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A Model of Expressive Timing in Tonal Music

A Model of Expressive Timing in Tonal Music. Neil Todd. Presented by Xiaodan Wu. Goal. Combine the generative musical theory with the principle of phrase-final lengthening to generate a duration structure corresponding to the rubato in a performance. Introduction. Duration and Intensity

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A Model of Expressive Timing in Tonal Music

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  1. A Model of Expressive Timing in Tonal Music Neil Todd Presented by Xiaodan Wu

  2. Goal • Combine the generative musical theory with the principle of phrase-final lengthening to generate a duration structure corresponding to the rubato in a performance.

  3. Introduction • Duration and Intensity • Music is organized hierarchically. Mozart - A Major Sonata K331

  4. Phrase-Final Lengthening • Phenomenon • Boundary Marker

  5. Generative Music Theory • Grouping structure • Metrical structure • Time-span reduction • Prolongation reduction

  6. Unit Time Span • It was introduced when we need to compare the real-time duration with metrical duration.

  7. Structural Endings and Embedding Depth • C is an ordered set of time spans. • cj is the time span containing the jth structural ending. • n is the total number of structural endings. • E is an ordered set of numbers with one-one correspondence with the elements of C. • ej is the embedding depth of the jth structure ending.

  8. Tree diagram of a time-span reduction Red for Cadence C = (4, 8, 12, 16) E = (1, 3, 1, 5) That is, E = [(0+1), (1+2), (0+1), (3+2)]

  9. Duration • Timing is organized on about 3 levels: • Global component • Intermediate components • Local components

  10. A model for Intermediate Components • Formulate it as a parabola m is rubato amplitude constant A is tempo constant

  11. A hypothetical performance duration structure generated by the model with the given TSR

  12. The Application • Mozart A Major Sonata K.331 • Haydn Sonata 59 Adagio • Chopin Trois Nouvelles Etudes No.3

  13. Conclusion • Is a approximation only. • Should consider harmonic structure or prolongation reduction in the future model. • Should consider intensity and other secondary expressive variables in the future model.

  14. Question?

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