User:Grady/Harmonic similarity: Difference between revisions

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=== Margin for error ===

Since our ears are imperfect (and perhaps even because the overtones we hear that may have trained our mental map of harmonic similarity aren't perfect integer harmonics either), it makes sense to assign some margin for error to the notion of harmonic similarity by adding the assertion that two notes are harmonically similar if they're very close in pitch. This allows us to treat two notes that are an interval such as a perfect fifth apart in a tempered system like [[12edo]] to be harmonically similar, even if the ratios are inexact.

== Lattice visualization ==

A very good way to visualize a map of harmonically similar pitches is using a [[3-limit]] [[lattice]], with octaves on one axis and tritaves on the other. In order to demonstrate that octaves are a significantly stronger harmonic similarity relation than tritaves, one might consider spacing the notes much farther apart on the tritave axis than the octave axis. (No diagram yet, but that might be something I can add to this page later!)

This essentially ignores the effects of any basic similarity relations beyond the third harmonic, which I believe is reasonable due to the extremely fast falloff mentioned earlier.

== String analogy ==

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 === Margin for error ===
 Since our ears are imperfect (and perhaps even because the overtones we hear that may have trained our mental map of harmonic similarity aren't perfect integer harmonics either), it makes sense to assign some margin for error to the notion of harmonic similarity by adding the assertion that two notes are harmonically similar if they're very close in pitch. This allows us to treat two notes that are an interval such as a perfect fifth apart in a tempered system like [[12edo]] to be harmonically similar, even if the ratios are inexact.
+== Lattice visualization ==
+A very good way to visualize a map of harmonically similar pitches is using a [[3-limit]] [[lattice]], with octaves on one axis and tritaves on the other. In order to demonstrate that octaves are a significantly stronger harmonic similarity relation than tritaves, one might consider spacing the notes much farther apart on the tritave axis than the octave axis. (No diagram yet, but that might be something I can add to this page later!)
+This essentially ignores the effects of any basic similarity relations beyond the third harmonic, which I believe is reasonable due to the extremely fast falloff mentioned earlier.
 == String analogy ==