Re: [tuning] Digest Number 3943

> > Wrong. Chord inversion never changes the notes of the chord, only the
> order of notes from bottom to top. It may be a misleading or odd use
> of the word in a gigantically global context, but that is the way the
> word has been used, at least AFAIK.
> > Cheers,
> Jon
> Jon,

There are (unfortunately) two usages of "inversion" in music theory. The first, harmonic use, which you mention, refers to the voicings or positions of a chord: for example "root" or 1st position = tonic in the basss (5/3), 2nd position = third in the bass (6/3), 3rd position = fifth in the bass (6/4). The second, equally legitimate usage, is more associated with melodic uses, and original with answers in imitative counterpoint. Answers are distinguished between real (the intervals are inverted exactly) or tonal (the contour is generally maintained, but intervals are adjusted to accommodate the tonal environment). Real answer becomes especially important in atonal and 12-tone contexts (where interchangeability between melodic and chordal material is also essential), but there are plenty of examples of real imitation to be heard in earlier repertoire as well: not only Partch was fond of chordal inversion at the 1/1 (To hell with it, I'm going to walk! 1/1 O7 - 1/1 U7).

DJW

--- In tuning@yahoogroups.com, Daniel Wolf <djwolf@...> wrote:

> Answers are distinguished between real (the intervals are
> inverted exactly) or tonal (the contour is generally maintained, but
> intervals are adjusted to accommodate the tonal environment).

Is the vocabulary of "real" and "tonal" common in English? I've heard
"mirror inversion" for "real".

Daniel,

--- In tuning@yahoogroups.com, Daniel Wolf <djwolf@...> wrote:
> There are (unfortunately) two usages of "inversion" in music theory.

Right, and those are the two that I first was referring to in Jeremy's
descriptions. The first (harmonic use) is the more straightforward;
the second, melodic useage, can become much more flexible. We see it
extending all the way back to invertible counterpoint, and all the way
forward to serial analysis and construction.

I think the problem for Gene, and this may always be the case, is that
in many circumstances musical terminology is _not_ as codified,
ossified, and concrete as mathematical terminology. I can live with
that, but I don't think he can. :)

Cheers,
Jon ("Here she comes - a root, not a third, but a root...")

--- In tuning@yahoogroups.com, "Jon Szanto" <jszanto@...> wrote:

> I think the problem for Gene, and this may always be the case, is that
> in many circumstances musical terminology is _not_ as codified,
> ossified, and concrete as mathematical terminology. I can live with
> that, but I don't think he can. :)

It is a problem, but mathematicians don't have everything codified
either. When they don't, they say stuff like "In this chapter, by
'ring' we will mean a commutative ring with identity". Doing the same
thing in music would involve making clear exactly what was meant by
"inversion" or any other term in particular cases.

--- In tuning@yahoogroups.com, "Gene Ward Smith" <genewardsmith@...>
wrote:
>
> --- In tuning@yahoogroups.com, "Jon Szanto" <jszanto@> wrote:
>
> > I think the problem for Gene, and this may always be
> > the case, is that in many circumstances musical terminology
> > is _not_ as codified, ossified, and concrete as mathematical
> > terminology. I can live with that, but I don't think he can.
> > :)
>
> It is a problem, but mathematicians don't have everything
> codified either. When they don't, they say stuff like
> "In this chapter, by 'ring' we will mean a commutative
> ring with identity". Doing the same thing in music would
> involve making clear exactly what was meant by
> "inversion" or any other term in particular cases.

I certainly feel (and hope) that i'm doing my part with
the Encyclopedia.

There is a lot of value in having concise terminology,
which makes it *much* easier to elaborate on complex
topics.

To those who complain of too much jargon, i say
"tough cookies" (ok, that's a euphemism -- i really
mean "tough shit"). The Encyclopedia is there to
explain what the jargon means, and i do strive to
include every important term i come across.

Of course there's still a lot missing -- i've been
really busy working on Tonescape, but the goal is
to keep expanding the Encyclopedia. At this point,
i'm sure that it's going to be a lifelong project
for me.

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