Spectral properties of rhythm performance

1. Spectral propertiesof rhythm performance Carl Haakon Waadeland Department of Music Norwegian University of Science and Technology (NTNU) Trondheim E-mail: carl.haakon.waadeland@hf.ntnu.no

2. Introduction Basic axiom: Performance and experience of rhythm is intimately related to movements of the body Focus of investigation: To study possible relations between movement characteristics (or: movement categories) and rhythmic expression (expressive timing)

3. ….underlying this approach: we regard a musician’s various ways of moving when playing an instrument as an expression of timbral aspects of rhythm…..

4. A theoretical model (C.H.Waadeland, JNMR, 30(1), 2001) Idea: Rhythm performance is regarded as result of ”atomic” movements ”interacting” with each other. sinusoidal movements frequency modulation

5. Example: Swing groove in jazz:

6. Example: Swing groove in jazz: MIDI recording, quantized in triplets (Computer implementation by Sigurd Saue, NTNU)

7. Swing in sixteenth notes: A frequency modulation of a)

8. Swing in eighth notes: Another frequency modulation of a)

9. Conclusion: Various applications of FM to movement curves yield approximations to live performances of rhythm (swing/Vienna waltz/”springar” in Norwegian folk music) But: This model is based on theoretical movements (FM of sinusoidals) What do the real movements look like?

10. Empirical investigations of jazz drummers’ movements (C.H.Waadeland, 2001 ) General question: What can studies of a jazz drummer’s movements tell us about the way the drummer is performing swing grooves ?

11. Subjects: Jazz drummers, students and teachers at Dept. of Music, NTNU – section of jazz education. Task: Play swing groove restricted to various performance conditions.

12. Aim: Study possible relations between the drummers’ movements and the following performance parameters: Tempo Dynamics ”Swing ratio” (rhythmic subdivision)

13. Method/Equipment for Measuremets (Measurements assisted by Geir Oterhals, Section of Movement Science, NTNU) Cameras (6) transmitting infra red light ”Force plate” measuring force from drumstick Markers (5) reflecting the light

14. The following equipment is used: 6 cameras (Proreflex camera system) areused to measure movements of the arm and the drumstick (kinematics). Sampling rate: 240 Hz A force plate (Kistler) is used to give accurate measurements of attack points and musical dynamics. Sampling rate: 960 Hz A minidisk is used for audio recording of the experiment

15. What do the measurements look like ? A short animation of a performance of swing:

16. A graphic representation of a performance of swing (height vs. time): Wrist Hand Drumstick

17. Analytical approach: A method of analysis which seems to give interesting information related to connections between movement patterns and rhythmic phrasing, is spectral analysis of swing performance. By this method the sinusoidal components of the movement patterns are detected. The analysis is done by using Matlab calculating FFT (Fast Fourier Transform).

18. Example:Count-in tempo = 90bpm, subdivision in triplets:

19. Speculative thoughts: The measurements illustrate different movement patterns related to differences in tempo, accentuation and rhythmic subdivision The spectral approach suggests alternative ways of constructing models of rhythm production:

20. a)Additive synthesis: Adding sinusoidal movement curves to obtain approximations to movements of rhythm performance

21. b) Applying frequency modulation: FM Wave shaping ”Metronomic” Modulated Movement movement movement curves curves, curves through approximating representing attack pointsmovements of note values approximating rhythm rhythm performance performance New model of rhythm performance?