Functional systems: Difference between revisions

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== 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 ===

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 == 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 ===