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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 2      April, 1993      ISSN:  1067-3040   |
  General Editor                          Lee Rothfarb
  Co-Editors                              David Butler
                                          Justin London
                                          Elizabeth West Marvin
                                          David Neumeyer
                                          Gregory Proctor
  Reviews Editor                          Claire Boge
  Consulting Editors
	Bo Alphonce		Thomas Mathiesen
	Jonathan Bernard	Benito Rivera
	John Clough		John Rothgeb
	Nicholas Cook		Arvid Vollsnes
	Allen Forte		Robert Wason
	Stephen Hinton		Gary Wittlich
  Editorial Assistants                    Natalie Boisvert
                                          Cynthia Gonzales
  All queries to: mto-editor@husc.harvard.edu
AUTHOR: London, Justin M.
TITLE: Loud Rests and Other Strange Metric Phenomena (or, Meter as Heard) 
KEYWORDS: meter, rhythm, accent, parameter, perception, cognition, entrainment, ontology, dynamic model of meter
Justin M. London
Carleton College
Department of Music
Northfield, MN 55057
ABSTRACT:  This is an excerpt from a work-in-progress, portions of 
which will be read at the 1993 meeting of the Society for Music 
Perception and Cognition.  In order to give an adequate account of 
"loud" rests, metric articulations, and meter's propulsive character 
(as noted by theorists such as Berry and Zuckerkandl), a dynamic model 
of meter is proposed.  In framing this model a brief overview of 
theoretical strategies for metric models is given.  The dynamic model 
regards meter as a listener-generated framework for the understanding 
musical time.  The theoretical implications of the dynamic model are 
discussed, as it challenges traditional notions of meter as "part of 
the music," that is, as musical parameter with the same ontological 
status as pitch, loudness, timbre, texture, and rhythm.
ACCOMPANYING FILES: mto.93.0.2.london.gif
[0] NOTE: The three musical examples in the .gif file, while helpful, 
are not absolutely necessary for comprehension of this article; verbal 
descriptions of the salient features of each example are given in the 
text.  Also, there are several citations to the author's dissertation 
in the following article which are the natural outcome of the close 
relationship between the essay below and the dissertation, the former 
being an extension of some ideas already explored in the latter.
[1] Cooper and Meyer have noted that the downbeat of measure 280 in 
the first movement of Beethoven's "Eroica" symphony "must be the 
loudest silence in musical literature."(1)  This moment, where triple 
meter has at last been re-established following an extended 
duple-vs.-triple conflict (in mm. 250-75) is unequivocally striking, 
a moment whose poignancy and power is immediately felt.(2)  But what 
exactly happens on the downbeat of measure 280?  First and foremost, 
does something happen, or is it the absence of something which strikes 
us so profoundly?  But if something does happen, what kind of thing is 
1. Cooper, Grosvenor, and Meyer, Leonard. *The Rhythmic Structure of 
Music*, Chicago: Phoenix Press (1960): 139.
2. Cooper and Meyer (op. cit.) view this moment as the culmination of 
an extended anacrusis, the moment of thesis following an 8 mm. arsis.  
While I would not describe mm. 272-79 as an extended anacrusis, as I 
feel it is an inappropriate application of a phrase-level phenomenon 
to higher structural levels, nonetheless I agree with Cooper and 
Meyer's characterization of the essential rhythmic feel of the passage. 
[2] The downbeat of measure 280 in Beethoven occurs in an incredibly 
rich musical context--as there are not only metric intrigues here, 
but also a nexus of motivic, phrasing, tonal, and formal events--and 
thus it may be helpful to consider the metric issues in a simpler 
context, and so I have composed the following two (and admittedly banal) 
examples.  [EX. 1 and EX. 2].  In example 1 we have another "loud" 
downbeat, though one not as markedly loud as m. 280 in the Beethoven 
example.  Following a clear antecedent phrase in 3/8 time which ends 
with a melodic half-cadence, the consequent phrase leads us to expect a 
tonic arrival on the downbeat of the eighth measure.  But in example 1, 
nothing happens.  Instead, we have an 8th rest and then a shift in 
motivic pattern, with the melody coming in on the mediant (i.e. on the 
third of the tonic chord rather than the expected root/do which would 
complete the "sol-la-ti" melodic line).  While nothing happens on the 
downbeat of measure 8 in the music, what happens at that moment in 
the listener's mind?  Similarly, in example 2, a dactylic pattern 
(strong-weak-weak) of rhythmic grouping is established in the first 
two measures, a pattern than is congruent with the 3/4 metric context.  
