INTRODUCTION
MARTIN’S (2025) article is a significant contribution to the fields of empirical musicology and country music research, which have often ignored each other. [1] It is also a significant contribution to research on swing music, which has focused exclusively on jazz. Drawing on findings from prior research which suggest a decline in tempo in popular music (Schellenberg & von Scheve, 2012) and research on swing usage in jazz music which suggests tempo constraints (Friberg & Sundström, 1997), Martin extracts data related to simple and compound backbeats, backbeat tempo, and whether swing rhythms occur at first and second levels of the backbeat’s subdivision. Martin’s findings, drawn from a corpus of 750 songs sampled from the Billboard charts, are consistent with an average tempo decrease, but suggest a more complicated story around tempo thresholds. Martin’s work is substantial in its scope and the volume of data collected and analyzed. Within the framing Martin establishes in the introduction, literature review, and general discussion, I have little problem with the data or analysis as presented. [2]
Rather, I focus on the broader conception of meter employed in Martin’s study. This conception, often called the metrical hierarchy after Lerdahl and Jackendoff (1983), is the prevailing model of meter in contemporary music research and pedagogy. My primary contention is that, while the metrical hierarchy provides a concise and clear conception of meter that affords practical implementation and interpretation, it also misses out on several features of temporality listeners are faced with during real-time listening experiences. In Martin’s study, this limitation of the metrical hierarchy is exposed by the operational definitions of swing, meter, and rhythm. I argue three specific points: (1) it is necessary to clarify the definition of swing as it relates to rhythm and meter; (2) it is necessary to distinguish a straight compound meter from an uneven swing rhythm; and (3) future research on meter should consider continuous measurement of factors such as duration and tempo, and how temporal variability influences meter perception.
First, I provide an overview of the metrical hierarchy as formulated by Lerdahl and Jackendoff (1983). Second, I summarize Martin’s operational definitions, and then I examine some of the limitations and ambiguities of these definitions that are reflective of the underlying metrical hierarchy model. Third, I briefly review findings in a closely related field of research—the swing ratio in jazz music—to give an example of how real-time temporal variability in musical performances may impact perceived rhythm and meter. Lastly, by way of conclusion, I point to a few avenues for future research.
THE METRICAL HIERARCHY MODEL
Martin’s methodology of assigning each song to a duple or triple category of metric organization and first and second levels of subdivision is reflective of an underlying conception of meter as a metrical hierarchy, though Martin does not use this term.
The metrical hierarchy model of meter was popularized by Lerdahl and Jackendoff (1983, pp. 18–21). [3] Under the metrical hierarchy model, a listener generates multiple levels of periodic pulses in response to a musical surface. These levels are related to each other by grouping; faster pulses are grouped by slower pulses, usually in periods of two or three. The levels of the hierarchy correspond to levels of subdivision, beat, and measure. This model affords a concise conception of meter as a set of either duple or triple periods. In empirical studies, this conception allows for categorical operational definitions of metrical terms (meter, beat, subdivision, etc.) that are relatively simple to implement and interpret.
In Martin’s (2025) study, the assumption of a metrical hierarchy model is reflected in three variables: metric organization, first level of subdivision, and second level of subdivision (See Martin's Table 1, p. 4). That is, a song’s meter is defined as a hierarchy of three pulse levels, namely a tactus level (See next section) and two subdivision levels. These pulse levels can be sorted into one of two categories, duple or triple, by how pulses are perceived to be grouped.
MARTIN’S DEFINITIONS
Martin (2025) defines the meter of a song as being “organized in groups of two or three (i.e., evenly or unevenly spaced)” (p. 3). To assign a song to one of these two categories, Martin relies on the arrangement of popular music around a percussive rhythm section, using kick and snare drum hits and percussive strumming and bowing on guitar and violin to articulate the beat. Note that Martin’s categorization at the beat level is not based on how beats are spaced, that is, a simple organization of two subdivisions or a compound organization of three subdivisions. Instead, meters are categorized at the beat level only by the number of beats in a measure. Put differently, Martin defines meter as a binary, categorical phenomenon consisting only of duple or triple groupings of beats. Martin’s definition of tempo is related to this definition of meter, as he defines tempo as the rate of alternation, in beats per minute (BPM), between the duple or triple downbeat and backbeat.
