Glossary of scale properties: Difference between revisions
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* **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:** 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. | ||
** | **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). | ||
* **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 | * **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. | ||
**Trivalence Property:** Same as Myhill's property, but replace "two Interval sizes" with "three Interval sizes." If we form a scale from the notes of a Dominant 7th chord, (e.g. C-E-G-Bb-C) this scale has the Trivalence Property. | **Trivalence Property:** Same as Myhill's property, but replace "two Interval sizes" with "three Interval sizes." If we form a scale from the notes of a Dominant 7th chord, (e.g. C-E-G-Bb-C) this scale has the Trivalence Property. | ||
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<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 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 /> | <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> | <strong>Distributional Evenness:</strong> 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).<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 | <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 Distributionally Even.</li></ul><br /> | ||
<strong>Trivalence Property:</strong> Same as Myhill's property, but replace &quot;two Interval sizes&quot; with &quot;three Interval sizes.&quot; If we form a scale from the notes of a Dominant 7th chord, (e.g. C-E-G-Bb-C) this scale has the Trivalence Property.<br /> | <strong>Trivalence Property:</strong> Same as Myhill's property, but replace &quot;two Interval sizes&quot; with &quot;three Interval sizes.&quot; If we form a scale from the notes of a Dominant 7th chord, (e.g. C-E-G-Bb-C) this scale has the Trivalence Property.<br /> | ||
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<strong>Symmetrical:</strong> A scale is symmetrical if at least one mode of the scale is symmetrical. Therefore, every interval of that mode must have an inverse. These scales will always have an odd number of notes per <u>period</u>. They may not always have an odd number of notes per <u>octave</u>, however. The 12-tone diatonic scale is symmetrical.</body></html></pre></div> | <strong>Symmetrical:</strong> A scale is symmetrical if at least one mode of the scale is symmetrical. Therefore, every interval of that mode must have an inverse. These scales will always have an odd number of notes per <u>period</u>. They may not always have an odd number of notes per <u>octave</u>, however. The 12-tone diatonic scale is symmetrical.</body></html></pre></div> | ||