Differential Operators and Regression
We give statistical evidence from 28 performances of Schumann’s “Träumerei”, as measured by Bruno Repp  that the rhythmic, motivic, and harmonic analyses provided by RUBATO® are shaping structures for the agogical streams. The statistical model is based on regression analysis and realizes shaping of agogics by a second degree linear differential operator as a function of analytical weights which are averaged over a natural grouping hierarchy (as described in Chapter 43) of the score.
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