Martin (2025) also defines rhythm categorically, sorting each song into “duple” (encoded 2) or “non-duple” (encoded 3) as perceived from the “prominent rhythmic feel” (p. 4) of the first and second levels of subdivisions of the beat rate (the two levels were encoded separately). A third category, encoded as zero, represents “no audible subdivision at a particular metric level” (p. 4) or the “second subdivision layer if further subdivisions proved meaningless to the rhythmic makeup of the song” (p. 4).
Lastly, Martin (2025) defines a “Swung Layer Rate” (p. 4). Measured in BPM, the Swung Layer Rate is the rate or tempo of a subdivision level that contains swing rhythm.
Limitations of the Metrical Hierarchy in Martin’s Definitions
One problem evidenced by these definitions is how to clearly distinguish meter from rhythm. In the metrical hierarchy model, the division is made between phenomenal events in the musical surface (rhythm) and mental events generated within the listener by some cognitive system (meter, beats, pulses). But phenomenal events and mental events are not entirely independent; phenomenal events serve as inputs to the cognitive systems, and therefore determine to some extent a listener’s perception and cognition. For example, if the listener generates a metrical hierarchy in which the periods are duple, then the musical surface the listener is attending to presumably contains rhythmic events related to each other in proportions of two and not three. What happens, however, when the musical surface presents the listener with inputs that cannot be mapped onto a categorically determined cognitive representation, such as a duple or triple metrical hierarchy?
Martin’s operational definitions resolve this problem by separately categorizing a song’s meter from its rhythm in its first and second subdivision levels. By defining meter only as the number of beats in a measure, a song’s meter can be categorized independently of whether it uses simple, compound, or mixed subdivisions. But when categorizing the first and second subdivision levels, it becomes impossible to ignore the problem of mixed subdivisions. There are two challenges when studying swing rhythm: (1) the possibility that a song will have some mixture of subdivision types, and (2) distinguishing a swing rhythm from a perceptibly similar straight rhythm, especially a compound rhythm. Because Martin defines rhythm essentially as a two-level categorical variable (I discuss the “zero” category below), it is not possible to meaningfully consider mixed subdivisions or the swing rhythm as a distinct rhythmic type. When a categorical definition is in place, this results in a method of forcing instances whose properties are not strictly those of any category being either removed from the data set or, in Martin’s case, being placed into the category perceived to be most similar. That is, songs in which both simple and compound subdivisions, or both straight and swing rhythms, are perceptible are grouped with songs that only contain compound subdivisions.
A second problem of the metrical hierarchy model is that it does not account for stylistic, expressive, and accidental variations in microrhythm and microtiming, or larger manipulations of tempo such as rubato. This problem is similar to the first in that it is one of periodicity; but where the first problem concerned the mixing of periodicities, the problem here is what happens when performed periodicities are not strictly regular. The swing rhythm is often simplified in musical notation and discourse to being a triplet rhythm. But, as the research reviewed below reveals, there are considerable expressive and microtiming variations present in recordings of swing jazz music. Presumably, such variability is also present in swung country-western music. To incorporate these expressive and microtiming variations into a corpus study like Martin’s, though, would require some continuous measurement of performed durations. Granted, measuring performed durations is a formidable task in its own right, and certainly not one easily scalable to a corpus of Martin’s size (to say nothing of the issue of audio quality in older recordings).
To circumvent this and other difficulties, Martin’s methodology relies heavily on individual aural perception. Some definitions are ambiguous for this reason. Consider the “zero” level of the rhythm categorical variable as defined in the summary above. Some songs were assigned to the “zero” category if “no audible subdivision at a particular metric level” was present (Martin, 2025, p. 4). It is certainly conceivable that some songs have straightforward rhythmic content, and so only one or two rhythmic layers are present. For example, a song may only comprise quarter notes as the tactus or beat layer, whose only audible subdivision is the eighth note. In such a case, there would be no second level of subdivision.
Other songs were assigned to this category if “further subdivisions proved meaningless to the rhythmic makeup of the song” (Martin, 2025, p. 4). It is not clear, however, what should determine if subdivisions that are audible in the music should also be considered “meaningless.” Perhaps some degree of selective attention is involved in metrical and rhythmic perception, but presumably the potential exists for listeners to rely on any part of the “rhythmic makeup” during a musical experience even if they do not rely on all of it.
