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.)

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.

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 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.

Revision as of 00:53, 3 August 2025 view source Grady (talk \| contribs) 55 edits Expanded on Definition section Tag: Visual edit ← Older edit		Revision as of 00:55, 3 August 2025 view source Grady (talk \| contribs) 55 edits m Changed variable names to reduce confusion Tag: Visual edit Newer edit →
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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.		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 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.