User:Grady/Harmonic similarity: Difference between revisions

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=== Why this causes octave equivalence ===

Presumably, for one of these reasons or the other, or perhaps both, our brains create the abstraction that notes any number of octaves apart fall within the same pitch class. I believe this is essentially something our brains do just because they can, since it creates a useful layer of abstraction without any real downsides.

Presumably, for one of these reasons or the other, or perhaps both, our brains create the abstraction that notes any number of octaves apart fall within the same pitch class. I believe this is essentially something our brains do just because they can, at least after receiving some musical training, since it creates a useful layer of abstraction without any real downsides.

It's only a useful layer of abstraction to do this with octaves only, because if we attempted to do it with both octaves and tritaves simultaneously, then every possible pitch would fall within the same pitch class, making the abstraction useless. This is because any two notes relate to each other by some combination of octaves and tritaves (within some arbitrarily small margin of error), but most pairs of notes cannot be related to each other by octaves only. In more technical terms, this means any possible interval is arbitrarily close to some [[3-limit]] interval, but not arbitrarily close to some [[2-limit]] interval.

@@ Line 49: / Line 49: @@
 === Why this causes octave equivalence ===
-Presumably, for one of these reasons or the other, or perhaps both, our brains create the abstraction that notes any number of octaves apart fall within the same pitch class. I believe this is essentially something our brains do just because they can, since it creates a useful layer of abstraction without any real downsides.
+Presumably, for one of these reasons or the other, or perhaps both, our brains create the abstraction that notes any number of octaves apart fall within the same pitch class. I believe this is essentially something our brains do just because they can, at least after receiving some musical training, since it creates a useful layer of abstraction without any real downsides.
 It's only a useful layer of abstraction to do this with octaves only, because if we attempted to do it with both octaves and tritaves simultaneously, then every possible pitch would fall within the same pitch class, making the abstraction useless. This is because any two notes relate to each other by some combination of octaves and tritaves (within some arbitrarily small margin of error), but most pairs of notes cannot be related to each other by octaves only. In more technical terms, this means any possible interval is arbitrarily close to some [[3-limit]] interval, but not arbitrarily close to some [[2-limit]] interval.