In the third measure, however, instead of three quarter notes we have 
a half note and a quarter.  Yet is there not some sense in which the 
dactylic pattern persists in this measure?  And if so, why?
[3] The quick answer to such questions is, of course, "because one 
hears a beat or a downbeat in these cases."  But what exactly is meant
 by "hearing a beat?"  I am quick to add that to come up with adequate 
definitions for "beat" and "downbeat" is no easy task, as the work of 
theorists past and present will attest.  Since beats and downbeats are
"primitives" in most metric theories, these questions ultimately drive
us down the slippery slope to ask "what is meter?"
[4] Meter is often regarded as one of the parameters of music, an 
aspect of musical structure (or to put it another way, a dimension 
of musical description) that taken together with pitch, duration, 
timbre, articulation, dynamics, and texture allows for a thorough 
account of a musical event.  Kramer puts it most boldly: "Meter is 
not separate from music, since music itself determines the pattern 
of accents we interpret as meter. . . .Music not only establishes, 
but also reinforces and sometimes redefines meter."(3)  But meter is 
not cut of the same cloth as the other parameters.  Let us consider 
how a musician and a physicist would describe these different aspects 
of musical sound:
The MUSICIAN                    The PHYSICIST
Pitch                           Frequency of waveform
Rhythm                          Duration in microseconds of event 
Timbre                          Shape of waveform
Articulation                    Envelope of waveform 
Loudness                        Amplitude of waveform
Meter                           (????)
While these pairs of terms are not merely synonymous, they do show to 
serve how the physical attributes of sound inhere in the various 
musical parameters (for example, the physicist's understanding of 
frequency is stated in terms of cycles per second of periodic 
vibration, and even if she takes octaves into account by mapping the 
frequencies onto a logarithmic scale, this is still quite different 
from the notion of "pitch" which defines tones relative to some scale 
or tuning context).  And I hasten to add that these features are 
interdependent, especially those of timbre, articulation, and loudness. 
But where is meter for the physicist?
(3) Jonathan Kramer, *The Time of Music,* New York: Schirmer Books, 
(1988): 82.
[5] Well, meter has something to do with musical time, so one might 
place meter under rhythm, as the term "rhythm" is admittedly vague. 
For clearly "rhythm" is more than just the duration of single 
notes/events; it also involves patterns of durations (i.e rhythmic 
groups), and patterns of patterns, and so forth.  Perhaps meter can 
be subsumed under rhythmic grouping, that is, a special kind of 
temporal patterning.(4)  We will allow our physicist, with help from 
a friendly, nearby music theorist, to consider meter to be a special 
kind of periodicity present in the music, one which is based on 
hierarchically regular isochronous durations.
4. The author is well aware of the fact that rhythmic groups consist of 
patterns of duration, that is, of time spans, versus metric patterns 
which may be viewed as an ordering of time-points.  I do not wish to 
imply here that I regard meter as a time-span phenomenon (as will be 
made clear below).  It has also been posited that metric patterns need 
not be isochronous, especially on higher metric levels (see Kramer, op. 
cit., Ch. 4).  For the moment, let us allow our physicist to struggle 
toward meter as best she can, with an admittedly over-simplified metric 
[6] We give our physicist the following example [example 3], where the 
duration of each pitch is an 8th note, and each rest two eighth notes 
(rests are indicated by (r)), at a tempo of a quarter-note = 100:
	c-d-e-f-g-a (r) d-e-f-g-a-bb (r) b-c-b-c-b-c (r) d-c-bb-a-g-f
(N.B. "b"= b-natural and "bb"= b-flat)The physicist notes that there 
are clear periodicities for every 8th-note duration as well as every 
8 eighth-notes, the latter marked by the rests.  Furthermore, with a 
nudge from her theorist companion, the physicist is able to interpolate 
two intervening levels of duple organization.  But of course, she has 
not yet found the meter--for where is the downbeat (that is, where 
does the metric pattern properly begin)?  Well, with another nudge 
from the theorist, the physicist learns that there are two possibilities 
in this passage, either (a) the downbeat occurs on the very first 
note/musical event, or (b) it doesn't.  In the latter case, one must 
then look for other information (tonal cues, dynamic stress, textural 
changes, etc.) which would mark another note/event as the downbeat.  
