Rhythm and timing, cont'd

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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.

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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.

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Two elements

• Grouping which is the manner in which music is
  segmented at a whole variety of levels, from
  groups of two notes up to large-scale form of the
  work
• 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)

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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

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Chopin Prelude Op. 28, No. 7
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• Model by Todd (1994)
• energy-integrating low pass filters with
  different time constraints
• rhythmogram

Chopin Prelude Op. 28, No. 7
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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)

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• 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.

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• 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 12

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• 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

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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.

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• Davis (1978) Music in the Western classical
  tradition is tonally extremely sophisticated but
  rhythmically naïve.
• Two reasons
• 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.
• Western music has confined itself largely to the
  use of meters involving units of two, three, or
  four beats.

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• 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")

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• 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.

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Cross rhythms
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• 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.

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Alternative ways of presenting two conflicting
meters
Two possible ways of hearing a two-cross-three
rhythm
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Alternating perception
Leonard Bernstein, West Side Story, "America"
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• 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.

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Cross rhythms
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• 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?

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Miles Davis, 'Seven Steps to heaven'

• Improvised drum break

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• Alternative way of perceiving snare drum solo

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(No Transcript)
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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.

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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

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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)

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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

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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

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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

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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".