Karmarkar, U R, and D V Buonomano. 2007. Timing in the absence of clocks: encoding time in neural network states. Neuron 53, no. 3: 427-438.
Dear Eliot,I don't know of direct measurements of the discrimination of such patterns.One hypothesis that I can think of is that for such discriminations it isnecessary to count the beats. This would be easiest if theduration of the temporal unit of which the pattern is constructed is in between375 and 750 ms, with a shift to the latter for untrained people.But perceiving directly the beat in such sequences could be difficult.Cf:Van Noorden, L., & Moelants, D. (1999). Resonance in the Perception of Musical Pulse. Journal of New Music Research, 28(1), 43--66.For discrimination of tempo as such you should look at work of Michon.Kind regards,Leon van NoordenOn 20 Dec 2010, at 18:31, Eliot Handelman wrote:On 20/12/2010 10:52 AM, Guy Madison wrote:Hi Eliot,there are virtually countless variations of short rhythms like these. It's not clear to me what scientific question you want to address with them, and that determines to a large extent which references that may be relevant.
Sorry to be unclear, thanks for speedy reply. I am asking specifically about the effect of tempo on rhythmic discrimination,
and the example I gave was only intended to illustrate. I selected it because it is especially simple:
2 1 1 can be divided into two parts, a long, and two shorts which add up to the long. Now vary the rhythm such that
the shorts are all the same size but don't quite add up to the long, eg 10 6 6.
My question is: at what tempo will such variations tend to be perceived as being just the same as 2 1 1?
If, eg, the tempo is extremely slow (1= 1 day, or maybe 8 seconds). then I guess we do not perceive any difference.
If the tempo is extremely fast, then some variations will certainly also be indistinguishable from 2 1 1 (eg, 1000, 499, 499).
To be clear: I'm asking about the effect of tempo/rate of discrimination. I am guessing that there's some window
with optimal discrimination.
The first of the references you gave below, for example, found tempo to be a complex variable to control. The author
also seems to be working with rather complex rhythms of the sort that occur in serial music and probably wanted to
know whether anyone can hear these. Sorry if I munged this, as I only looked rather quickly. In contrast, I'm asking
about very simple rhythms and what happens to simple inequalities as the tempo is varied from very slow to very fast.
The research problem behind this has to do with representations of music at various levels of rhythmic approximation,
in particular I am studying patterns of alternation that be induced over rhythmic groups, given segmentation
criteria. In order to construct different quantal levels, I'm just using clustering algorithms on IOIs to generate base
structures used for further analysis, but it occurred to me that there's one area roughly between 80 & 800ms
where (I think) very fine discriminations can be made -- to which the clustering algorithm should be sensitive.
This is all part of my Jack & Jill automatic composition system: for more information see my home page.
-- eliotHowever, here are a few papers that should be relevant. Please mail me directly if you can provide more detailed description of your goal, in which case I might be able to give more specific tips.
Best, Guy1. Carson, B. (2007). Perceiving and distinguishing simple timespan ratios without metric reinforcement. Journal of New Music Research, 36, 313-336.