Rhythm and Meter

Mike Oldﬁeld, Tubular bells, theme song for the Exorcist

Note Percepon of groupings 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 (funconal magneto resonance imaging) respond to regular beats

Grahn & Bre (2007), Journal Cognive Science 19:5, 893 Expectaons and Tapping experiments

• First listen. • Then everybody tap aer the sound ﬁle ends

• This is the ﬁrst beat paern in the next ﬁgure and based on one of Dessain’s experiments tapping experiments

Expectancy of next beat

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

Dessain 92 Time shrinking • Duraon of short me intervals is conspicuously underesmated if they are preceded by shorter neighboring me intervals.

Figure by Petra Wagner and Andreas Windmann Sound clip from hp://listverse.com/2008/02/29/top-10-incredible-sound-illusions/ Subjecve duraon

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 Figure from Psychoacouscs top would be half the interval for the percepon of by Zwicker and Fastl 1/8th note. But this is not the case. Groupings

with diﬀerent mbres

19/20

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

With diﬀerent mbre emphasis the perceived starng posion varies

Images and clips from Rhythm and Transform by W. Sethares Necklace Notaon

Images and clips from Rhythm and Transform by W. Sethares Numerical Notaons

Image and clip from Rhythm and Transform by W. Sethares MIDI event data MIDI = Musical Instrument Digital Interface) image from audacity

MIDI DATA CHANNEL TIME NOTE DURATION VELOCITY Measures beat cks beats+cks velocity/oﬀ 1 4:3:0 F2 1:100 100:64

A certain number of cks makes up each beat Tabla Talas

Image from hp:// www.chandrakantha .com/tablasite/ quick.htm Science of Tabla

Image and clip from hp:// www.chandrak antha.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, repeang Cyclic paern of rhythm if repeve • Beats: underlying pulse • Tatums or Ticks. Small unit of me. Beats and note onsets are described in units of tatums from the beginning of measure or cycle Above is an example of a hierarchy • Classiﬁcaon of a series of onsets into a type of rhythm based on minimizing the complexity of the required hierarchy or minimizing the syncopaon. Microming measurements for a Samba While we might perceive a rhythm in terms of regular intervals, however musicians may with systemac small deviaons from calculated intervals/ duraons Fabien Gouyon, SBCM 2007 proceedings Microming Variaons

systemac shis in ming of order 20ms associated with musicianship Fabien Gouyon, SBCM 2007 proceedings and musical style/genre Bar Wrapping Visualizaon of Meter

Mahew Wright et al. 08 ISMIR 2008 – Session 5c me

tempo Tempo is varying Beat idenﬁcaon done in soware Microming variaons then shown in this way Musicianship in ming

Note double hits by bass Percy Jones

Diﬀerences in ming of bass compared to drum make each instrument stand out yet rhythm is sll strong Rubato

• Harpsichord and rubato, • someday a good clip will illustrate this! 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 paerns in me that can be perceived as rhythmic (following Sethares’s statement in 4.3.8). -- Boundaries = Quick Variaons in mbre, pitch or loudness Algorithms for Finding Onsets

Can be referred to as Feature vectors • Reduce sampling rate • Paron into frequency bands • Search for variaons in total energy (volume) spectral mean or center, spectral dispersion or large variaons in energy in any parcular band • Soware developed such as beatroot outputs a MIDI event ﬁle of onsets • With beatroot you can adjust locaon of individual onsets and add or remove them Finding meter and tempo

• For tempo: – Autocorrelaon or Fourier methods (J. Brown) – Periodicity transforms (Sethares) • These fail if the tempo is varying – Adapve oscillators work if tempo varies smoothly – Percepve idea of “internal clock” • Hierarchy of levels to idenfy meter (Rosenthal) • Minimizaon of number of syncopaons (Longuet-Higgens & Lee 84) • Stascal models • If you have a score or a MIDI ﬁle then synching the sound ﬁle may be more straighorward • My impression is that this is an acve area of research Musicianship in rhythm

Not captured by simple descripons or classificaons of rhythms: - meter changes, accent changes - accelerandos and ritardos (tempo variaons) - microming variaons Delays or jumps shiing the enre beat, bending me Displacements, delays or jump in onsets that don’t change the beat - mbre variaons --- different types of sounds (like different drums) substuted - omissions, doublings of strokes - graces notes added - rhythm paern reset (shied?) 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 tracking allows interesng composion experiments (such Beat regularizaon or stretching for eﬀect can be done in the studio, but as above) soware is not necessarily -For other composional ideas standardized or cheep. see Sethare’s sound clips in his book Remake atrocious

Lao Schifrim

Adam Clayton Character of song can remain despite large mbre changes

Christopher Tyng