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 12- | * **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. | ||
**Maximal Evenness:** A scale is Maximally Even if there are no more than two Interval sizes for each Generic Interval class (e.g. Major/Minor thirds, Perfect/Augmented fourths, etc). Usually when someone is talking about Maximal Evenness, they are talking about Equal Divisions of the Octave. The definition can be extended to other scales, however. | **Maximal Evenness:** A scale is Maximally Even if there are no more than two Interval sizes for each Generic Interval class (e.g. Major/Minor thirds, Perfect/Augmented fourths, etc). Usually when someone is talking about Maximal Evenness, they are talking about Equal Divisions of the Octave. The definition can be extended to other scales, however. | ||
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<ul><li><strong>Strict Propriety:</strong> A scale is strictly proper if the Generic Interval classes are discrete. Replace the word &quot;larger&quot; with &quot;larger-than-or-equal-to&quot; in the definition above. The 12-tone diatonic scale is proper, but not strictly proper.</li></ul><br /> | <ul><li><strong>Strict Propriety:</strong> A scale is strictly proper if the Generic Interval classes are discrete. Replace the word &quot;larger&quot; with &quot;larger-than-or-equal-to&quot; in the definition above. The 12-tone diatonic scale is proper, but not strictly proper.</li></ul><br /> | ||
<strong>Weakly Epimorphic:</strong> A scale is weakly epimorphic if, under some val, all scale degrees are &quot;filled,&quot; no matter which note you choose as the fundamental.<br /> | <strong>Weakly Epimorphic:</strong> A scale is weakly epimorphic if, under some val, all scale degrees are &quot;filled,&quot; no matter which note you choose as the fundamental.<br /> | ||
<ul><li><strong>Epimorphic:</strong> Something silly that basically means your scale is non-negative, or something like that. The 12- | <ul><li><strong>Epimorphic:</strong> 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.</li></ul><br /> | ||
<strong>Maximal Evenness:</strong> A scale is Maximally Even if there are no more than two Interval sizes for each Generic Interval class (e.g. Major/Minor thirds, Perfect/Augmented fourths, etc). Usually when someone is talking about Maximal Evenness, they are talking about Equal Divisions of the Octave. The definition can be extended to other scales, however.<br /> | <strong>Maximal Evenness:</strong> A scale is Maximally Even if there are no more than two Interval sizes for each Generic Interval class (e.g. Major/Minor thirds, Perfect/Augmented fourths, etc). Usually when someone is talking about Maximal Evenness, they are talking about Equal Divisions of the Octave. The definition can be extended to other scales, however.<br /> | ||
<ul><li><strong>Myhill's Property:</strong> 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 Maximally Even.</li></ul><br /> | <ul><li><strong>Myhill's Property:</strong> 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 Maximally Even.</li></ul><br /> | ||