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Glossary of scale properties: Difference between revisions

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**Weakly Epimorphic:** A scale is weakly epimorphic if, under some val, all scale degrees are "filled," no matter which note you choose as the fundamental.
**Weakly Epimorphic:** A scale is weakly epimorphic if, under some val, all scale degrees are "filled," no matter which note you choose as the fundamental.
* **Epimorphic:** Something silly that basically means your scale is non-negative, or something like that. The diatonic scale is epimorphic in general. The diatonic scale in 12-EDO is only considered to be epimorphic if it's being viewed as a set of notes in an infinite rank-2 space, in which some notes just happen to be tuned the same.
* **Epimorphic:** A weakly epimorphic scale is epimorphic if it keeps rising in pitch as you go to higher scale degrees--the (n+1)st degree is higher than the nth degree.


**Distributional Evenness:** A scale is Distributionally Even if there are no more than two Interval sizes for each Generic Interval class (e.g. Major/Minor thirds, Perfect/Augmented fourths, etc).
**Distributional Evenness:** A scale is Distributionally Even if there are no more than two Interval sizes for each Generic Interval class (e.g. Major/Minor thirds, Perfect/Augmented fourths, etc).
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&lt;ul&gt;&lt;li&gt;&lt;strong&gt;Strict Propriety:&lt;/strong&gt; A scale is strictly proper if the Generic Interval classes are discrete. Replace the word &amp;quot;larger&amp;quot; with &amp;quot;larger-than-or-equal-to&amp;quot; in the definition above. The 12-tone diatonic scale is proper, but not strictly proper.&lt;/li&gt;&lt;/ul&gt;&lt;br /&gt;
&lt;ul&gt;&lt;li&gt;&lt;strong&gt;Strict Propriety:&lt;/strong&gt; A scale is strictly proper if the Generic Interval classes are discrete. Replace the word &amp;quot;larger&amp;quot; with &amp;quot;larger-than-or-equal-to&amp;quot; in the definition above. The 12-tone diatonic scale is proper, but not strictly proper.&lt;/li&gt;&lt;/ul&gt;&lt;br /&gt;
&lt;strong&gt;Weakly Epimorphic:&lt;/strong&gt; A scale is weakly epimorphic if, under some val, all scale degrees are &amp;quot;filled,&amp;quot; no matter which note you choose as the fundamental.&lt;br /&gt;
&lt;strong&gt;Weakly Epimorphic:&lt;/strong&gt; A scale is weakly epimorphic if, under some val, all scale degrees are &amp;quot;filled,&amp;quot; no matter which note you choose as the fundamental.&lt;br /&gt;
&lt;ul&gt;&lt;li&gt;&lt;strong&gt;Epimorphic:&lt;/strong&gt; Something silly that basically means your scale is non-negative, or something like that. The diatonic scale is epimorphic in general. The diatonic scale in 12-EDO is only considered to be epimorphic if it's being viewed as a set of notes in an infinite rank-2 space, in which some notes just happen to be tuned the same.&lt;/li&gt;&lt;/ul&gt;&lt;br /&gt;
&lt;ul&gt;&lt;li&gt;&lt;strong&gt;Epimorphic:&lt;/strong&gt; A weakly epimorphic scale is epimorphic if it keeps rising in pitch as you go to higher scale degrees--the (n+1)st degree is higher than the nth degree.&lt;/li&gt;&lt;/ul&gt;&lt;br /&gt;
&lt;strong&gt;Distributional Evenness:&lt;/strong&gt; A scale is Distributionally Even if there are no more than two Interval sizes for each Generic Interval class (e.g. Major/Minor thirds, Perfect/Augmented fourths, etc).&lt;br /&gt;
&lt;strong&gt;Distributional Evenness:&lt;/strong&gt; A scale is Distributionally Even if there are no more than two Interval sizes for each Generic Interval class (e.g. Major/Minor thirds, Perfect/Augmented fourths, etc).&lt;br /&gt;
&lt;ul&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;/li&gt;&lt;/ul&gt;&lt;br /&gt;
&lt;ul&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;/li&gt;&lt;/ul&gt;&lt;br /&gt;
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