Re: inversions (was dumb as a unison)

Gene wrote:

> > Well, if you did want an axis of inversion you could also choose 13/2
> > (thirteen halves i.e. 6.5). My point in saying "there doesn't have to
> > be an axis of inversion" is that there doesn't have to be (and there
> > usually isn't) a pitch that things are disposed around symmetrically,
> > unlike the case for reflection in pitch-space.
>
> There is a pitch around which the reflection is an inversion in pitch
> space half of the time.

Think of C-E-G, all in the octave starting at middle C. Now think of
C#-F#-A. Considered as pitch-classes, the meaningful axis of inversion
is the diameter of the circle of 12 pcs passing in between 0 and 1 at
one end and 6 and 7 at the other. Considered as pitches, there is no
axis of inversion, because there is no symmetry in the pitch domain.
This is what I meant.

Your sentence above means "in pitch-class reflection, half the time
the diameter that is an axis of symmetry passes through one of the 12
pitches".