Epimorphic scale: Difference between revisions

Revision as of 06:29, 20 February 2024 view source Inthar (talk \| contribs) autopatrolled, emailconfirmed 15,004 edits mNo edit summary ← Older edit		Revision as of 06:39, 20 February 2024 view source Inthar (talk \| contribs) autopatrolled, emailconfirmed 15,004 edits mNo edit summary Newer edit →
Line 1:		Line 1:
	A JI scale ''S'' is '''epimorphic''' if on the [[JI subgroup]] <math>A \leq \mathbb{Q}_{>0}</math> generated by the intervals of ''S'', there exists a linear map~~, called an~~ '''~~epimorphism~~''', ''v'': ''A'' ~~→ ℤ~~ such that ''v''(''S''[''i'']) = ''i'' for all ''i'' ∈ ℤ.		A JI scale ''S'' is '''epimorphic''' if on the [[JI subgroup]] <math>A \leq \mathbb{Q}_{>0}</math> generated by the intervals of ''S'', there exists a linear map ''v'': ''A'' → ℤ, called an '''epimorphism''', such that ''v''(''S''[''i'']) = ''i'' for all ''i'' ∈ ℤ.

	An '''epimorphic temperament''' of an epimorphic scale ''S'' on a JI subgroup ''A'' is a temperament [[support]]ed by its epimorphism on ''A''. Some [[temperament]]s (including [[val]]s for small edos) can be used as epimorphic temperaments for small epimorphic scales despite their relatively low accuracy:		An '''epimorphic temperament''' of an epimorphic scale ''S'' on a JI subgroup ''A'' is a temperament [[support]]ed by its epimorphism on ''A''. Some [[temperament]]s (including [[val]]s for small edos) can be used as epimorphic temperaments for small epimorphic scales despite their relatively low accuracy: