recent Rothenberg

John Chalmers...

>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.

Yes, it is cool the R. worked all this out. Unfortunately, the
computations are beyond me, at least for the time being. My next area of
interest will actually be the graph and node stuff, which attempts to
explain chromaticism.

That, and I'd like to do a rigorous search for all 5-10 tone scales in all
ET's from 21-41 with high Stability and Efficiency. I think my PC is
actually powerful enough to do it in a reasonable time...

>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.

John- do you have these materials?

Paul Erlich...

>This is a particularly interesting point; Rothenberg would assume that any
>interval, not just the octave, can function as an interval of equivalence if
>the scale is symmetrical at that interval. This is quite the opposite of
>supposing an acoustical foundation for octave equivalence.

Whether you use this language to refer to Rothenberg the man, or to his
model, I don't think it is accurate. Nowhere have I found Rothenberg to
ignore the importance of acoustics in the phenomena he was trying to model.

In fact I believe he has paid more attention than just about anybody. His
stuff is full with cautionary remarks about the effects of acoustics-- it
may be said that his goal is to model everything but acoustics, in such a
way that acoustics can then be added in. Which seems to me like a better
approach than what had come before him in 200 years of music theory. And
unlike the Babbit and other serialist theory I have read, I think he was
sucessful in describing the acoustic-independent, and it seems you agree...

>However, there is clearly an "ambiguity of tonal function" between the
block->equivalent notes in any symmetrical scale.

-C.