Functional systems - Revision history

Godtone: typo

2026-04-04T15:32:07Z

typo

← Older revision		Revision as of 15:32, 4 April 2026
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	== The 50-function system ==		== The 50-function system ==
	The derivation is not currently documented on the xen wiki, but the basic premise of ''n''-function systems is defining [[interval class]]es that are ambiguous between more basic interval classes, where what is considered basic is defined derivative of superimposing all perfect [[Ringer scale]]s to form a (or multiple) category system(s), chosen for their exceptional combination of properties as JI scales and relevance to perception of harmony. The main result — the 50-function system — primarily forms from 24-grid (and to a lesser extent 36-grid) defined indirectly via superimposing all the categorical alignments and misalignments of the 10-form and 14-form, themselves derived from reconciling the 5-form and 7-form (as having the most predictive power) with the more unusual 4-form, where the connection to Ringer scales is very explicit but "form" is used to describe a distinction from corresponding [[edo]]s, as the optimal ~~perceptial~~ xenmelodic placement will be at least slightly off from perfect in some specific cases.		The derivation is not currently documented on the xen wiki, but the basic premise of ''n''-function systems is defining [[interval class]]es that are ambiguous between more basic interval classes, where what is considered basic is defined derivative of superimposing all perfect [[Ringer scale]]s to form a (or multiple) category system(s), chosen for their exceptional combination of properties as JI scales and relevance to perception of harmony. The main result — the 50-function system — primarily forms from 24-grid (and to a lesser extent 36-grid) defined indirectly via superimposing all the categorical alignments and misalignments of the 10-form and 14-form, themselves derived from reconciling the 5-form and 7-form (as having the most predictive power) with the more unusual 4-form, where the connection to Ringer scales is very explicit but "form" is used to describe a distinction from corresponding [[edo]]s, as the optimal perceptual xenmelodic placement will be at least slightly off from perfect in some specific cases.

	=== A starting point: The 12-form ===		=== A starting point: The 12-form ===

Godtone: /* The 50-function system */ finish sentence

2026-04-01T13:36:24Z

The 50-function system: finish sentence

← Older revision		Revision as of 13:36, 1 April 2026
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	== The 50-function system ==		== The 50-function system ==
	The derivation is not currently documented on the xen wiki, but the basic premise of ''n''-function systems is defining [[interval class]]es that are ambiguous between more basic interval classes, where what is considered basic is defined derivative of superimposing all perfect [[Ringer scale]]s to form a (or multiple) category system(s), chosen for their exceptional combination of properties as JI scales and relevance to perception of harmony. The main result — the 50-function system — primarily forms from 24-grid (and to a lesser extent 36-grid) defined indirectly via superimposing all the categorical alignments and misalignments of the 10-form and 14-form, themselves derived from reconciling the 5-form and 7-form (as having the most predictive power) with the more unusual 4-form, where the connection to Ringer scales is very explicit but "form" is used to .		The derivation is not currently documented on the xen wiki, but the basic premise of ''n''-function systems is defining [[interval class]]es that are ambiguous between more basic interval classes, where what is considered basic is defined derivative of superimposing all perfect [[Ringer scale]]s to form a (or multiple) category system(s), chosen for their exceptional combination of properties as JI scales and relevance to perception of harmony. The main result — the 50-function system — primarily forms from 24-grid (and to a lesser extent 36-grid) defined indirectly via superimposing all the categorical alignments and misalignments of the 10-form and 14-form, themselves derived from reconciling the 5-form and 7-form (as having the most predictive power) with the more unusual 4-form, where the connection to Ringer scales is very explicit but "form" is used to describe a distinction from corresponding [[edo]]s, as the optimal perceptial xenmelodic placement will be at least slightly off from perfect in some specific cases.

	=== A starting point: The 12-form ===		=== A starting point: The 12-form ===

Godtone: Godtone moved page N-function systems to Functional systems over redirect: lowercase n not available

2025-12-29T21:21:53Z

Godtone moved page N-function systems to Functional systems over redirect: lowercase n not available

← Older revision	Revision as of 21:21, 29 December 2025
(No difference)

Godtone: Godtone moved page Functional systems to N-function systems

2025-12-29T21:20:11Z

Godtone moved page Functional systems to N-function systems

← Older revision	Revision as of 21:20, 29 December 2025
(No difference)

Godtone at 21:13, 29 December 2025

2025-12-29T21:13:28Z

← Older revision		Revision as of 21:13, 29 December 2025
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	The ''n''-function systems (alternately '''functional systems'''[[idiosyncratic]]) are defined by [[osmium]] as a systematic way to try to heuristically find a best guess to the answer of approximately most universal enumeration of [[relative interval qualities]] theoretically perceivable by a sufficiently trained xenmelodic listener.		The ''n''-function systems (alternately '''functional systems'''{{idiosyncratic}}) are defined by [[osmium]] as a systematic way to try to heuristically find a best guess to the answer of approximately most universal enumeration of [[relative interval qualities]] theoretically perceivable by a sufficiently trained xenmelodic listener.

