point of it all

Some readers may wonder what Constant Structures and Propriety are good for.

They both seem to assume that when we hear music, we attempt to assign scale degree numbers to melodic pitches. I won't argue about that here; if you don't think it happens, then propriety and CS aren't for you. But if you're interesting in getting it to happen or not, then they are for you.

Propriety and CS both measure how easy it is for the listener to un-ambiguously assign scale degree numbers to pitches as he hears them. CS assumes that a listener can recognize intervals by their _specific_ size -- a 3:2 is distinct from a 7:5, and so on. So CS asks, once you recognize the interval, will there be any doubt as to what scale degree it is? If you can answer "no", your scale is CS. In the diatonic scale in 12-tet, you can answer no for all the intervals but the tritone -- it can be a fourth or a fifth; you need other notes to clarify its position in the scale.

Propriety does the same thing, except it assumes that listeners recognize intervals by their _relative_ size -- that the listener ranks the intervals he hears by how big they are. The specific tuning of the intervals doesn't matter, so long as their ranks are preserved. This means the theory can be tested to see if people percieve a similarity between different tunings of a scale with the same "rank-order", and if they percieve a difference between two tunings of a scale with a different rank-order. Rothenberg has actually suggested some very cool experiments to test many aspects of his theory, which are as yet un-tested (enthno-musicology is simply not a source of reliable scientific information here).

-Carl

Carl Lumma said:

> Rothenberg has
> actually suggested some very cool experiments to test many aspects of his
> theory, which are as yet un-tested (enthno-musicology is simply not a
> source of reliable scientific information here).

This sounds very interesting, Carl. I missed any earlier discussion of this.
Who is Rothenberg and where can I learn more about his project?

Jerry

>>Rothenberg has actually suggested some very cool experiments to test many
>>aspects of his theory, which are as yet un-tested (enthno-musicology is
>>simply not a source of reliable scientific information here).
>
>This sounds very interesting, Carl. I missed any earlier discussion of this.
>Who is Rothenberg and where can I learn more about his project?

David Rothenberg is a mathematician who did some work in the 60's and 70's on a theory of the perception of melody. Check the Microtonal bibliography for references...

ftp://ella.mills.edu/ccm/tuning/papers/bib.html

...or try searching the onelist archives for "Rothenberg".

-Carl