Glossary of scale properties: Difference between revisions

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; Epimorphism

* '''Epimorphism''': A JI scale is ''epimorphic'' if, under some val, all scale degrees are "filled," no matter which note you choose as the tonic and successive degrees are always increasing. Without the ~~increasing~~ condition, the scale is only ''weakly epimorphic''.

* '''Epimorphism''': A JI scale is ''epimorphic'' if, under some val, all scale degrees are "filled," no matter which note you choose as the tonic, and successive degrees are always increasing. Without the second condition, the scale is only ''weakly epimorphic''.

* '''Epimorph val/temperament''': A val that witnesses that a JI scale is epimorphic is called the ''epimorph val'' of the scale, and a temperament supported by an epimorph val is an ''epimorph temperament''. Many low-accuracy edos and temperaments are useful as epimorph vals and temperaments; a CS scale may be constructed as a detempering of the low-accuracy tuning implied by such a temperament.

* Example: 5-limit [[Zarlino]] is a 2.3.5 JI scale that is epimorphic under the val {{val|7 11 16}}, and the 2.3.5 temperament [[dicot]] is an epimorph temperament for Zarlino.

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 ; Epimorphism
-* '''Epimorphism''': A JI scale is ''epimorphic'' if, under some val, all scale degrees are "filled," no matter which note you choose as the tonic and successive degrees are always increasing. Without the increasing condition, the scale is only ''weakly epimorphic''.
+* '''Epimorphism''': A JI scale is ''epimorphic'' if, under some val, all scale degrees are "filled," no matter which note you choose as the tonic, and successive degrees are always increasing. Without the second condition, the scale is only ''weakly epimorphic''.
 * '''Epimorph val/temperament''': A val that witnesses that a JI scale is epimorphic is called the ''epimorph val'' of the scale, and a temperament supported by an epimorph val is an ''epimorph temperament''. Many low-accuracy edos and temperaments are useful as epimorph vals and temperaments; a CS scale may be constructed as a detempering of the low-accuracy tuning implied by such a temperament.
 * Example: 5-limit [[Zarlino]] is a 2.3.5 JI scale that is epimorphic under the val {{val|7 11 16}}, and the 2.3.5 temperament [[dicot]] is an epimorph temperament for Zarlino.