Consider, for example, Johnny Cash’s “I Walk the Line.” I have selected this as an example because the recording is clean and each part can be heard clearly in the mix. Martin assigned this song to the following categories: duple backbeat, triple first layer of subdivision, and zero second layer of subdivision. I agree with Martin that “I Walk the Line” has a duple backbeat. Though the snare part is a shuffle without the familiar single hits on beats 2 and 4, the bass is playing a two-note “low-high” pitch pattern that rules out a triple meter. I do not, however, hear the first layer of subdivision as predominantly compound or swung. Rather, in both the electric guitar and voice parts, there is a prominent “three-and-four-and-ONE” rhythm (or “one-and-two-and-ONE” if one hears 2/4 instead of 4/4). This rhythm suggests a duple first layer of subdivision. A preference for duple subdivision is further clarified by the second layer. The snare part comprises a shuffle for the entirety of the song. Apart from the duple rhythm just mentioned, this shuffle is the most rhythmically active layer in the texture and it draws the attention immediately. I hear this shuffle as repeating an “and-uh-ONE-and-uh-TWO-…” rhythm. In notation, this rhythm may be represented as 16-16-8-16-16-8-… and so on. Assuming a beat represented by the quarter note, the snare’s shuffle rhythm is thus mixing the first and second layers of subdivision throughout the song and both of these layers are duple. Since the second layer of subdivision is audibly present, Cash’s “I Walk the Line” was presumably assigned to the “zero” category because the second layer of subdivision was “meaningless to the rhythmic makeup of the song” (Martin, 2025, p. 4). But, in this example, the second layer of subdivision is present in a salient part of the texture, lasts throughout the duration of the song, and is not consistent with the categorization of the first layer as triple. Note also that, because both songs with no second layer and songs with a “meaningless” second layer were assigned “zero,” it is not possible to tell from the categorization alone why a given song was assigned to this category.
Lastly, the “Swung Layer Rate” is only measured for songs that have swing, but swing is “subjectively determined” (Martin, 2025, p. 4), and it is not obvious how swing rhythms were identified or if any attempt was made to distinguish swing rhythms from compound rhythms. Similarly, it is not obvious what the “rhythmic feel” of a song is.
SWING RHYTHMS IN PREVIOUS RESEARCH
A considerable body of research on swing rhythms in jazz music exists. I will not attempt to summarize all this research here. Rather, I will focus on a few findings as they relate to the problem that arose with Martin’s definitions in the previous section, namely, how swing rhythms relate to a categorical conception of meter. Previous research on swing focuses on (1) measuring the swing ratio or beat-upbeat ratio, and (2) relating the swing ratio to tempo. Benadon (2006) defined the beat-upbeat ratio, or BUR, as the “temporal proportion between two subsequent eighth-notes” (p. 74). The swing rhythm is commonly represented as eighth-note triplet subdivisions grouped in a two-note long-short pattern. The swing ratio or beat-upbeat ratio describes the time interval for these two notes.
Butterfield (2011) defined the BUR as the ratio between the “absolute duration of the long, downbeat eighth note [and] that of the short upbeat” (p. 4). Straight eighth notes using this measure have a ratio of 1:1, while swing eighth notes with no expressive or microtiming variations have a strict ratio of 2:1. Butterfield analyzed performances by John Coltrane, Lee Konitz, and Sonny Clark. These analyses showed that not only do these three performers often not play a strict BUR of 2:1, but they vary the ratio frequently, usually from beat to beat.
Corcoran and Frieler (2021) analyzed 456 jazz solos found in the Weimar Jazz Database. They found that the average BUR is 1.3:1, that is, less uneven than the 2:1 ratio. They also found, supporting Friberg and Sundström (1997), that BURs are related to tempi, with high BURs being more common at slow and moderate tempi. Frane (2017) analyzed the swing ratio in 30 drum breaks commonly sampled in hip-hop, finding an average ratio of 1.2:1, similar to Corcoran and Frieler (2021). However, Frane’s tempo analyses were not consistent with the finding that swing ratio is related to tempo.
