Taxonomies of xen approaches - Revision history

Inthar: /* Inthar's taxonomy */

2026-02-14T00:02:44Z

Inthar's taxonomy

← Older revision		Revision as of 00:02, 14 February 2026
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	* JI-based, non-stacking-based: [[Primodality]] and [[neji]]s.		* 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.) For more (in context of edos), see [[EDO vs ET#Temperament-agnostic EDO paradigms]].		* 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~~.		* JI-agnostic, non-stacking-based: E.g. using exact [[delta-rational]] chords and [[isodifferential]] series.

	[[Category:Impression]]		[[Category:Impression]]
	{{todo\|expand}}		{{todo\|expand}}

BudjarnLambeth at 07:53, 17 November 2024

2024-11-17T07:53:52Z

← Older revision		Revision as of 07:53, 17 November 2024
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			'''See also: [[Approaches to Musical Tuning]]'''

	== Inthar's taxonomy ==		== Inthar's taxonomy ==
	One possible taxonomy of approaches to xen:		One possible taxonomy of approaches to xen:

BudjarnLambeth: Categories

2024-11-17T07:53:29Z

BudjarnLambeth: Added category "todo:expand"

2023-04-19T08:19:02Z

Added category "todo:expand"

← Older revision		Revision as of 08:19, 19 April 2023
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	* 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, 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.		* JI-agnostic, non-stacking-based: This is a more wide-open area.
			[[Category:Todo:expand]]

Cmloegcmluin: Undo revision 80270 by Cmloegcmluin (talk): actually the original link is better. I was just thrown off by those two different pages for mapping at first.

2021-11-08T19:37:14Z

Undo revision 80270 by Cmloegcmluin (talk): actually the original link is better. I was just thrown off by those two different pages for mapping at first.

← Older revision		Revision as of 19:37, 8 November 2021
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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.		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 [[~~Temperament_mapping_matrices\|~~mapping]]. 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-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.) For more (in context of edos), see [[EDO vs ET#Temperament-agnostic EDO paradigms]].		* 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.		* JI-agnostic, non-stacking-based: This is a more wide-open area.

Cmloegcmluin: /* Inthar's taxonomy */ fix link

2021-11-05T20:28:31Z

Inthar's taxonomy: fix link

← Older revision		Revision as of 20:28, 5 November 2021
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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.		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 [[mapping]]. 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 [[Temperament_mapping_matrices\|mapping]]. So is prime-limited or lattice-based JI.
	* JI-based, non-stacking-based: [[Primodality]] and [[neji]]s.		* 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.) For more (in context of edos), see [[EDO vs ET#Temperament-agnostic EDO paradigms]].		* 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.		* JI-agnostic, non-stacking-based: This is a more wide-open area.

Cmloegcmluin: /* Inthar's taxonomy */ map → mapping

2021-11-05T20:16:31Z

Inthar's taxonomy: map → mapping

← Older revision		Revision as of 20:16, 5 November 2021
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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.		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-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.) For more (in context of edos), see [[EDO vs ET#Temperament-agnostic EDO paradigms]].		* 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.		* JI-agnostic, non-stacking-based: This is a more wide-open area.

Inthar at 16:57, 3 September 2021

2021-09-03T16:57:35Z

← Older revision		Revision as of 16:57, 3 September 2021
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	* 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 map. So is prime-limited or lattice-based JI.
	* JI-based, non-stacking-based: [[Primodality]] and [[neji]]s.		* 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.		* JI-agnostic, non-stacking-based: This is a more wide-open area.

Inthar at 16:51, 3 September 2021

2021-09-03T16:51:00Z

← Older revision		Revision as of 16:51, 3 September 2021
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	* 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 map. So is prime-limited or lattice-based JI.
	* JI-based, non-stacking-based: [[Primodality]] and [[neji]]s.		* 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]]es.)		* 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, non-stacking-based: This is a more wide-open area.		* JI-agnostic, non-stacking-based: This is a more wide-open area.

Inthar at 16:50, 3 September 2021

2021-09-03T16:50:47Z

← Older revision		Revision as of 16:50, 3 September 2021
Line 8:		Line 8:
	* 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 map. So is prime-limited or lattice-based JI.
	* JI-based, non-stacking-based: [[Primodality]] and [[neji]]s.		* 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.		* 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]]es.)
	* JI-agnostic, non-stacking-based: This is a more wide-open area.		* JI-agnostic, non-stacking-based: This is a more wide-open area.