Functional systems: Difference between revisions

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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 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 ===

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}}

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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 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 ===
-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}}
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