musical grammar [was: Re: Calling all Conlangers!]

At 12:51 AM +0000 01/22/02, Chris Palmer wrote:
>Roger Mills writes:
>
>>-- Any creative endeavor has an underlying "language"; I believe Bernstein's
>>1960s lectures on music showed this quite nicely, using the then-popular
>>Transformational model. "Phonology"-- the notes of the scale; "Morphology"
>>and "Syntax" including "transformations"; even "Historical"; Dialects;
>>Languages (e.g. Western vs. Indian or Chinese music. The same goes for
>>painting, sculpture, architecture--- cooking!
>
>I have those speeches on VHS. Absolutely hilarious and an embarrassment for
>Bernstein, in my opinion. The basic idea is interesting, but as Bernstein
>presents it it hardly holds up to any scrutiny.
Well, "embarrassment" is a bit harsh. He was certainly naive about
the application of linguistic methods to musical analysis, but his
lectures sparked interest in possible connections between the two
fields which resulted in a faculty seminar at MIT on music,
linguistics, and aesthetics in 1974. One of the happy results of this
seminar was a book written collaboratively by Fred Lerdahl, a
composer and music theorist, and Ray Jackendoff, a syntactician and
practicing musician (clarinetist; I believe he even played with the
Boston Pops orchestra). The book, _A Generative Theory of Tonal
Music_ (GTTM) is a fascinating study; I'm rereading it now and am
almost finished.

In GTTM Lerdahl and Jackendoff set themselves the task of producing a
formal description of the intuitions of listeners who are experienced
in a musical idiom (in GTTM, the tonal idiom of most 18th and 19th
century classical music). They divide their theory into four modules:
grouping, metrical structure, time span reduction, and prolongational
reduction. Grouping deals with the heirarchical chunking together of
notes into groups (phrases); that is, large groups are built up out
of smaller groups. Metrical structure deals with the rhythmic
intuitions by which certain beats are related hierarchically. Time
span reduction deals with the hierarchical arrangement of pitch
events in time spans, which are constructed from the interaction of
grouping and metrical structure. Prolongational reduction is the
hierarchical arrangement of intuitions of tension and relaxation over
time-span reductions.

Each module is discussed independently, but they interact in complex
ways. For each module, a set of well-formedness rules (WFRs) is
proposed which generate the class of possible objects in the
respective modules. Since the WFRs overgenerate, they also develop a
set of "preference rules" (PRs) for each module which are used to
determine "preferred hearings" for musical passages. The PRs
essentially "thin out" the possible structures which the WFRs
generate. They also discuss transformational rules which govern the
relationship between the musical surface (the sequence of pitch
events which are heard) and the underlying musical structure (which
is generated by the WFRs and the PRs).

To me it seems that the most obvious connections GTTM draws with
linguistic theory is i) the assumption that there is an underlying
musical structure separate from the musical surface, and ii) a set of
rules which generates possible structures. More recent connections
with linguistic theory can be seen in Optimality Theory, which deals
with "preferences" in a way similar to GTTM; PRs in GTTM can directly
conflict with each other, with the context determining which one wins
out in generating structure. Similarly, in OT constraints on
linguistic structures conflict with each other, with the outcome
determined contextually. GTTM certainly does not claim that there are
musical "parts of speech" or direct analogues to phrases and
sentences.

Lerdahl has recently published a "sequel" called _Tonal Pitch Space_.
As far as I can tell, it uses the theory of time-span reduction and
prolongational reduction as a starting point (I haven't read it yet),
and makes use of the distinction between WFRs and PRs introduced in
GTTM. He also deals with atonal music as well.

Dirk
--
Dirk Elzinga                                            Dirk_Elzinga@byu.edu

"Speech is human, silence is divine, yet also brutish and dead;
therefore we must learn both arts."
- Thomas Carlyle