User:Grady/Harmonic similarity: Difference between revisions

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(Note that despite the choice of word, the concept of [[wikipedia:Similarity_(geometry)|similarity]] in geometry is actually an equivalence relation by this definition, not a similarity relation: it means both objects have the exact same shape, not that they're close in shape.)

It follows from this that if we want to define a notion of two auditory pitches being similar or related in their harmonic function, said notion should also follow this pseudo-transitive property as well. This is the core principle that differentiates the notion of harmonic similarity from that of consonance, since it doesn't necessarily follow that if note X and note Y are consonant together, and note Y and note Z are consonant together, that notes X and Z ought to be consonant together to some degree.

It follows from this that if we want to define a notion of two auditory pitches being similar or related in their harmonic function, said notion should also follow this pseudo-transitive property as well. This is the core principle that differentiates the notion of harmonic similarity from that of consonance, since it doesn't necessarily follow that if note X and note Y are consonant together, and note Y and note Z are consonant together, that notes X and Z ought to be consonant together to some degree as well.

=== Basic similarity relations ===

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 (Note that despite the choice of word, the concept of [[wikipedia:Similarity_(geometry)|similarity]] in geometry is actually an equivalence relation by this definition, not a similarity relation: it means both objects have the exact same shape, not that they're close in shape.)
-It follows from this that if we want to define a notion of two auditory pitches being similar or related in their harmonic function, said notion should also follow this pseudo-transitive property as well. This is the core principle that differentiates the notion of harmonic similarity from that of consonance, since it doesn't necessarily follow that if note X and note Y are consonant together, and note Y and note Z are consonant together, that notes X and Z ought to be consonant together to some degree.
+It follows from this that if we want to define a notion of two auditory pitches being similar or related in their harmonic function, said notion should also follow this pseudo-transitive property as well. This is the core principle that differentiates the notion of harmonic similarity from that of consonance, since it doesn't necessarily follow that if note X and note Y are consonant together, and note Y and note Z are consonant together, that notes X and Z ought to be consonant together to some degree as well.
 === Basic similarity relations ===