*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.