"Dimensionality" of Musical "Transformations":

To use 12EDO transpositions and inversions as an example,
the transposition operation is only one-dimensional, since
you're only raising or lowering a scale/melody in pitch/regsitral
space, like raising or lowering an oil painting mounted on
peg board.

Inversion is a 3-dimensional transformation, since you're
rotating the melody/scale 180 degrees in pitch/registral
space.

What I'm trying to say that is that various operations aren't
on the same "plane", so they have to be ranked heirarchically,
and in that sense inversion is a much more musically
significant transformation than transposition.

Bill Flavell

On 3/16/06, Bill Flavell <bill_flavell@email.com> wrote:
>
> To use 12EDO transpositions and inversions as an example,
> the transposition operation is only one-dimensional, since
> you're only raising or lowering a scale/melody in pitch/regsitral
> space, like raising or lowering an oil painting mounted on
> peg board.
>
> Inversion is a 3-dimensional transformation, since you're
> rotating the melody/scale 180 degrees in pitch/registral
> space.
[...]

I don't follow you. You can rotate something 180 degrees in 2D. Also,
rotation should be equivalent to retrograde inversion, not inversion
alone.

More importantly, what does all this have to do with tuning?

Keenan