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Re: Auditory wheel

Your cyclical fade construct looks to be versatile and closely analogous to the color wheel.
After all, the color wheel is an artificail construct having more to do with application (use) than perception of color.

That said:
The most common (to western musicians anyway) auditory circular function would be "the circle of fifths".
Though this is a set of relationships rather than a quality inherent to "a sound", it is generally
perceptible and is closely related to consonance and dissonance. 

There are, historically speaking, many ways to present the circle of fifths.
eg.  You could generate wide band (c1 c2 c3 c4 c5 c6...) "notes" for each pitch class  (a b c d e f...)
and divide the circle of fifths various ways.
- close and simple, by fifths  (c g d a e...)
- distant and complex, by tritones ( c fs c fs c fs...)

Perhaps you could look at some ways the color wheel is used to determine color schemes and
imagine using the circle of fifths in a like manner.  Pitch being analogous perhaps to brightness,
and pitch class being analogous to "color".