Friberg and Sundström (2002) studied swing rhythms played on the ride cymbal by drummers. They found that drummers’ performed swing ratio varied and was related to tempo, with the ratio varying between 3.5:1 at slow tempi and 1:1 at fast tempi. Collier and Collier (2002) analyzed the swing ratio in two mid-tempo soli by Louis Armstrong, and found that the trumpet player’s ratio averaged 1.6:1.
Honing and de Haas (2008) had professional jazz drummers perform on a Musical Instrument Digital Interface (MIDI) drum kit, which allows for the measurement of the performer’s timing. Honing and de Haas found that each performer’s swing ratio was not constant. Their data did not support Friberg and Sundström’s assertion that swing ratio and tempo are linearly related, but their data does support the notion that jazz drummers “adapt their timing to the tempo of their performance to obtain (or sustain) the effect of swing” (Honing & de Haas, 2008, p. 475).
From this terse review, it is evident that the swing ratio in jazz is more subtle than a strict 2:1, long-short rhythm. Rather, the swing ratio varies by performer, is possibly related to tempo, and even varies at the local beat-to-beat level.
CONCLUSION
Martin’s (2025) paper is a significant contribution to swing and country music research. I have argued that this corpus study assumes a metrical hierarchy model of meter as reflected in the operational definitions related to meter, rhythm, and swing. To be clear, Martin’s assumption of a metrical hierarchy model is not unwarranted; this model is the prevailing model in music theory and pedagogy, as well as in corpus studies and related scholarship in digital and computational musicology. The model allows for researchers to define metrical concepts like meter and beat in a manner that is practical to implement and interpret, chiefly because the metrical hierarchy simplifies meter to a few layers of regular, periodic pulses that can be categorically sorted into groups.
I have also summarized previous research on swing rhythm in jazz. This research shows that not only do swing rhythms vary by performer and tempo, but that the ratio is often smaller than the strict 2:1 ratio that would be necessary to meaningfully group swing rhythms with compound rhythms, which is required by Martin’s sorting of songs based on the first and second subdivision layer. The cited research on swing rhythm in jazz instead suggests that swing rhythms temporally lie between simple and compound metrical groupings. Unfortunately, and as Martin points out in his paper, we do not yet have a comparable body of research examining precise microtiming differences among country-western swing musicians. Nevertheless, assuming that similar patterns of variability related to performer, tempo, and beat would be found amongst these musicians as are found amongst jazz musicians, the picture of swing rhythms and their historical development in country music is probably nuanced and subtle compared to that offered by the binary (duple or triple) sorting of the data encouraged by the metrical hierarchy model.
There are a few paths for future research. At a high level of theorizing and speculation, research on meter, rhythm, and tempo must account for the fact that ecological performances of music often contain considerable, non-negligible levels of stylistic, expressive, and accidental microrhythmic and microtiming variations, in contrast to our common treatment of meter and rhythm as abstractly periodic, isochronous, regular, and predictable (Roeder, 1998). Though attempts have been made in some theories of entrainment to account for temporal variability (Jones, 2019, p. 170; London, 2012, p. 174), this topic has remained marginal. Additionally, theories of meter should take into account the fact that meter is not stagnant. I mentioned above that Martin’s classification of songs into either duple or triple categories is challenged by songs that alternate or mix duple and triple subdivisions in some way. At a low level, one way to improve on this methodology is to adopt a continuous rather than a categorical operational definition of meter. With such a definition, the researcher would not sort songs in their entirety into one of a set of categorical levels, but instead would analyze songs at a beat-to-beat level. Each beat, for example, could be assigned to a simple, compound, or swung category, and the statistical analysis would then be focused on something like proportions of beat types within a song or some other category (e.g., year of recording if testing the hypothesis that tempo has decreased over time in popular music). Note that such a methodology would need to consider texture as a factor to handle the possibility that duple and triple subdivisions are heard simultaneously.
Within the narrow domain of research on the incidence of swing in country-western music, future research could pursue treatments of meter and rhythm as continuous data through analysis of microtiming in the beat-upbeat ratios performed by country-western musicians. Results of these studies could be compared to those of the existing studies on jazz to see if any systematic stylistic differences emerge between the two genres. Lastly, more research is needed to clarify the relationship between swing rhythm and tempo.
ACKNOWLEDGMENTS
This article was copyedited by Jonathan Tang and layout-edited by Niels Chr. Hansen.
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