User:Grady/Harmonic similarity: Difference between revisions

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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.

== Other implications ==

In addition to providing an attempted explanation for the perception of octave equivalence, the theory of harmonic similarity provides explanations for various other noteworthy phenomena.

=== Neutrality of the major second ===

The [[9/8|major second]] is often regarded as a dissonant interval, but it seems rather unique in that it produces auditory roughness, but doesn't necessarily feel emotionally jarring in the way something like one of the various flavors of [[tritone]] does. This is easily explained by the fact that two notes a major second apart are somewhat harmonically similar, due to being related by two factors of 3 and three factors of 2, which gives the major second a more emotionally neutral flavor than other dissonant intervals.

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 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.
+== Other implications ==
+In addition to providing an attempted explanation for the perception of octave equivalence, the theory of harmonic similarity provides explanations for various other noteworthy phenomena.
+=== Neutrality of the major second ===
+The [[9/8|major second]] is often regarded as a dissonant interval, but it seems rather unique in that it produces auditory roughness, but doesn't necessarily feel emotionally jarring in the way something like one of the various flavors of [[tritone]] does. This is easily explained by the fact that two notes a major second apart are somewhat harmonically similar, due to being related by two factors of 3 and three factors of 2, which gives the major second a more emotionally neutral flavor than other dissonant intervals.