Luckily, our nearby theorist tells the physicist that if the downbeat 
is not on the first note, one then usually has a conventionalized 
anacrustic pattern, the most common of which goes "sol-la-ti-DO" (with 
the tonic pitch on the downbeat).  And of course that is what we have 
here.  So our physicist, with a little help, has found periodic 
patterns of duration within the musical signal.  She can then assign 
the following index to these spans:
  c-d-e-f-g-a (r) d-e-f-g-a-bb (r) b-c-b-c-b-c (r) d-c-bb-a-g-f
[7] So, the physicist can assign a unique label each note/event based 
on its position within the hierarchy of periodicities (for example, 
the "a" which starts the second rhythmic/motivic group can be labelled 
as occurring at "," that is, Measure #1, 2nd half-note span of 
Measure #1, first quarter-note span of 2nd half note, 2nd 
eighth-note-span of first quarter-note).  But (again, leaving the 
time-span versus time-point question aside for the moment) what does 
the physicist have?  Is it meter?  More to the point, what can the 
physicist *do* with her periodic recognition?  Well, along with a 
particular pitch, duration, waveform, articulation, and dynamic, she 
can now give each musical event a location (e.g. relative 
to the other events in this passage.(5)  Our physicist now has an 
acoustical correlate for meter (though we admittedly have fudged 
quite a bit on the problem of finding the downbeat).  While our 
physicist is now happy, our theorist is not.  Clearly something is 
lacking in this meter-as-periodicity account, and that something is 
the listener, or rather, the listener who can use meter as something 
more than a temporal yardstick.
5. The physicist's metric labels function as a temporal index for each 
event--but one could also give an equally-useful index (at least for a 
physicist) by simply labelling each event at the 8th-note level as 
1,2,3,4,5,6,7  . .  etc.  What we have here is an index that at least 
appears to be hierarchically organized--but is it?  The physicist is 
counting in modulo 2 up to the level of the downbeat--but does this 
counting method create a true set of subordinate and super-ordinate 
relationships?  The answer to this question depends, I think, on how 
the counting system is applied *to* the events, which is rather 
different than reading the counting system *off of* the events.  So 
for the moment, all we can say is that we have a method of locating 
musical events relative to others--a sophisticated measurement of a 
note/event's being "before X and yet after Y."  I would also add that 
we should not be troubled by the fact that this system is relativistic 
(i.e. dependent on the knowledge of surrounding events)--for after all, 
the assignation of scale degree and harmonic function in the pitch 
domain is similarly relativistic, as they are not context-free 
attributes of a musical sound the way that frequency measurements are 
context-free descriptions of sonic events.
[8] Our unhappy theorist has read a bit of psychology; he knows that 
when we listen to a periodically regular stimulus (to speak in  
psychological terms for a moment), psychological experiment has shown 
that we tend to respond by "entraining" our perceptions; that is, we 
tune our rates of attending to the rhythms present in our environment.  
As a result of this entrainment, we anticipate the occurrence of future 
events.  We also seem to have particular range of sensitivity (whether 
learned or innate is another question) for attending to periodicities, 
what psychologists have termed "natural pace" or "preferred tempo"
 which falls in the range of 60-120 beats/minute.(6)  Given these 
cognitive proclivities, we would expect that not only is meter used to 
give a location to previous events, but also to anticipate the location 
of future musical events.  Furthermore, the presence of this 
projected/anticipatory framework can and at times does affect our 
interpretation of the ensuing musical events.  Thus, to assuage his 
displeasure, our unhappy theorist turns to the current literature to 
see if his colleagues have provided an account of meter which can 
accommodate both the physicist's periodicity and the psychologists 
6. For a detailed overview of psychological research in these areas 
see Justin London, "The Interaction Between Meter and Phrase Beginnings 
and Endings in the Mature Instrumental Music of Haydn and Mozart," Ph.D. 
Diss., U. of Pennsylvania (1990), Ch. 1, and David Butler, *The 
Musician's Guide to Perception and Cognition* New York: Schirmer (1992).
[9] There are three broad strategies for defining meter and metric 
accent: (a) one may divide time spans into smaller chunks, and then 
sub-divide the chunks, and so forth, with meter as the fallout of this 
segmentation process; (b) one may have an emergent hierarchy of time 
points independent of (though still interdependent with) concomitant 
durations; or (c) one may have an ordered series of time points (that 
is, counting patterns) whose accent is not hierarchically determined by 
"external" factors, but rather whose generative process itself gives 
rise to a modest time-point hierarchy.(7)  In the previous paragraphs 
our physicist used the first strategy to determine the meter in example 
3.  The end product of all three strategies is a set of temporal 
locations for musical events--either the "edges" of real durations, 
or time-points apart from durational phenomena.  But if we assume 
that meter is crucially linked to our cognitive process, then we must 
ask which of these three strategies is best suited to the way(s) we 
actually deal with musical structures in our real-time listening 
experience--in other words, meter-as-heard.
