Invertible counterpoint

Please. Not inversion of ..., inversion AT ... or inversion BY ... It is
afterall a matter of transposing the lower voice up or the upper voice down.

SNIP

>
> As I said, in multiple ways, which you sort out through context. Most
> people mistakenly associate the notion of the "inversion of an
> interval" with the "turning something upside down" idea because it
> uses the same name, but in fact the "inversion of an interval" is
> really a permutation of its elements, same as the inversion of a chord
> from root-position to first inversion. (I prefer the use of "position"
> for this sense when not modified by an ordinal e.g. "what position is
> the seventh chord in?" "Third inversion".) And both of these have the
> same underlying sense as the kind of inversion in invertible
> counterpoint--a permutation of the voices.
>
> In "inversion at the octave", you invert (in the sense of permute) the
> two-voice structure, but given the specific interval mentioned, the
> operation might lead to some intervals in the resulting counterpoint
> not exchanging positions, but rather being brought an octave closer
> together (a tenth might become a third or vice-versa, if the parts
> were crossed to begin with). A tenth isn't what Ozan would consider
> "the inversion of a third" either, but it IS a result of the
> contrapuntal operation that we call "inversion at the octave".
>
> Same goes for other intervals of inversion: when you're performing
> "invertible counterpoint at the twelfth", an octave inverts into a
> fifth. So in that case it's true to say "the inversion of an octave is
> a fifth".
>
> Best --Jeremy
>

Could we please stop starting new threads about this?

Sorry, but the subject is invertible counterpoint now.

----- Original Message -----
From: "Keenan Pepper" <keenanpepper@gmail.com>
To: <tuning@yahoogroups.com>
Sent: 09 Mart 2006 Per�embe 1:38
Subject: Re: [tuning] Invertible counterpoint

> Could we please stop starting new threads about this?
>
>