Defactoring: Difference between revisions

Line 1:

'''Defactoring''' is a operation on the mapping for a regular temperament which ensures it represents the same information but without any enfactoring, or in other words, redundancies due to a common factor found in its rows. It is also defined for comma-bases, the duals of mappings, where it instead checks its columns for enfactoring.

Being enfactored is a bad thing. Enfactored matrices — those in the RTT domain, at least — are sick, in a way<ref>According to [[saturation]], "...if [an RTT matrix] isn't saturated the supposed temperament it defines may be regarded as pathological..." </ref>; it's no accident that "enfactored" sounds sort of like "infected". We'll discuss this pathology in detail in [[~~canonical_form~~#the_pathology_of_enfactoredness|a later section of this article]]. Fortunately, the remedy is simple: all one has to do is "defactor" it — identify and divide out the common factor — to produce a healthy mapping.

Being enfactored is a bad thing. Enfactored matrices — those in the RTT domain, at least — are sick, in a way<ref>According to [[saturation]], "...if [an RTT matrix] isn't saturated the supposed temperament it defines may be regarded as pathological..." </ref>; it's no accident that "enfactored" sounds sort of like "infected". We'll discuss this pathology in detail in [[defactoring#the_pathology_of_enfactoredness|a later section of this article]]. Fortunately, the remedy is simple: all one has to do is "defactor" it — identify and divide out the common factor — to produce a healthy mapping.

Due to complications associated with enfactored matrices which we'll get into later in this article, we discourage treating them as representations of true temperaments.<ref>As Graham Breed writes [http://x31eq.com/temper/method.html here], "Whether temperaments with contorsion should even be thought of as temperaments is a matter of debate."</ref> Instead we recommend that they be considered to represent mere "temperoids": temperament-like structures.

@@ Line 1: / Line 1: @@
 '''Defactoring''' is a operation on the mapping for a regular temperament which ensures it represents the same information but without any enfactoring, or in other words, redundancies due to a common factor found in its rows. It is also defined for comma-bases, the duals of mappings, where it instead checks its columns for enfactoring.
-Being enfactored is a bad thing. Enfactored matrices — those in the RTT domain, at least — are sick, in a way<ref>According to [[saturation]], "...if [an RTT matrix] isn't saturated the supposed temperament it defines may be regarded as pathological..." </ref>; it's no accident that "enfactored" sounds sort of like "infected". We'll discuss this pathology in detail in [[canonical_form#the_pathology_of_enfactoredness|a later section of this article]]. Fortunately, the remedy is simple: all one has to do is "defactor" it — identify and divide out the common factor — to produce a healthy mapping.
+Being enfactored is a bad thing. Enfactored matrices — those in the RTT domain, at least — are sick, in a way<ref>According to [[saturation]], "...if [an RTT matrix] isn't saturated the supposed temperament it defines may be regarded as pathological..." </ref>; it's no accident that "enfactored" sounds sort of like "infected". We'll discuss this pathology in detail in [[defactoring#the_pathology_of_enfactoredness|a later section of this article]]. Fortunately, the remedy is simple: all one has to do is "defactor" it — identify and divide out the common factor — to produce a healthy mapping.
 Due to complications associated with enfactored matrices which we'll get into later in this article, we discourage treating them as representations of true temperaments.<ref>As Graham Breed writes [http://x31eq.com/temper/method.html here], "Whether temperaments with contorsion should even be thought of as temperaments is a matter of debate."</ref> Instead we recommend that they be considered to represent mere "temperoids": temperament-like structures.