale formed from the notes of a dominant 7th chord (e.g. C-E-G-Bb-C) is an example of a trivalent scale.</li></ul></li><li>Moment of Symmetry: Both DE and Myhill's are essentially synonymous with <a class="wiki_link" href="/MOS">MOS</a>; Myhill's property is sometimes called &quot;strict MOS&quot;.</li></ul>

An example of a scale which is MOS/DE but non-Myhill is the diminished scale, which is an MOS with a 1/4-octave period. Because there is only one interval size at the period, it does not have exactly two interval sizes per interval class.

An EDO is a kind of degenerate MOS, in that it is distributionally even. It does not have Myhill's property. In other words, it has no more than two interval sizes for each generic interval class, but does not have exactly two interval sizes.

Convexity

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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:spt3125|spt3125]] and made on <tt>2014-05-24 19:41:55 UTC</tt>.<br>
+: This revision was by author [[User:jdfreivald|jdfreivald]] and made on <tt>2016-01-17 23:12:05 UTC</tt>.<br>
-: The original revision id was <tt>511026652</tt>.<br>
+: The original revision id was <tt>572182331</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 36: / Line 36: @@
 **MOS/DE/Myhill's**
 * **Distributional Evenness:** A scale is distributionally even (DE) if there are no more than two interval sizes for each generic interval class (e.g. major/minor thirds, perfect/augmented fourths, etc).
-* **Myhill's Property:** A scale has Myhill's property if every generic interval class contains exactly two interval sizes (bar periods/octaves). The 12-tone diatonic scale has Myhill's property, and is also distributionally even.
+* **Myhill's Property:** A scale has Myhill's property if every generic interval class contains exactly two interval sizes (except octaves or other equivalence intervals such as tritaves). The 12-tone diatonic scale has Myhill's property, and is also distributionally even.
 ** **Trivalence Property:** Same as Myhill's property, but replace "two interval sizes" with "three interval sizes." The scale formed from the notes of a dominant 7th chord (e.g. C-E-G-Bb-C) is an example of a trivalent scale.
 * **Moment of Symmetry:** Both DE and Myhill's are essentially synonymous with [[MOS]]; Myhill's property is sometimes called "strict MOS".
+An example of a scale which is MOS/DE but non-Myhill is the diminished scale, which is an MOS with a 1/4-octave period. Because there is only one interval size at the period, it does not have exactly two interval sizes per interval class.
+An EDO is a kind of degenerate MOS, in that it is distributionally even. It does not have Myhill's property. In other words, it has no more than two interval sizes for each generic interval class, but does not have exactly two interval sizes.
 **Convexity**
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 &lt;br /&gt;
 &lt;strong&gt;MOS/DE/Myhill's&lt;/strong&gt;&lt;br /&gt;
-&lt;ul&gt;&lt;li&gt;&lt;strong&gt;Distributional Evenness:&lt;/strong&gt; A scale is distributionally even (DE) if there are no more than two interval sizes for each generic interval class (e.g. major/minor thirds, perfect/augmented fourths, etc).&lt;/li&gt;&lt;li&gt;&lt;strong&gt;Myhill's Property:&lt;/strong&gt; A scale has Myhill's property if every generic interval class contains exactly two interval sizes (bar periods/octaves). The 12-tone diatonic scale has Myhill's property, and is also distributionally even.&lt;ul&gt;&lt;li&gt;&lt;strong&gt;Trivalence Property:&lt;/strong&gt; Same as Myhill's property, but replace &amp;quot;two interval sizes&amp;quot; with &amp;quot;three interval sizes.&amp;quot; The scale formed from the notes of a dominant 7th chord (e.g. C-E-G-Bb-C) is an example of a trivalent scale.&lt;/li&gt;&lt;/ul&gt;&lt;/li&gt;&lt;li&gt;&lt;strong&gt;Moment of Symmetry:&lt;/strong&gt; Both DE and Myhill's are essentially synonymous with &lt;a class="wiki_link" href="/MOS"&gt;MOS&lt;/a&gt;; Myhill's property is sometimes called &amp;quot;strict MOS&amp;quot;.&lt;/li&gt;&lt;/ul&gt;&lt;br /&gt;
+&lt;ul&gt;&lt;li&gt;&lt;strong&gt;Distributional Evenness:&lt;/strong&gt; A scale is distributionally even (DE) if there are no more than two interval sizes for each generic interval class (e.g. major/minor thirds, perfect/augmented fourths, etc).&lt;/li&gt;&lt;li&gt;&lt;strong&gt;Myhill's Property:&lt;/strong&gt; A scale has Myhill's property if every generic interval class contains exactly two interval sizes (except octaves or other equivalence intervals such as tritaves). The 12-tone diatonic scale has Myhill's property, and is also distributionally even.&lt;ul&gt;&lt;li&gt;&lt;strong&gt;Trivalence Property:&lt;/strong&gt; Same as Myhill's property, but replace &amp;quot;two interval sizes&amp;quot; with &amp;quot;three interval sizes.&amp;quot; The scale formed from the notes of a dominant 7th chord (e.g. C-E-G-Bb-C) is an example of a trivalent scale.&lt;/li&gt;&lt;/ul&gt;&lt;/li&gt;&lt;li&gt;&lt;strong&gt;Moment of Symmetry:&lt;/strong&gt; Both DE and Myhill's are essentially synonymous with &lt;a class="wiki_link" href="/MOS"&gt;MOS&lt;/a&gt;; Myhill's property is sometimes called &amp;quot;strict MOS&amp;quot;.&lt;/li&gt;&lt;/ul&gt;&lt;br /&gt;
+An example of a scale which is MOS/DE but non-Myhill is the diminished scale, which is an MOS with a 1/4-octave period. Because there is only one interval size at the period, it does not have exactly two interval sizes per interval class.&lt;br /&gt;
+&lt;br /&gt;
+An EDO is a kind of degenerate MOS, in that it is distributionally even. It does not have Myhill's property. In other words, it has no more than two interval sizes for each generic interval class, but does not have exactly two interval sizes. &lt;br /&gt;
+&lt;br /&gt;
 &lt;strong&gt;Convexity&lt;/strong&gt;&lt;br /&gt;
 &lt;br /&gt;