7. Given the scope of this essay I wish to avoid specific critiques 
of other recent work in metric theory.  Also, several fine overviews 
of current work in metric theory are available elsewhere; see Fred 
Lerdahl and Ray Jackendoff, *A Generative Theory of Tonal Music,* 
Cambridge, MA: MIT Press (1983), esp. Chs. 2 and 4; Jonathan Kramer, 
op. cit., Ch 4; and Justin London, op. cit., Chs 1 and 5.
[10] The first observation one might make regarding meter-as-heard is 
that we can differentiate two distinct phases of metric cognition.  
The first phase involves the initial recognition/discovery of the 
metric context, as happens either (a) at the very beginning of the 
piece, or (b) when we find ourselves thrown into a piece *in medias 
res* (as when we turn on the radio to the middle of a symphony or 
blues song).  The second phase involves the continuation of an 
established context.  The cognitive tasks are very different in these 
two phases.  The first involves a rather high processing load, as 
every event an equal amount of metric significance (or potential 
significance).  At the same time the listener is searching to find 
the most salient parameter(s) for metric information.  Fortunately, 
in this first phase normally we are not trying to re-invent the metric 
wheel, as it were, but rather simply trying to match the initial 
series of musical events to a small number of metric archetypes.(8)  
Once the meter has been recognized the cognitive load drops considerably.  
Now the listener is entrained and needs relatively little information 
to maintain the metric pattern.  Indeed, as is well known, we will 
continue to maintain the chosen pattern even when confronted with a 
fair amount of contradictory information (e.g. an extended passage of 
syncopation, or a series of stressed weak beats, etc.).  In order to 
break or shift an established metric pattern we must be presented with 
a strong and continuing series of cues in order to achieve a metric 
8. The number of metric archetypes is quite small: binary or ternary 
patterns of beats, and simple versus compound subdivisions of those 
beats.  Moreover, I would posit that listeners have a store of 
durational and pitch/durational templates which fit into the metric 
archetypes.  And so, for example, our anacrustic figure in example 3
involves the matching of a pitch-durational sequence (sol-la-ti-do 
in even durations) into a limited number of metric possibilities.  If 
the notes are assumed to be subdivisions of the beat (a reasonable 
assumption given the notion of natural pace) then the metric 
recognition task boils down to simple versus compound subdivision--that
is, if do is the downbeat, then are the beats quarters or dotted 
quarters?  Furthermore, in actual performance (that is, by a human 
player as opposed to a "deadpan" realization on a synthesizer) it is 
likely that timing and dynamic cues within the sol-la-ti anacrusis 
would indicate simple or compound time; see, for example,  Eric F. 
Clarke, "Categorical Rhythmic Perception: An Ecological Perspective" 
in *Action and Perception in Rhythm and Music,* ed. Alf Gabrielsson, 
Stockholm: Royal Swedish Academy of Music (1987): 19-33. 
[11] While all three metric strategies listed above may be used as means 
for metric recognition/ discovery--that is, during the first phase of 
metric cognition--one realizes that the first two strategies create 
problems in the second phase of metric cognition in that they allow 
only for the retrospective hearing of metric patterns.  In the case of 
time-span segmentation this limitation is readily apparent, for one 
cannot begin sub-dividing a time span until its duration is complete.  
For the hierarchically-minded time-span segmenter this becomes an 
especially acute problem, for if the determination of the beat is 
determined by the partitioning of the measure, one must first have the 
location of the downbeats.  But if the downbeats are determined by the 
partitioning of the next-larger span, then one must wait--and so on, 
and so on--and thus one does not know the location of the first beat 
(if a top-down partitioning plan is rigorously followed) until the 
piece is over (!).  The problem is alleviated somewhat if we employ 
the second strategy and consider meter to be a hierarchy of time 
points built from the bottom up.  Here we can (usually) read the 
lowest level of subdivision "right off the surface," as it were.  
As soon as periodicities emerge we can retrospectively (but relatively 
quickly) tag particular moments at higher levels, such as the beat.  
