Rhythm and Meter

1. Rhythm and Meter Note Perception of groupings Mike Oldfield, Tubular bells, theme song for the Exorcist

2. Beat • Beat – underlying even pulse common in many types of music • Range typical of that given on a metronome • frequency30 to 200 beats/minute OR 0.5-4 Hz • periods between 250ms and few seconds. • For clicks closer together than 100 ms, they run together. • Separated longer than a few seconds we don’t feel that they are associated • same range as sung vibratro or tremolo, or heartbeat • beats we feel are slower than frequencies we hear • We tend to move spontaneously to the beat. • Newborn babies respond to the beat (e.g. Winkler et al. 2009 – recent press on this, as seen from electric signals picked up near the brain).

3. Areas of the brain (as seen by fMRI (functional magneto resonance imaging) respond to regular beats Grahn & Brett (2007), Journal Cognitive Science 19:5, 893

4. Expectations and Tapping experiments • First listen. • Then everybody tap after the sound file ends • This is the first beat pattern in the next figure and based on one of Dessain’s experiments

5. Expectancy of next beat tapping experiments Peter Dessain, Music Perception: An Interdisciplinary Journal, Vol. 9, No. 4 (1992), pp. 439- 454

6. Tapping experiments Dessain 92

7. Time shrinking • Duration of short time intervals is conspicuously underestimated if they are preceded by shorter neighboring time intervals. Figure by Petra Wagner and Andreas Windmann

8. Sound clip from http://listverse.com/2008/02/29/top-10-incredible-sound-illusions/

9. Subjective duration Note decaying envelopes are not heard as they are equivalent to echoes and so are suppressed. Because of this we would have expected that the flat top would be half the interval for the perception of 1/8th note. But this is not the case. Figure from Psychoacoustics by Zwicker and Fastl

10. Groupings with different timbres 19/20 Images and three sound clips from W. Sethares book on Rhythm and Transform

11. Necklace Notation With different timbre emphasis the perceived starting position varies Images and clips from Rhythm and Transform by W. Sethares

12. Necklace Notation Images and clips from Rhythm and Transform by W. Sethares

13. Numerical Notations Image and clip from Rhythm and Transform by W. Sethares

14. MIDI event data MIDI = Musical Instrument Digital Interface) image from audacity A certain number of ticks makes up each beat

15. TablaTalas Image from http://www.chandrakantha.com/tablasite/quick.htm

16. Science of Tabla Image and clip from http://www.chandrakantha.com/tala_taal/jhoomra/jhumra.html Figure From Rhythm and Transforms by W. Sethares Jhumra

17. Hierarchy of levels David Rosenthal, Computer Music Journal, Vol. 16, No. 1 (1992), pp. 64-76

18. Measures/Beats/Tatums • Measures: groupings of beats, repeating Cyclic pattern of rhythm if repetitive • Beats: underlying pulse • Tatums or Ticks. Small unit of time. Beats and note onsets are described in units of tatums from the beginning of measure or cycle Above is an example of a hierarchy • Classification of a series of onsets into a type of rhythm based on minimizing the complexity of the required hierarchy or minimizing the syncopation.

19. Microtiming measurements for a Samba While we might perceive a rhythm in terms of regular intervals, however musicians may with systematic small deviations from calculated intervals/durations Fabien Gouyon, SBCM 2007 proceedings

20. Microtiming Variations systematic shifts in timing of order 20ms associated with musicianship and musical style/genre Fabien Gouyon, SBCM 2007 proceedings

21. Bar Wrapping Visualization of Meter Matthew Wright et al. 08 ISMIR 2008 – Session 5c time tempo Tempo is varying Beat identification done in software Microtiming variations then shown in this way

22. Musicianship in timing Note double hits by bass Percy Jones Differences in timing of bass compared to drum make each instrument stand out yet rhythm is still strong

23. Rubato • Harpsichord and rubato, • someday a good clip will illustrate this!

24. Onsets Opposite of synthesis Groups of overtones moving together appear as one sound Fast clicks appear as one element Any factors that can create auditory boundaries can create patterns in time that can be perceived as rhythmic (following Sethares’s statement in 4.3.8). -- Boundaries = Quick Variations in timbre, pitch or loudness

25. Algorithms for Finding Onsets Can be referred to as Feature vectors • Reduce sampling rate • Partition into frequency bands • Search for variations in total energy (volume) spectral mean or center, spectral dispersion or large variations in energy in any particular band • Software developed such as beatrootoutputs a MIDI event file of onsets • With beatroot you can adjust location of individual onsets and add or remove them

26. Finding meter and tempo • For tempo: • Autocorrelation or Fourier methods (J. Brown) • Periodicity transforms (Sethares) • These fail if the tempo is varying • Adaptive oscillators work if tempo varies smoothly • Perceptive idea of “internal clock” • Hierarchy of levels to identify meter (Rosenthal) • Minimization of number of syncopations (Longuet-Higgens & Lee 84) • Statistical models • If you have a score or a MIDI file then synching the sound file may be more straightforward • My impression is that this is an active area of research

27. Musicianship in rhythm Not captured by simple descriptions or classifications of rhythms: • meter changes, accent changes • accelerandos and ritardos (tempo variations) • microtiming variations Delays or jumps shifting the entire beat, bending time Displacements, delays or jump in onsets that don’t change the beat • timbre variations --- different types of sounds (like different drums) substituted • omissions, doublings of strokes • graces notes added • rhythm pattern reset (shifted?) or varied

28. Hacking a recording to change meter • James Bond Theme Song by Monty Norman- arranged by John Barry and from the movie Dr. No • Bond Waltz - W. Sethares Beat tracking allows interesting composition experiments (such as above) -For other compositional ideas see Sethare’s sound clips in his book Beat regularization or stretching for effect can be done in the studio, but software is not necessarily standardized or cheep.

29. Remake atrocious Lao Schifrim Adam Clayton

30. Character of song can remain despite large timbre changes Christopher Tyng