Re: inversions (was "as dumb as a unison")

Gene, quoting Monz:

>> And yes, since both the Bach and Schoenberg versions
>> generally invoke octave-equivalence, when looked at
>> that way, you get the "major turns into minor" effect
>> you're talking about, but the intervals also become
>> totally different, i.e., when a major-3rd upward becomes
>> a major-3rd downward, that's the same as a minor-6th upward.
>
> Which means you have still more variant notions of inversion,
> depending on whether octave equivalency is assumed or not. As I
> pointed out, you can also define inversion on classes of chords.

Monz is wrong here - the kind of inversion you hear Bach using on a
fugue subject does *not* make use of octave equivalence. Contour is
strictly preserved (reversed) and 3rds do not become 6ths.

Gene, this isn't a new kind of inversion; both of these were covered
in my summing-up from several messages ago. I'll repost it, expanded a
little:

Summing up, we have:

inversion can mean reflection or permutation.

Permutation happens to a multi-voice structure (like a passage of
counterpoint, or a chord--which is a multi-voice structure where each
voice has just one note). Reflection can happen to a melody (ordered
set) OR a chord (unordered set).

Reflection can be in pitch space (i.e. for a melody, contour is
preserved, just upside-down; for a chord, reflection is a generalised
utonal<->otonal type of operation) or in pitch-class space (this is a
much more recently explored possibility; probably not until
Schoenberg).

Reflection can be exact (chromatic), or diatonic.

"Tonal" imitation (including tonal inversion) is an even looser kind
of imitation/inversion than diatonic imitation/inversion. (Examples in
previous posts)

Is that all clear now Gene?

--- In tuning@yahoogroups.com, "Jeremy Targett" <jeremy.targett@...>
wrote:

> Is that all clear now Gene?

You seem, more or less, to be saying I was right to start with. But I
wouldn't call the situation clear.

Hi Jeremy,

--- In tuning@yahoogroups.com, "Jeremy Targett" <jeremy.targett@...>
wrote:
>
> Gene, quoting Monz:
>
> >> And yes, since both the Bach and Schoenberg versions
> >> generally invoke octave-equivalence, when looked at
> >> that way, you get the "major turns into minor" effect
> >> you're talking about, but the intervals also become
> >> totally different, i.e., when a major-3rd upward becomes
> >> a major-3rd downward, that's the same as a minor-6th upward.
> >
> > Which means you have still more variant notions of
> > inversion, depending on whether octave equivalency is
> > assumed or not. As I pointed out, you can also define
> > inversion on classes of chords.
>
> Monz is wrong here - the kind of inversion you hear Bach
> using on a fugue subject does *not* make use of octave
> equivalence. Contour is strictly preserved (reversed)
> and 3rds do not become 6ths.

I understand what you're saying. I was simply saying
that in Bach's music, octave-equivalence is always invoked.
What you wrote is true, he doesn't actually *employ*
octave-equivalence in any way when he inverts a
fugue subject. But all C's are still considered to
be C's, etc. So harmonically, he is using it.

-monz
http://tonalsoft.com
Tonescape microtonal music software