	== The 50-function system ==		== The 50-function system ==
	The derivation is not currently documented on the xen wiki, but the basic premise of ''n''-function systems is defining [[interval class]]es that are ambiguous between more basic interval classes, where what is considered basic is defined derivative of superimposing all perfect [[Ringer scale]]s to form a category system, chosen for their exceptional combination of properties as JI scales and relevance to . The main result — the 50-function system — primarily forms from 24-grid (and to a lesser extent 36-grid) defined indirectly via superimposing all the categorical alignments and misalignments of the 10-form and 14-form, themselves derived from reconciling the 5-form and 7-form (as having the most predictive power) with the more unusual 4-form, where the connection to Ringer scales is very explicit but "form" is used to .		The derivation is not currently documented on the xen wiki, but the basic premise of ''n''-function systems is defining [[interval class]]es that are ambiguous between more basic interval classes, where what is considered basic is defined derivative of superimposing all perfect [[Ringer scale]]s to form a (or multiple) category system(s), chosen for their exceptional combination of properties as JI scales and relevance to perception of harmony. The main result — the 50-function system — primarily forms from 24-grid (and to a lesser extent 36-grid) defined indirectly via superimposing all the categorical alignments and misalignments of the 10-form and 14-form, themselves derived from reconciling the 5-form and 7-form (as having the most predictive power) with the more unusual 4-form, where the connection to Ringer scales is very explicit but "form" is used to .

	=== A starting point: The 12-form ===		=== A starting point: The 12-form ===

Godtone: add more info, as this page references a body of theory i wrote about on discord

2025-12-29T21:04:14Z

add more info, as this page references a body of theory i wrote about on discord

← Older revision		Revision as of 21:04, 29 December 2025
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	The '''functional systems''' are defined by [[~~Osmium~~]] as a way to ~~categorize [[interval]]s. The basic premise~~ of ~~the functional systems is defining~~ [[interval ~~class\|interval classes~~]] ~~that are ambiguous between more basic interval classes~~.		The ''n''-function systems (alternately '''functional systems'''[[idiosyncratic]]) are defined by [[osmium]] as a systematic way to try to heuristically find a best guess to the answer of approximately most universal enumeration of [[relative interval qualities]] theoretically perceivable by a sufficiently trained xenmelodic listener.

	== The 50-function system ==		== The 50-function system ==
			The derivation is not currently documented on the xen wiki, but the basic premise of ''n''-function systems is defining [[interval class]]es that are ambiguous between more basic interval classes, where what is considered basic is defined derivative of superimposing all perfect [[Ringer scale]]s to form a category system, chosen for their exceptional combination of properties as JI scales and relevance to . The main result — the 50-function system — primarily forms from 24-grid (and to a lesser extent 36-grid) defined indirectly via superimposing all the categorical alignments and misalignments of the 10-form and 14-form, themselves derived from reconciling the 5-form and 7-form (as having the most predictive power) with the more unusual 4-form, where the connection to Ringer scales is very explicit but "form" is used to .

	=== A starting point: The 12-form ===		=== A starting point: The 12-form ===
	Even outside of [[12edo]], the 12-form is a ~~common harmonic structure, found in 3-limit and 5-limit chromatic scales, which influences~~ the human perception of intervals.		Even outside of [[12edo]], the 12-form is a significant organising principle influencing the human perception of intervals.

	{{Todo\|expand\|inline=1\|text=Add derivation of 50-function system}}		{{Todo\|expand\|inline=1\|text=Add detailed derivation of 50-function system}}
	{\| class="wikitable"		{\| class="wikitable"
	\|+		\|+

Fredg999 category edits: Moving from Category:Interval region to Category:Interval regions using Cat-a-lot

2025-09-03T21:08:31Z

Moving from Category:Interval region to Category:Interval regions using Cat-a-lot

← Older revision		Revision as of 21:08, 3 September 2025
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	\|}		\|}

	[[Category:Interval ~~region~~]]		[[Category:Interval regions]]

BudjarnLambeth: Categorise uncategorised page

2025-05-07T10:20:24Z

Categorise uncategorised page

← Older revision		Revision as of 10:20, 7 May 2025
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	\|600c		\|600c
	\|}		\|}

			[[Category:Interval region]]

BudjarnLambeth: /* A starting point: The 12-form */

2025-04-20T11:10:44Z

A starting point: The 12-form

← Older revision		Revision as of 11:10, 20 April 2025
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	=== A starting point: The 12-form ===		=== A starting point: The 12-form ===
	Even outside of 12edo, the 12-form is a common harmonic structure, found in 3-limit and 5-limit chromatic scales, which influences the human perception of intervals.		Even outside of [[12edo]], the 12-form is a common harmonic structure, found in 3-limit and 5-limit chromatic scales, which influences the human perception of intervals.

	{{Todo\|expand\|inline=1\|text=Add derivation of 50-function system}}		{{Todo\|expand\|inline=1\|text=Add derivation of 50-function system}}

BudjarnLambeth: Links

2025-04-20T11:10:30Z

Links

← Older revision		Revision as of 11:10, 20 April 2025
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	The functional systems are defined by [[Osmium]] as a way to categorize ~~intervals~~. The basic premise of the functional systems is defining interval classes that are ambiguous between more basic interval classes.		The '''functional systems''' are defined by [[Osmium]] as a way to categorize [[interval]]s. The basic premise of the functional systems is defining [[interval class\|interval classes]] that are ambiguous between more basic interval classes.

	== The 50-function system ==		== The 50-function system ==