Downbeats remain a potential problem, however, in that one is always 
looking backward for cues which mark a higher-level metric 
9. Downbeats are, by definition, metrically-accented beats.  Yet there 
are a considerable number of problems with the notion of an accented 
beat, for how do phenomenal properties, such as length, loudness, 
contour salience, tonal emphasis, etc. inhere in a time-point?  While 
it is clear that these parametric differences can and do give rise to 
rhythmic accent, how can one connect these to a nearly durationless 
instant?  Well aware of these problems Wallace Berry has spoken of 
downbeats as "iterative impulses" (*Structural Functions in Music*, 
2nd ed., Mineola: Dover Publications (1987): 327) and Kramer has 
approached metric accent as an "accent of initiation" (op. cit., 
p.86).  The problem here is that in order to recognize that something 
has been initiated, it must endure for a while (and the higher the 
structural level, the longer one must wait), and thus metric 
accents--if they are accents of initiation--can only be tagged 
[12]. Fortunately, there is a fairly simply solution to the problem of 
retrospective metric hearing, and that is to combine a model of meter as 
hierarchic patterning of time-points with a knowledge of metric 
templates and our proclivities for entrainment--in other words, let's 
tap our feet and count along.  In counting along, we not only mark 
locations for events as they occur--we also anticipate the locations 
(and musical salience) of future events.  This is a *dynamic* model of 
meter which assumes that meter is an active part of the listening 
process.  It is the listener who, once the meter has been recognized, 
creates the "generative process that gives rise to a modest 
time-point hierarchy."  This assumption is admittedly restrictive, in 
that meter, for the most part, requires known archetypes.  Similarly, 
since metric hearing is assumed to be a form of temporal entrainment, 
it demands that metric patterns be largely isochronous.(10)  However, 
the dynamic model accords nicely with the simulations of metric 
attention proposed by Gjerdingen, where events at metrically important 
locations are assumed to be of greater structural importance, as well 
as Clarke's experimental studies of metric perception, which use known 
metric patterns along with two basic durational categories (long vs. 
short) to account for a wide variety of rhythmic phenomena.(11)
10. Two comments regarding these restrictions: first, I stress/repeat 
that the known archetypes are not "2/4," "3/4," "6/8," "12/8" but rather 
a matrix of "duple or triple" orderings for three to four layers of 
time points.  Thus one could "build" a template for a new or unusual 
metric pattern even if one had not experienced it before.  Second, 
and following from the first, by "largely isochronous" I mean that
most (but not necessarily *all*) layers of the metric pattern be 
isochronous.  One can entrain to a pattern which encompasses some 
irregularity.  For example, Dave Brubeck's jazz standard "Blue Rondo 
al a Turk" is based on a complex meter of 2+2+2+3/8, where the 
8th-note level is isochronous, the downbeat level is also isochronous, 
but the intermediate "beat" level is not.  Nonetheless, once the 
pattern is recognized, one can tap along to the "limping" meter quite 
11. Robert O. Gjerdingen, "Meter as a Mode of Attending: A Network 
Simulation of Attentional Rhythmicity in Music," *Integral* 3 (1989): 
67-91;  Eric F. Clarke, op. cit.
[13] If we adopt the meter-as-counting-time-point-patterns model, we 
have made some rather far-reaching commitments regarding meter's 
ontological status.  Under this framework meter is a listener-generated 
construct that is intertwined with the musical surface.  Meter is not 
"part of the music" in the same way that pitch, timbre, and duration 
*are*.  This commitment may be more troubling for some theorists than 
others, and to explain (at least in part) this uneasiness I will 
arbitrarily divide my colleagues into two groups, the "structuralists" 
and the "phenomenologists."
[14] The structuralist regards music as existing "out there," apart 
from the listener, and thus treats our listening and cognition 
experiences as our efforts to understand these external sound 
objects.  Given this assumption, meter as I have defined it is a 
particular kind of response to a particular kind of sound stimulus.  
As such, meter would then seem to be in the same basket as our other 
responses to sonic stimuli, such as feelings of sadness, surprise, or
pain (if the music is unbearably loud), evoked remembrances, and so 
forth.  This stimulus-response approach to meter, with its behaviorist 
overtones, is justifiably suspect.  By contrast, the phenomenologist 
regards musical structure(s) as the product of the interaction between 
a sound object and our cognitive faculties; she disdains the notion 
that music qua *music* is only an external sound object, separate from 
the listener.  For her the meter-as-counting model is more plausible.  
