Periodic scale: Difference between revisions
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=== Epimorphism === | === Epimorphism === | ||
If there exists a linear map h: G → ℤ so that h(s[''i'']) = ''i'', then s is weakly epimorphic with the map h. If s is monotone and weakly epimorphic, it is epimorphic. An important special case is where G is a JI group and h is a val. Epimorphic scales in this restricted sense were first considered by Yves Hellegouarch.<ref>Yves Hellegouarch, ''A Mathematical Interpretation of Expressive Intonation'', in ''Mathematics and Art'', p. 141-148, Springer-Verlag, 2002</ref> The name comes from the fact that h is an {{w|epimorphism}} onto the integers (i.e. the map h is surjective). | If there exists a linear map h: G → ℤ so that h(s[''i'']) = ''i'', then s is weakly epimorphic with the map h. If s is monotone and weakly epimorphic, it is epimorphic. An important special case is where G is a JI group and h is a val. Epimorphic scales in this restricted sense were first considered by Yves Hellegouarch.<ref>Yves Hellegouarch, ''A Mathematical Interpretation of Expressive Intonation'', in ''Mathematics and Art'', p. 141-148, Springer-Verlag, 2002</ref> The name comes from the fact that h is an {{w|epimorphism}} onto the integers (i.e. the map h is surjective). | ||
Epimorphism is explained in more detail on [[detempering]]. | |||
=== Myhill's property === | === Myhill's property === | ||