Transcript Biological clocks - Jacobs University Mathematics

Rhythm and timing, cont'd
 Clarke, E.F. Rhythm and timing in music. In Deutsch, D.
Chapter 13
 Krumhansl, C.L. (2000). Rhythm and pitch in music
cognition. Psychological Bulletin, 126, 1, 159 – 179
 Davies, J.B. (1978) The psychology of music. Stanford
University Press.
A.Diederich – International University Bremen – USC – MMM – Spring 2005
Implications of basic research for
rhythmic patterns in music
1. Although humans quite accurately estimate
time and detect small differences in duration,
the most impressive abilities are found in the
perception and production of rhythms. (The
patterns of duration, rather than absolute
durations, are psychological primary.)
2. Rhythm perception is strongly linked to
rhythm production.
A.Diederich – International University Bremen – USC – MMM – Spring 2005
Two elements
1. Grouping – which is the manner in which
music is segmented at a whole variety of
levels, from groups of two notes up to largescale form of the work
2. Meter – which is the regular alternation of
strong and weak elements in the music
The two domains deal respectively with time
span (grouping) and time points (meter)
A.Diederich – International University Bremen – USC – MMM – Spring 2005
Grouping
 Lerdahl & Jackendoff (1983): Grouping is essentially
a hierarchical property of music.
 Grouping Well-Formedness Rules (GPR) outline the
formal conditions for hierarchical structure.
 Three components:
 formalized Gestalt principles (principle of proximity in
time, change in pith, duration, loudness, or articulation)
 more abstract formal concerns (principles of symmetry and
the equivalent of variants of the same segment or passage)
 principles relating to pitch stability
 No empirical evidence
A.Diederich – International University Bremen – USC – MMM – Spring 2005
Chopin Prelude Op. 28, No. 7
A.Diederich – International University Bremen – USC – MMM – Spring 2005
 Model by Todd (1994)
 energy-integrating low
pass filters with
different time
constraints
 rhythmogram
Chopin Prelude Op. 28, No. 7
A.Diederich – International University Bremen – USC – MMM – Spring 2005
Meter
 Lerdahl & Jackendoff (1983): Three kinds of accent
 phenomenal accents (points of local intensification caused
by physical properties of the stimulus such as changes in
intensity, simultaneous note density, register, timbre, or
duration)
 structural accents (points of arrival or departure in the
music that are the consequences of structural properties
such as tonality)
 metrical accents (defined as time points in music that are
perceived as accented by virtue of their position within a
metrical scheme)
A.Diederich – International University Bremen – USC – MMM – Spring 2005
 Perceiving meter = process of detecting and
filtering phenomenal and structural accents so
as to discover underlying periodicities
 These constitute the rate of repetition that
define the meter and confer metrical status on
regularly recurring phenomenal (and
structural) accents.
A.Diederich – International University Bremen – USC – MMM – Spring 2005
 Povel (1981): Beat-based model – the perception of
rhythmic sequences depends on two steps
 the segmentation of the sequence into parts of equal length
(beats), based on the detection of regularly occurring
accents
 the identification of the individual events as specific
subdivisions of these beats into a small number (usually
only two or three) of equal parts or parts relating to one
another in a ratio of approximately 1:2
A.Diederich – International University Bremen – USC – MMM – Spring 2005
 Longuet-Higgins & Lee (1982): Metrical
analysis begins as soon as the sequence of
elements begins.
 The first duration (between the first and
second tones) is used to predict the time of the
third element.
 confirmed ! additional level in a binary tree
 disconfirmed ! the basic temporal interval is
stretched to the interval between the first and the
third events
A.Diederich – International University Bremen – USC – MMM – Spring 2005
Primitive music?
 Davis (1978): Rhythm is seen as an order which the
listener imposes upon sequences of events, solely on
the bases of their relative intensities, and their relative
times of onset. Duration is a characteristic of tones,
and from a psychological point of view has nothing to
do with rhythm.
 Rhythm, from the listeners' point of view, is (in part,
at least) a system of temporal anticipations.
A.Diederich – International University Bremen – USC – MMM – Spring 2005
 Davis (1978): Music in the Western classical
tradition is tonally extremely sophisticated but
rhythmically naïve.
 Two reasons:
1. The rhythm of a piece tends to be carried by the notes
themselves, whereas in rhythmically more complex
music, the rhythm is to a greater extent expressed
independently of any tune, perhaps by ways of drums,
gongs, whistles or pipes.
2. Western music has confined itself largely to the use of
meters involving units of two, three, or four beats.
A.Diederich – International University Bremen – USC – MMM – Spring 2005
 Early exception: E.g., Holst's "Mars" from the
Planet suite
 Twos and threes has also dominated jazz
 Dave Brubeck, jazz pianist, was one of the first
well-know performers to try experiments with
"new times". E.g., five-four "Take five"
 (seven-four ("Unsquared dance"), nine-four
("Blue rondo a la Turk")
A.Diederich – International University Bremen – USC – MMM – Spring 2005
 What makes the rhythmic aspect of much
"primitive" music to difficult to comprehend?
