User:Grady/Harmonic similarity: Difference between revisions

Line 17:

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.

=== Base similarity relations ===

Of course, the knowledge that harmonic similarity should follow this pseudo-transitive property isn't very helpful in determining which notes are harmonically similar without establishing some basic similarity relationships first. Essentially, two pitches have a basic similarity relation if the frequency of one is a low integer multiple of the other. The reason for this might be that we're highly accustomed to hearing harmonic timbres, so usually when we hear a note, we also somewhat prominently hear low integer multiples of that frequency as well, and this causes our brains to associate those higher harmonics as "similar" to the fundamental. The lower the integer multiple, the more prominently we hear it in those harmonic timbres, which corresponds to the fact that lower integer multiples represent stronger harmonic similarity relationships.

@@ Line 17: / Line 17: @@
 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.
+=== Base similarity relations ===
+Of course, the knowledge that harmonic similarity should follow this pseudo-transitive property isn't very helpful in determining which notes are harmonically similar without establishing some basic similarity relationships first. Essentially, two pitches have a basic similarity relation if the frequency of one is a low integer multiple of the other. The reason for this might be that we're highly accustomed to hearing harmonic timbres, so usually when we hear a note, we also somewhat prominently hear low integer multiples of that frequency as well, and this causes our brains to associate those higher harmonics as "similar" to the fundamental. The lower the integer multiple, the more prominently we hear it in those harmonic timbres, which corresponds to the fact that lower integer multiples represent stronger harmonic similarity relationships.