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       M U S I C          T H E O R Y         O N L I N E
                     A Publication of the
                   Society for Music Theory
          Copyright (c) 1993 Society for Music Theory
| Volume 0, Number 3      June, 1993      ISSN:  1067-3040    |
  All queries to: mto-editor@husc.harvard.edu
AUTHOR: Parncutt, Richard
TITLE: Commentary on Justin London's MTO 0.3 article
REFERENCE: mto.93.0.2.london.art
File: mto.93.0.3.parncutt.tlk
I'd like to return to the recent analyses of Justin London's rhythm  
example by Robert Judd and myself. JL's example 3 began with the 6  
notes c d e f g a, where all notes had the same duration except the  
last (a) which was longer.
The story so far: I looked at the phenomenal accent of each note and  
concluded that c had a "primacy" accent, a had a durational accent,  
and d, f, and a were candidates for harmonic accents. RJ concluded  
that the sequence could be parsed in either of two ways -- either  
duple note groups with (metric) accents on d, f, and a, or triple  
note-groups with accents on e and a.
The main difference between these two interpretations is the role of  
the primacy accent on the first note, c. My perceptual analysis  
referred to surface features heard on a first listening, while RJ  
performed a retrospective analysis of possible meters, arrived at  
after many listenings. In Judd's analysis, the primacy accent on c  
seemed relatively unimportant "in retrospect" -- at least by  
comparison to the durational accent on a.
The difference between these two analyses points to a fundamental  
difference between music theory and psychology, of the kind alluded  
to by Greg Sandell in his recent letter to the list. Music-theoretic  
analyses generally assume previous familiarity with and understanding  
of the music, and are often based on "isolating ... passages of music  
and playing them several times" (a quote from Greg Sandell, somewhat  
out of context -- the point I want to make is that the theorist hears  
or imagines the music many more times than does the average  
listener). Psychological or perceptual approaches often go to the  
other extreme, exploring spontaneous responses to unfamiliar music or  
sound sequences presented in the "constrained conditions of an  
experiment run in a lab." I believe that a balanced combination of  
these two approaches could lead to significant progress in music  
The difference between the approaches of Robert Judd and myself also  
involved levels of analysis. My analysis was focussed on a relatively  
low or "primitive" level -- phenomenal accent. Judd's concentrated on  
the next level up, the level of rhythmic strata (Yeston) or pulse  
sensations (my preferred term). In a systematic approach to rhythm,  
it may be useful to regard phenomenal accent and pulse sensations as  
independent and distinct, by first analysing phenomenal accents, and  
only then considering the resultant pulse sensations.
Which of RJ's two solutions (duple, triple) is more likely? The  
relative importance of the two parsings may depend simply on the  
number of phenomenal accents that coincide with pulse events. This  
idea favors the duple grouping, as it involves more matching events  
than the triple grouping. Another effect is that of tempo. Research  
in rhythm perception (summarised by Fraisse, 1982) has suggested that  
pulse sensations are confined to a restricted range of tempi centered  
on about 100 beats per second ("moderate tempo"), and that most  
perceived pulses lie between a half and twice that value, that is,  
between about 50 and 200 beats per minute. According to this theory,  
at slow tempi, the RJ's duple note groups will be closer to moderate  
tempo, and will probably be preferred for that reason. At fast tempi,  
the triple note groups are more likely.
The long-term aim of my research in rhythm is to develop an algorithm  
that predicts perceptual properties of simple rhythms in notated or  
performed music by the systematic application of a minimum number of  
specific rules or principles. Principles may be either perceptually  
"primitive" or specific to western music. The validity of the rules  
or principles may be checked by comparing predictions of the model  
with corresponding experimental results. This approach differs from  
most other music theory, in which the validity of analytic rules or  
principles is primarily determined by the perception and intuition of  
theorists. Traditional music theory nevertheless remains the primary  
foundation of, and motivation for, the model -- as well as most other  
research in music perception.  
Fraisse, P. (1982). Rhythm and tempo. In Deutsch, D. (Ed.), The  
psychology of Music (pp. 149-180). New York: Academic.
Richard Parncutt
McGill University
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