User:Grady/Harmonic similarity: Difference between revisions

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=== 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 over time 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.

With this knowledge, we can use the pseudo-transitive property to discover higher-order harmonic similarity relationships. For example, two notes a perfect fifth apart (an interval of 3/2) aren't perceived as harmonically similar because the upper note is present in the harmonics of the lower note (which it isn't, assuming a typical harmonic spectrum). Rather, they're similar because two notes an octave apart (an interval of 2/1) ''are'' similar for that reason, and so are two notes a perfect twelfth, or tritave, apart (an interval of 3/1), and thus by the pseudo-transitive property, two notes a perfect fifth apart must be similar as well.

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 === 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 over time 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.
+With this knowledge, we can use the pseudo-transitive property to discover higher-order harmonic similarity relationships. For example, two notes a perfect fifth apart (an interval of 3/2) aren't perceived as harmonically similar because the upper note is present in the harmonics of the lower note (which it isn't, assuming a typical harmonic spectrum). Rather, they're similar because two notes an octave apart (an interval of 2/1) ''are'' similar for that reason, and so are two notes a perfect twelfth, or tritave, apart (an interval of 3/1), and thus by the pseudo-transitive property, two notes a perfect fifth apart must be similar as well.