User:Grady/Harmonic similarity

This page serves to document a personal theory of mine that attempts to explain the perception of octave equivalence and other related phenomena, as well as the various implications of the theory. I've seen other people get at similar ideas, but I'm not sure if the concept in this exact form has been articulated before. If anyone knows if it has, I'd love to know more!

Quick aside: Naming

I wasn't exactly sure what term to use for this concept, but I settled on harmonic similarity for now, at least for the purpose of deciding what to name this page. Some other terms I've considered are harmonic relatedness, harmonic affinity, and harmonic correlation. I'm sure all of these terms have been used before, and some of them have certainly been used to get at a similar concept as I'm putting forth here. If you have any opinions on what the most suitable name would be, I'd be glad to hear them!

Motivation

Harmonic similarity is a measure of how similar in harmonic function two pitches are. This is in contrast to consonance or concordance, which is generally defined as a measure of how harmonious or stable two or more pitches sound when played together, or perhaps less commonly a measure of how much timbral fusion occurs when playing them together.

Often, harmonic similarity between two notes correlates very strongly with consonance, but this is not always the case. For example, two notes a major second apart (an interval of 9/8) are more harmonically similar to each other than two notes a major third apart (an interval of 5/4), but typically less consonant when played simultaneously. I'll be elaborating more on what I mean by this, but it aligns with how Western music theory would approach the question: two notes a major second apart are more closely related via the circle of fifths.