Taxonomies of xen approaches: Difference between revisions

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'''See also: [[Approaches to Musical Tuning]]'''

== Inthar's taxonomy ==

One possible taxonomy of approaches to xen:

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Stacking-based approaches obtain all pitches by stacking a finite set of intervals. Non-stacking based approaches do not think of pitches in systems this way, even if e.g. [[edo]]s are trivially stacking-based.

* JI-based, stacking-based: Traditional, JI-based [[RTT]] is a major approach that belongs to this, in JI-based RTT the JI ''interpretations'' of two intervals stack according to the temperament ~~map~~. So is prime-limited or lattice-based JI.

* JI-based, stacking-based: Traditional, JI-based [[RTT]] is a major approach that belongs to this, in JI-based RTT the JI ''interpretations'' of two intervals stack according to the temperament [[mapping]]. So is prime-limited or lattice-based JI.

* JI-based, non-stacking-based: [[Primodality]] and [[neji]]s.

* JI-agnostic, stacking-based: Uninterpreted [[mos]]ses and k-step scales. This could be thought of as RTT but with abstract intervals instead of JI. The goal of these systems is not to approximate JI (though close JI intervals can be considered sometimes), but to give the pitch system or scale a regular structure (e.g. a finite number of scale steps or a [[maximum variety]] condition such as [[mos]]ses.)

* JI-agnostic, stacking-based: Uninterpreted [[mos]]ses and k-step scales. This could be thought of as RTT but with abstract intervals instead of JI. The goal of these systems is not to approximate JI (though close JI intervals can be considered sometimes), but to give the pitch system or scale a regular structure (e.g. a finite number of scale steps or a [[maximum variety]] condition such as [[mos]]ses.) For more (in context of edos), see [[EDO vs ET#Temperament-agnostic EDO paradigms]].

* JI-agnostic, non-stacking-based: This is a more wide-open area.

[[Category:Impression]]

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+'''See also: [[Approaches to Musical Tuning]]'''
 == Inthar's taxonomy ==
 One possible taxonomy of approaches to xen:
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 Stacking-based approaches obtain all pitches by stacking a finite set of intervals. Non-stacking based approaches do not think of pitches in systems this way, even if e.g. [[edo]]s are trivially stacking-based.
-* JI-based, stacking-based: Traditional, JI-based [[RTT]] is a major approach that belongs to this, in JI-based RTT the JI ''interpretations'' of two intervals stack according to the temperament map. So is prime-limited or lattice-based JI.
+* JI-based, stacking-based: Traditional, JI-based [[RTT]] is a major approach that belongs to this, in JI-based RTT the JI ''interpretations'' of two intervals stack according to the temperament [[mapping]]. So is prime-limited or lattice-based JI.
 * JI-based, non-stacking-based: [[Primodality]] and [[neji]]s.
-* JI-agnostic, stacking-based: Uninterpreted [[mos]]ses and k-step scales. This could be thought of as RTT but with abstract intervals instead of JI. The goal of these systems is not to approximate JI (though close JI intervals can be considered sometimes), but to give the pitch system or scale a regular structure (e.g. a finite number of scale steps or a [[maximum variety]] condition such as [[mos]]ses.)
+* JI-agnostic, stacking-based: Uninterpreted [[mos]]ses and k-step scales. This could be thought of as RTT but with abstract intervals instead of JI. The goal of these systems is not to approximate JI (though close JI intervals can be considered sometimes), but to give the pitch system or scale a regular structure (e.g. a finite number of scale steps or a [[maximum variety]] condition such as [[mos]]ses.) For more (in context of edos), see [[EDO vs ET#Temperament-agnostic EDO paradigms]].
 * JI-agnostic, non-stacking-based: This is a more wide-open area.
+[[Category:Impression]]
+{{todo|expand}}