Differential Operators and Regression

Research output: Chapter in Book/Report/Conference proceedingChapter


We give statistical evidence from 28 performances of Schumann’s “Träumerei”, as measured by Bruno Repp [886] 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.

Original languageEnglish (US)
Title of host publicationComputational Music Science
PublisherSpringer Nature
Number of pages24
StatePublished - 2017

Publication series

NameComputational Music Science
ISSN (Print)1868-0305
ISSN (Electronic)1868-0313

Bibliographical note

Funding Information:
This research was supported by grants from the National Key Research and Development Program of China (2017YFA0505602, 2017YFC1601100, 2017YFC1601101, 2017YFC1 601102, and 2017YFC1601104) and National Natural Science Foundation of China (81521064, 81872408, 81572889, 31570837, 81790252, 31430021, and 81672275).

Publisher Copyright:
© 2017, Springer International Publishing AG, part of Springer Nature.


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