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Is anyone familiar with fuzzy transposition? If so, could you please elaborate on the concept and its formulas?

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In academic music theory, the notion of "fuzzy" just means that there is some level of imprecision.

The concept actually started out in mathematics; you can read about it briefly on this Wikipedia page for "fuzzy sets." I'm not sure I can help with any "formulas" per se, but that page may be of use.

In terms of fuzzy transposition, the idea is simply that whatever is being transposed isn't being transposed exactly. If you have C D E, a fuzzy transposition may move it to E F G#. Note that the F in the latter case wasn't transposed up a major third like E and the G#; this would be an example of a "fuzzy" operation.

If you're working with fuzzy transposition, make sure you also consider the notion of transposition in chromatic space and transposition in diatonic space. If you move C D E up by major third in chromatic space, you get E F# G#. But if you move C D E up by third in the diatonic space of C major, you get E F G, since those are the pitches a third higher in the key of C major.

  • I think it gets a little more complicated with Atonal music. As far as I can tell, they resorted to Fuzzy Transposition as a tool for working with Atonal music where "pitch class" isn't so cut and dry? Not well read on this. – Yorik Feb 21 '17 at 22:06
  • It's definitely more complicated, and it has been expanded far beyond just the concept of transposition. For better or worse, I treated this as an ELI5 answer. – Richard Feb 21 '17 at 22:10
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    Well.... TIL a new initialism (ELI5) :-) – Carl Witthoft Feb 22 '17 at 13:40

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