 The answer lies in the deliberate crossing of
meters to produce either ambiguity or apparent
confusion.
A.Diederich – International University Bremen – USC – MMM – Spring 2005
Cross rhythms
A.Diederich – International University Bremen – USC – MMM – Spring 2005
 The beat appears to alternate between a 'two feel'
(white pegs) and a more rapid three to the bar created
by the accents occurring on the first, fourth and
seventh beats where the pegs coincide
 The ambiguity is heightened by the perverse accents
on the black pegs
 This very simple two-cross-three rhythm is often
encountered in the music of Latin American
countires.
A.Diederich – International University Bremen – USC – MMM – Spring 2005
Alternative ways of presenting two
conflicting meters
Two possible ways of hearing a two-cross-three rhythm
A.Diederich – International University Bremen – USC – MMM – Spring 2005
Alternating perception
Leonard Bernstein, West Side Story, "America"
A.Diederich – International University Bremen – USC – MMM – Spring 2005
 The accents may be subjective rather than real.
 Depending on how we group the notes (i.e.,
the way in which we dispose our subjective
accents) we hear the rhythmic groups on one
fashion or the other.
A.Diederich – International University Bremen – USC – MMM – Spring 2005
Cross rhythms
A.Diederich – International University Bremen – USC – MMM – Spring 2005
 For example, the white pegs accentuate respectively the first
beat in the first group of three, then the gap between groups,
then the last of the third group, and the second of the last
group.
 We can just see, from the coincidence of the white pegs and
the triangular pegs, that this cycle is about to repeat itself,
thereby threatening to make the whole thing into just one bar.
 Or is it really three bars of four-four?
 Or four bars of three-four?
 And just which four and which three are we talking about?
A.Diederich – International University Bremen – USC – MMM – Spring 2005
Miles Davis, 'Seven Steps to heaven'
Improvised drum break
A.Diederich – International University Bremen – USC – MMM – Spring 2005
 Alternative way of perceiving snare drum solo
A.Diederich – International University Bremen – USC – MMM – Spring 2005
A.Diederich – International University Bremen – USC – MMM – Spring 2005
Clock theories
 Biological clocks: Our perception of time has
a biological or physiological basis.
 Cognitive clocks: Times is viewed as a purely
cognitive process that is not tied to any
objective or "clock" time but is based on how
much sensory information is processed, how
many events occur within a given trial, or how
much attention is paid to ongoing events.
A.Diederich – International University Bremen – USC – MMM – Spring 2005
Biological clocks
The flow of subjective time ( the impression
that time passes) is related to some body
mechanism that acts in a periodic manner, with
each period serving as one "tick" of the
biological timer.
 Circadian rhythms
 Short-term timers
 Biological pacemakers
A.Diederich – International University Bremen – USC – MMM – Spring 2005
Circadian rhythms
 Examples: sleep-wakefulness cycle, pulse, blood
pressure, temperature of the body
 Entrainment: the process by which the biological
clock is synchronized to physical time cycles
 Zeitgeber: the stimulus used to calibrate, or entrain,
the biological clock (e.g., light)
 Suprachiasmatic nucleus (SCN): a center in the
hypothalamus that is believed to be responsible for
circadian rhythms (affected light and a hormone,
melatonin)
A.Diederich – International University Bremen – USC – MMM – Spring 2005
Short-term timers
 Examples: Heartbeats, electrical activity in the
brain, breathing, hormonal and metabolic
activities, walking steps
 Perceptual moment: the hypothetical basic
psychological time, between 25 and 150 ms in
duration, depending on the task and how it is
measured
A.Diederich – International University Bremen – USC – MMM – Spring 2005
Biological pacemaker
 A: clock time
 B: estimated minute
when body temperature
was 39 deg C
 C: estimated minute
when body temperature
was 1 deg C lower then
usually
A.Diederich – International University Bremen – USC – MMM – Spring 2005
Other factors affecting our estimates of
time
 Fatigue: lengthening time estimates
 Anesthetics: shortening time estimates
 Drugs, e.g., amphetamines, caffeine,
marijuana, mescaline, psilocybin, LSD :
lengthening of time experience
 It has been argued that all these changes in
time perception are caused by acceleration or
deceleration of the pacemaker that serves our
internal timer
A.Diederich – International University Bremen – USC – MMM – Spring 2005
Cognitive clocks
 Perception of the passage of time is based not
on physical time but rather on the mental
processes that occur during an interval.
 Time is not directly perceived but rather
"reconstructed" or "inferred".
A.Diederich – International University Bremen – USC – MMM – Spring 2005