Monday, November 19, 2012

Getting Some Satisfaction from the Literature

It turns out that my concern over that claim I cited that "freely generated rhythms always have interval ratios of 1:2 or 1:3" may have been a result of a misreading on the part of its authors. This weekend my reading took me to what may have been the source of the claim, a paper entitled "Hierarchical Organization of Temporal Patterns" by Peter J. Essens (whose work I used to follow when I was a more "serious" researcher. This paper was published in 1986, quite some time before the paper in which I found the claim appeared, which was in 2004.

First of all, the claim itself can probably be traced to the follow sentence from Essens' abstract:
From the systematic errors subjects made in reproducing temporal patterns, it is concluded that an accurate internal representation will be arrived at only if the temporal structure of a pattern enables an organization in which hierarchical levels relate as integers with prime factors 2 or 3.
While this sentence is, indeed, consistent with the experimental data, the paper concludes with a "General Discussion" section, which, in turn, concludes as follows:
The research reported here restricts itself to conceptual structures used by subjects from a western culture. In other cultures, different conceptual structures might be used. Data across cultures could provide insights into the universal nature of our results.
Exactly. Essens was careful to establish the limitations of his conclusions based on the limitations of his data, and it is more than a pity that some of those who read those conclusions did not respect those same limitations.

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