Re: Tonal Smear

Two of the more difficult, but extremely valuable, parts of Rothenberg's
model are the concepts of "blur" and "range" which deal with scalar
inflections in performance. The range of an individual note is the
amount of variation it can exhibit without changing the propriety of the
scale (or its equivalence class, IIRC). Blur is the amount ALL the notes
can vary without changing the apparent gestalt of the scale. Needless to
say, the computations and theory are more complex than propriety,
sufficient sets and efficiency.

I would think such ideas would be very applicable to Turkish music.

I should mention that there has never been a rigorous test of David
Rothenberg's models, though Connie Chang did some elementary tests for a
Masters at Princeton in the late 60's or early 70's.

Over to you, Carl...

--John

At 08:58 8/13/99 -0800, you wrote:
>From: John Chalmers <jhchalmers@UCSD.Edu>
>
>Two of the more difficult, but extremely valuable, parts of Rothenberg's
>model are the concepts of "blur" and "range" which deal with scalar
>inflections in performance. The range of an individual note is the
>amount of variation it can exhibit without changing the propriety of the
>scale (or its equivalence class, IIRC). Blur is the amount ALL the notes
>can vary without changing the apparent gestalt of the scale. Needless to
>say, the computations and theory are more complex than propriety,
>sufficient sets and efficiency.
>
>I would think such ideas would be very applicable to Turkish music.
>
>
>--John
>

Dear Mr. Chalmers,

What I am observing in my investigations on Turkish music is not an
'equivalence class' phenomenon. Instead, the distributions or smears
or sound clusters along the pitch axis serve as 'warehouses' for the
collection of pitches the musician is using to construct 'local'
scales at the micro level within the framework of a macro scale whose
elements (notes) are the smears themselves. During the course of an
improvisation (taksim~taqsiim) the musician visits the underlying smears,
drawing a certain pitch (only one) from each cluster at any point in
time. Such collection of pitches form the notes of a micro scale created
at that moment during the evolution of the improvisation. When the taksim
re-visits a given cluster at a different point in time, a different pitch
is selected from the cluster to contribute to a different local scale
pertinent to the evolution of the taksim at that time.

Based on these speculations on my part, the phenomenon does not appear
to be a 'blur' as suggested in Rothenberg's model. I might be looking
at a similar phenomenon from a totally different angle though. In fact
the two models may turn out to be complementary!
Dr. Can Akkoc
Alabama School of Mathematics and Science
1255 Dauphin Street
Mobile, AL 36604
USA

Phone: (334) 441-2126
Fax: (334) 441-3290
Web: http://199.20.31.100/GIFT/