Contextual Xenharmonics: Difference between revisions

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== Portals ==

Portals are musical situations where you end up in a place different than expected or compared to another system. Usually associated with [[Comma pump|comma-pumps]]. For example, [[15edo|15 edo]]'s chain of fifths contains a portal somewhere between the third and fourth fifth in the cycle.{{clarify}}

Portals are musical situations where you end up in a place different than expected or compared to another system. Usually associated with [[Comma pump|comma-pumps]]. For example, [[15edo|15 edo]]'s chain of fifths contains a portal somewhere between the third and fourth fifth in the cycle, because the result of stacking four fifths in 15edo produces a categorical error compared to standard diatonic theory.{{clarify}}

== Breaks ==

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'''Duality:''' Two types of something exist sounding like it belongs to the same context. Such as major and minor thirds.

'''Triality:''' Three types of something exist in the same class.

etc...

Fringe Region - An area of categories where adjacent ones blend together. For example [[13/10]].

'''Anchors:''' Representative, relatively simple intervals of a category, which are often JI intervals but not always. For example, [[3/2]] is an anchor of the perfect fifth region, and [[5/4]] is an anchor of the major third region. Anchors can vary in their pull and recognizability. For example, [[6/5]] is more recognizable than [[7/6]] as an anchor of the minor third region, which in turn is more recognizable than [[13/11]] as an anchor. Note however that these secondary anchors can still be strong anchors of adjacent or subregions, with [[7/6]] for example acting as an anchor of the subminor region. A major goal of RTT is to ensure that these anchor intervals are in tune as possible while still maintaining a simple lattice tuning system. Thus, anchors in JI can be transformed to RTT or edo anchors after being mapped into these tuning systems, albeit with a somewhat vague limit on how much they can be detuned. In this way, this concept helps connect subjective and objective parts of xenharmonic music theory.

== Projection ==

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 == Portals ==
-Portals are musical situations where you end up in a place different than expected or compared to another system. Usually associated with [[Comma pump|comma-pumps]]. For example, [[15edo|15 edo]]'s chain of fifths contains a portal somewhere between the third and fourth fifth in the cycle.{{clarify}}
+Portals are musical situations where you end up in a place different than expected or compared to another system. Usually associated with [[Comma pump|comma-pumps]]. For example, [[15edo|15 edo]]'s chain of fifths contains a portal somewhere between the third and fourth fifth in the cycle, because the result of stacking four fifths in 15edo produces a categorical error compared to standard diatonic theory.{{clarify}}
 == Breaks ==
@@ Line 29: / Line 29: @@
 '''Duality:''' Two types of something exist sounding like it belongs to the same context. Such as major and minor thirds.
 '''Triality:''' Three types of something exist in the same class.
 etc...
 Fringe Region - An area of categories where adjacent ones blend together. For example [[13/10]].
+'''Anchors:''' Representative, relatively simple intervals of a category, which are often JI intervals but not always. For example, [[3/2]] is an anchor of the perfect fifth region, and [[5/4]] is an anchor of the major third region. Anchors can vary in their pull and recognizability. For example, [[6/5]] is more recognizable than [[7/6]] as an anchor of the minor third region, which in turn is more recognizable than [[13/11]] as an anchor. Note however that these secondary anchors can still be strong anchors of adjacent or subregions, with [[7/6]] for example acting as an anchor of the subminor region. A major goal of RTT is to ensure that these anchor intervals are in tune as possible while still maintaining a simple lattice tuning system. Thus, anchors in JI can be transformed to RTT or edo anchors after being mapped into these tuning systems, albeit with a somewhat vague limit on how much they can be detuned. In this way, this concept helps connect subjective and objective parts of xenharmonic music theory.
 == Projection ==