> We're really talking about imitatative counterpoint in general,of course. It is
> unfortunate that an approach to writing music so??loaded with potential for the
> individual stamp or even originality??should be saddled with such a moniker,
> but this is the technical term we've inherited.


My point was that it's not the imitation per se that is difficult
about writing any kind of fugue -- it's imitation in some kind of
harmonic/contrapuntal context that is difficult, and which to me is
what makes imitation interesting in the first place. The requirements
for such a context can be pretty broad, of course. See more below.


>>I've been working on the "xenharmonic fugue" thing for a few years.>The
> difficulty comes in whether you think of fugue as a type of>strictly
> contrapuntal-motivic-formal thing for which there need be no>harmonic- and
> voice-leading-protocols to function or to "be a fugue,">or if you think of a
> fugue as a particular type of>contrapuntal-motivic-formal manifestation of a
> larger class of music>where harmony and voice-leading DO function under some
> kind of>grammar.
>
> This really boils down to whether we care about the vertical or not.But I think
> it doesn't matter- the vertical is going to happen whetherconsidered or not,
> and the piece cannot be percieved without thatvertical dimension, willy
> nilly.??
> The grammer of the harmony and voice-leading are going to depend??on the
> tuning. You can't have a V-I if there is no "V" or even"fifth" in a tuning.
> Predicating specific harmonic language effectivelyforbids the whole concept of
> a "xenharmonic" fugue. An importantreason for xenharmonic counterpoint would be
> to re-evolveharmony "otherwise".


"Whether we care about the vertical or not" could mean a lot of
things, but I think it does matter. Again, I think what makes canons
and fugues impressive (or substitute "interesting" if you'd rather),
is the fact that the imitation takes place in a context where
simultaneity is heavily constrained. I'd like to take it a step
further yet and not just constrain the "vertical," but also constrain
voice-leading, "chord progression," and larger scale harmonic
relationships. This basically means deducing a "tonal system" from the
properties of the tuning in question (equal temperaments are quite a
bit easier), from which the "sound world" emerges. You CAN have
something analogous to V-I, but most likely it won't sound anything
like V-I in traditional tonality, so in that sense you can't by fiat
dictate the sound of the chords you want to use and hope that there
will magically be a corresponding system of consistent harmony and
voice-leading in some tuning system.

In any case you also probably end up with a lot of systems where the
ordering of the "scale" and strict ascent/descent of the pitches in
the scale collection aren't as highly correlated as they are in
traditional tonal music, making definition of motive (and thus
imitation) in such a system that much harder. In other words you'll
probably end up with some scales that, as you move through them,
ascend in portions and descend elsewhere. Here's an example from
19-tET -- 0,3,6,9,8,11,14,17,1,0 (this sounds roughly
C-D-E-F#-F-G-A-B-C#-C) -- it's a scale that has lots of intervallic
consistency and that you can use to hierarchize harmony and make
strict voice-leadings, but notice the two places where the scale goes
down by one -- it's not strictly ascending the whole way. This makes
it hard to correlate motive as scale-degree phenomenon (e.g. treating
scale-degree successions 1-4-2-5-7 and 3-6-4-7-9 as members of the
same motive class), and motive as contour.


> More later, gotta run- I'd love to hear what you're up to,can you link to it,
> or send me a PM if you'd prefer?

You can check out "tetrahedron" in the "solo version" of this piece:
http://ecmc.rochester.edu/mbarb/web/music.php?filter=chrono#interface_chapel

It's not a fugue, but it is what I think "tonal counterpoint" would
sound like in an 11-tone equal temperament where 3:2 was the interval
of equivalence. "Dodecahedron" is a similar idea but for 24-tET per
2:1.


Also, you can listen to the 1st fugue in this:
http://ecmc.rochester.edu/mbarb/web/music.php?filter=chrono#atomes

It's not "xenharmonic" but it is highly constrained and harmonically
hierarchical, using the [014] set class as the harmonic norm. The 2nd
fugue is a strict transformation of the 1st, but with normal triads as
the harmonic norm -- and also the 2nd fugue is in a 3:4 tempo canon
with itself at the octave, obeying most traditional rules of harmony
and counterpoint (the vocal parts are quoted snippets from the rest of
the piece).


There's a bunch of similar stuff here:
http://ecmc.rochester.edu/mbarb/web/music.php?filter=chrono#parallel_circuit

But there are a lot of other things going in that piece which have
little to do with what we're talking about (2:13 of the 2nd track is
probably the most relevant).

I don't use this list much, but this discussion caught my attention --
anyway, my apologies if it's discourteous to link to one's music here.
Sorry also for the long post.

Matt


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