User:Grady/Harmonic similarity: Difference between revisions
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(Note that despite the choice of word, the concept of "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.) | (Note that despite the choice of word, the concept of "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 in 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 A and note B are consonant together, and note B and note C are consonant together, that notes A and C ought to be consonant together to some degree. | |||