While meter is *not* part of the sound object, it nonetheless may still 
be regarded as "part of the music."(12)  Meter is neither a parameter 
like pitch or timbre, nor is it part of a nested measuring of 
durational patterns and/or periodicities.  It is something that is 
heard and felt.  And this is of course why the physicist has so much 
trouble with meter, for physics is not phenomenology.  The physicist's 
job is to describe the structure of physical objects in the world.  
Understanding our interaction with those objects is beyond the scope 
of the physicist's mission--at least if we stay above the quantum level.
12. Of course, she now has another problem, and that is to confront 
the different kinds of "phenomenological fallout" that the interaction 
between the sound object and the listener may generate.  For clearly 
one would not want to put meter and remembrances of things past (as 
triggered by hearing "our song") in the same cognitive/phenomenological 
[15] The dynamism of the meter-as-actively-counting-time-point-patterns 
explains how and why we hear loud rests and metric articulations, as 
well as meter's propulsive character.  In most cases our self-supplied 
metric articulations go unnoticed because most of the time they are 
redundant: metric articulations at the levels of the downbeat, beat, 
and beat-subdivision(s) tend to be phenomenally present somewhere in 
the musical texture.  What makes the *Eroica* example so striking is 
the absence of that redundancy just where we expect it the most.  For 
at the very moment where we expect the culmination of a tissue of 
musical processes, all we get is the "default" articulation of the 
downbeat as we count along.  With so much riding on that moment, the 
little metric "click" we hear/create in our heads is deafeningly loud 
indeed.  In other cases, such as example 2, the metric clicks are not 
so loud, but they nonetheless may be heard.  A few theorists, most 
notably Berry and Zuckerkandl, have at length described meter's 
propulsive character.(13)  Here is Zuckerkandl's aptly-worded account:
   A measure, then, is a whole made up, not of equal fractions of time,
   but of differently directed and mutually complementary cyclical 
   phases.. . . With every measure we got through the succession of
   phases characteristic of wave motion: subsidence from the wave 
   crest, reversal of motion in the wave trough, ascent toward a new 
   crest, attainment ofthe summit, which immediately turns into a new 
   subsidence--a new wave has begun. (168)
He goes on to comment that:
   Now we see the wrong-headedness of the doctrine that musical time, 
   that is, the grouping of beats into measures, springs from 
   differentiation of accents.  There is no need for externally derived 
   accents in order to distinguish weak and strong beats from one 
   another and thus establish the metrical pattern.  It is the wave 
   released by the regular succession of marks in the time flux that 
   in each case emphasizes the beat which falls on "one"; brings all 
   the beats between "one" and "one" into a group.  The theory that 
   the metrical pattern depends upon accentual differences confuses 
   cause and effect.  It is not a differentiation of accents which 
   produces meter, it is meter which produces a differentiation of 
   accents. (168-69)
If meter were a partitioning of time-spans or a hierarchy of time points 
it would be difficult to see why meter should have such propulsive 
properties, but these properties are the natural fallout of a dynamic 
model.  Indeed, under such a model it seems difficult to avoid such 
13. Wallace Berry, op. cit., and Victor Zuckerkandl, *Sound and 
Symbol,* translated by Willard R. Trask, New York: Pantheon Books, 
[16] Embracing a dynamic model of meter is not without theoretical cost.  
First and foremost, one must confront the ontological considerations of 
meter noted above.  If meter is still "part of the music," it is no 
longer phenomenally part of musical sounds and structures in the same 
way as pitch, timbre, dynamics, articulation, and duration.  Since 
meter is based upon known archetypes, it is a facet of musical 
listening that is acquired, rather than innate (though metric hearing 
probably does not depend on formal training)--and so the theorist 
becomes interested in how we acquire such skills.  As part of our 
cognitive matrix for musical experience, our metric sensibilities 
would also appear to be bound up with our other kinesthetic activities, 
and thus that too becomes an area of interest.  One is also perhaps 
ruling out a number of structures that are often listed under the 
rubric of meter as non-metric phenomena, i.e."mixed meters" (where 
there is no substantially continuing metric pattern, but only a 
succession of ever-changing metric notations) and thoroughly irregular 
meters (as contrasted from the modestly irregular meter noted above).  
And of course, the dynamic approach to meter creates large (and perhaps 
insoluble) problems for hypermeter--but that is another paper.

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requirements must be approved in writing by the editors of MTO, 
who will act in accordance with the decisions of the Society for 
Music Theory.