Tempo Trace- Individual project question

*Individual project, depending on the decision of my group this will likely not be my final individual project.  I am quite interested in a question that I had proposed to the group dealing with quantized mappings between relatively prime metric cycle lengths.—This project would likely manifest as a research review and speculative argument.

Here is my alternate question:

Do subtle variations in tempo manifest consistently within a performer’s approach to a repertory?  If so, how might I be able to profitably discuss these consistent variations in a tempo-free environment—so that I could model variation in tempo variations across pieces at different tempi?

I would propose to investigate these variations in variations through the use of Sean Carson’s trace or an adaptation thereof–see: (Carson, Sean H. 2004. “The Trace, Its Relation to Contour Theory and an Application to Elliott Carter’s String Quartet 2.” Integral 18/19 (May): 113–49.).  My basic methodology might be something along the lines of: (1) take multiple single-line instrumental recordings by a single performer at different tempi and establish IOI’s of all adjacent notes; (2) Segment each piece into phrases at some level of grouping structure; (3) Apply Sean Carson’s trace to the IOI data within the phrase; his procedure essentially amounts to taking a polynomial best-fit of the data in a regularized space (his methodology was devised for semi-tone contour space) and using basic integral calculus to compare these regressions; (4) re-trend the data so that the tempo disparities (between the phrases) can now be used as a possible explanation in variability of tempo (within the phrases).

This exploration, as I envision it, would be primarily experimental with a strong emphasis on data analysis.

2 thoughts on “Tempo Trace- Individual project question

  1. Since the group has settled on question no. 2, which if I recall correctly was Stephen’s question, I assume that you will want to do the quantization question? Please confirm and post the question here for me to review (you might want to elaborate a bit, especially on how you would plan to explore the question and integrate aspect of empirical/psychological research).

  2. I’m sorry for the delay. I have had difficulty reformulating my other question so that it could be suited to experimental study. I am more than happy to do my tempo trace project if you see think this one is intractable.

    Constructing a Hypothesis: The Question of Quantization

    When a listener is primed to a rhythmic cycle Ro with length l of m equal pulses, how might the listener perceive the quantization of Ro onto a different cycle R1 with length l (the same as Ro) of n pulses?

    More generally, how are rhythms perceptually related to their different quantizations?

    Background: It has been noted that several pervasive non-even rhythm formations of different lengths, in time-span-units, are quantizations of one another if their cycle lengths are the same in absolute time. For instance, the ubiquitous diatonic and hyper-diatonic timelines, lengths 12 and 16 time-span units respectively, are quantizations of one another (Stover 2009, though not articulated in these terms). I hope to investigate the quantization of such rhythmic formations and posit an hypothesis on how people might perceive similarity between these quantizations. My approach would be a combination of formalist music theory inflected by music cognition research. First, I would create a general model of quantization between two rhythms (from rhythm A to rhythm B—this process is not isomorphic). Second, I would find points in the model in which rhythmic formation would change in type—in some locations on the model, rhythmic formations could be beats that form meters (under, for instance, London’s (2004) Well Formedness Rules), while others would not meet sufficient conditions. Third, I would attempt to inflect the model with cognitive research as a means of discussing how quantized meters can be perceived as equivalent or similar at different tempi. Finally, I might attempt an experiment using a same/different paradigm between the diatonic and hyper-diatonic timelines (with various priming) to test one facet of the model empirically.

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