A.Diederich – International University Bremen – USC – MMM – Spring 2005 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 large- scale 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

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".