Rhythm and Meter

Rhythm and Meter

Note Perception of groupings

Mike Oldfield, Tubular bells, theme song for the Exorcist

Beat• Beat – underlying even pulse common in many types of music• Range typical of that given on a metronome

- frequency 30 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).

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

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

Expectancy of next beat

Peter Dessain, Music Perception: An Interdisciplinary Journal, Vol. 9, No. 4 (1992), pp. 439- 454

tapping experiments

Tapping experiments

Dessain 92

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

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

Subjective duration

Figure from Psychoacoustics by Zwicker and Fastl

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.

Groupings

Images and three sound clips from W. Sethares book on Rhythm and Transform

with different timbres

19/20

Necklace Notation

Images and clips from Rhythm and Transform by W. Sethares

With different timbre emphasis the perceived starting position varies

Necklace Notation

Images and clips from Rhythm and Transform by W. Sethares

Numerical Notations

Image and clip from Rhythm and Transform by W. Sethares

MIDI event data MIDI = Musical Instrument Digital Interface)

MIDI DATA

CHANNEL TIME NOTE DURATION VELOCITY

Measures beat ticks beats+ticks velocity/off

1 4:3:0 F2 1:100 100:64

A certain number of ticks makes up each beat

image from audacity

TablaTalas

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

Science of TablaImage and clip from http://www.chandrakantha.com/tala_taal/jhoomra/jhumra.html

Figure From Rhythm and Transforms by W. Sethares

Jhumra

Hierarchy of levels

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

Measures/Beats/Tatums

• Measures: groupings of beats, repeatingCyclic 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.

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

Microtiming Variations

Fabien Gouyon, SBCM 2007 proceedings

systematic shifts in timing of order 20ms associated with musicianship and musical style/genre

Bar Wrapping Visualization of Meter

Matthew Wright et al. 08ISMIR 2008 – Session 5c

Tempo is varyingBeat identification done in softwareMicrotiming variations then shown in this way

tempo

time

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

Rubato

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

Onsets

Opposite of synthesis Groups of overtones moving together appear as one

soundFast 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

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 beatroot outputs a MIDI event file of onsets

• With beatroot you can adjust location of individual onsets and add or remove them

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

Musicianship in rhythmNot 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

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 regularization or stretching for effect can be done in the studio, but software is not necessarily standardized or cheep.

Beat tracking allows interesting composition experiments (such as above)-For other compositional ideas see Sethare’s sound clips in his book

Remake atrocious

Lao Schifrim

Adam Clayton

Character of song can remain despite large timbre changes

Christopher Tyng