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Re: Short rhythm patterns for imitation task

Aniruddh Patel wrote:
> Dear list,
> Can anyone suggest a set of short rhythm patterns of varying
> complexity for use in a rhythm imitation task with children?
The question is, what is rhythmic complexity? One of the closest things
in the literature I can think of is Gary Marcus' work with
7-month olds discerning simple grammars like AAB, ABA, and ABB. It would
be extremely interesting
to try complicating grammars like this & seeing to what extent children
could still recognize them.

For the purposes of rhythmic production you could view a rhythm as a
pattern of transformations of an underlying beat. 

For example,

AB ->  q (ee) q (ee) ... where q = quarter & e = eighth.
ABA -> q (ee) q
AABA -> q q (ee) q

ABAC -> q (ee) q (j) where j is a jagged rhythm like 3::1 or 2:;1.
A fairly simple metric for complexity following Chomsky, Halle,
Leeuwenberg, etc is just to count symbols
once the pattern has been reduced via a pattern reduction grammar.
Intuitively, AB is simpler than ABA. But it is not certain that
ABA is simpler than AABA, which permits a duple structural division
where the first does not, so that the whole, in some sense, is
reducible to AB, or this is what the pattern reduction grammar should
do. I've worked extensively on this, but
my results are not published.

In devising such a grammar it is important to remember the sorts of
results associated with Gentner's analogical experiments,
where "structure" rather than "feature" can dominate (in reference to
which Marcus' "Algebraic Mind" might also help).

That is,


are analogues in some sense irrespective of what B & C stand for.

Thus rhythms like

are in a structural sense sense simpler than
ABAA AAAC, which do not provide the same structural/analog simplicity.

To realize this rhythmically, eg:
AABA AACA => (ee) (ee) q (ee) / (ee) (ee) (triplet) (ee)
And the proposal is that this is simpler than
(ee) q (ee) (ee) (ee) (ee) (triplet) (ee)

At any rate, following these suggestions it should be rather easy to
devise a test rhythmic set with more or
less controlled degree of complexity variation.

-- eliot

> Ideally the patterns would be about 4-7 elements long
> and at 2 or 3 levels of rhythmic complexity. They would
> hear one pattern at a time and imitate it by tapping
> with a drum stick.
> If anyone knows of suitable stimuli, especially  
> batteries that have some published data associated with them,
> I would be most grateful.
> Thanks,
> Ani Patel
> Aniruddh D. Patel, Ph.D.
> Esther J. Burnham Senior Fellow
> The Neurosciences Institute
> 10640 John Jay Hopkins Drive
> San Diego, CA 92121
> 858-626-2085 tel
> 858-626-2099 fax
> apatel@xxxxxxx
> http://www.nsi.edu/users/patel