What factors influence listeners’ perception of meter in a musical piece or a musical style? Many cues are available in the musical “surface,” i.e., the pattern of sounds physically present during listening. Models of meter processing focus on the musical surface. However, percepts of meter and other musical features may also be shaped by reactivation of previously heard music, consistent with exemplar accounts of memory. The current study explores a phenomenon that is here termed metrical restoration : listeners who hear melodies with ambiguous meters report meter preferences that match previous listening experiences in the lab, suggesting reactivation of those experiences. Previous studies suggested that timbre and brief rhythmic patterns may influence metrical restoration. However, variations in the magnitude of effects in different experiments suggest that other factors are at work. Experiments reported here explore variation in metrical restoration as a function of: melodic diversity in timbre and tempo, associations of rhythmic patterns with particular melodies and meters, and associations of meter with overall melodic form . Rhythmic patterns and overall melodic form, but not timbre, had strong influences. Results are discussed with respect to style-specific or culture-specific musical processing, and everyday listening experiences. Implications for models of musical memory are also addressed.

T he present study tested two assumptions concerning the auditory processing of microtiming in musical grooves (i.e., repeating, movement-inducing rhythmic patterns): 1) Microtiming challenges the listener's internal framework of timing regularities, or meter, and demands cognitive effort. 2) Microtiming promotes a “groove” experience—a pleasant sense of wanting to move along with the music. Using professional jazz musicians and nonmusicians as participants, we hypothesized that microtiming asynchronies between bass and drums (varying from −80 to 80 ms) were related to a) an increase in “mental effort” (as indexed by pupillometry), and b) a decrease in the quality of sensorimotor synchronization (as indexed by reduced finger tapping stability). We found bass/drums-microtiming asynchronies to be positively related to pupil dilation and negatively related to tapping stability. In contrast, we found that steady timekeeping (presence of eighth note hi-hat in the grooves) decreased pupil size and increased tapping performance, though there were no conclusive differences in pupil response between musicians and nonmusicians. However, jazz musicians consistently tapped with higher stability than nonmusicians, reflecting an effect of rhythmic expertise. Except for the condition most closely resembling real music, participants preferred the on-the-grid grooves to displacements in microtiming and bass-succeeding-drums-conditions were preferred over the reverse.

I n order to be heard over the low-frequency energy of a loud orchestra, opera singers adjust their vocal tracts to increase high-frequency energy around 3,000 Hz (known as a “singer's formant”). In rap music, rhymes often coincide with the beat and thus may be masked by loud, low-frequency percussion events. How do emcees (i.e., rappers) avoid masking of on-beat rhymes? If emcees exploit formant structure, this may be reflected in the distribution of on- and off-beat vowels. To test this prediction, we used a sample of words from the MCFlow rap lyric corpus ( Condit-Schultz, 2016 ). Frequency of occurrence of on- and off-beat words was compared. Each word contained one of eight vowel nuclei; population estimates of each vowel's first and second formant (F1 and F2) frequencies were obtained from an existing source. A bias was observed: vowels with higher F2, which are less likely to be masked by percussion, were favored for on-beat words. Words with lower F2 vowels, which may be masked, were more likely to deviate from the beat. Bias was most evident among rhyming words but persisted for nonrhyming words. These findings imply that emcees use formant structure to implicitly or explicitly target the intelligibility of salient lyric events.

Adults can extract the underlying beat from music, and entrain their movements with that beat. Although infants and children are poor at synchronizing their movements to auditory stimuli, recent findings suggest they are perceptually sensitive to the beat. We examined five-year-old children’s perceptual sensitivity to musical beat alignment (adapting the adult task of Iversen & Patel, 2008). We also examined whether sensitivity is affected by metric complexity, and whether perceptual sensitivity correlates with cognitive skills. On each trial of the complex Beat Alignment Test (cBAT) children were presented with two successive videos of puppets drumming to music with simple or complex meter. One puppet’s drumming was synchronized with the beat of the music while the other had either incorrect tempo or incorrect phase, and children were asked to select the better drummer. In two experiments, five-year-olds were able to detect beat misalignments in simple meter music significantly better than beat misalignments in complex meter music for both phase errors and tempo errors, with performance for complex meter music at chance levels. Although cBAT performance correlated with short-term memory in Experiment One, the relationship held for both simple and complex meter, so cannot explain the superior performance for culturally typical meters.

This study investigated the role of repetition on listener response. It tested the hypothesis that repetition, in the form of looping during an exposure phase, would make random sequences of tones sound more musical when rated later during a test phase. In Experiment 1, participants without special music training rated the musicality of random sequences of tones on a Likert-like scale from 1 to 7. Experiment 2 used the highest and lowest rated sequences as stimuli. In an initial exposure phase, participants heard half these sequences presented six times in a loop, and half of them presented only once. In a subsequent test phase, they rated the musicality of each sequence. Sequences that had been repeated were rated as more musical, regardless of whether they had received a high or low musicality rating in Experiment 1, but the effect size was small. These results, although limited in some respects, support a large body of literature pointing to the importance of repetition in aesthetic experiences of music.

This paper undertakes a comparative study of concepts and visual representations of hierarchical aspects of musical structure. After consideration of the rhythmic components of grouping and meter, the discussion turns to pitch-event hierarchies and the tonal hierarchy (or pitch space). Contrasting notations are evaluated in terms of the efficacy of the concepts they exemplify.

In music, the rhythms of different instruments are often syncopated against each other to create tension. Existing perceptual theories of syncopation cannot adequately model such kinds of syncopation since they assume monophony. This study investigates the effects of polyphonic context, instrumentation and metrical location on the salience of syncopations. Musicians and nonmusicians were asked to tap along to rhythmic patterns of a drum kit and rate their stability; in these patterns, syncopations occurred among different numbers of streams, with different instrumentation and at different metrical locations. The results revealed that the stability of syncopations depends on all these factors and music training, in variously interacting ways. It is proposed that listeners’ experiences of syncopations are shaped by polyphonic and instrumental configuration, metrical structure, and individual music training, and a number of possible mechanisms are considered, including the rhythms’ acoustic properties, ecological associations, statistical learning, and timbral differentiation.

What determines the similarity of musical rhythms? According to the “family” theory, which this paper presents, one factor is the temporal sequence of the onsets of notes: rhythms with the same pattern of interonset intervals tend to sound similar. Another factor is meter. It determines whether or not rhythms are members of the same family, where families depend only on three types of possibility for each metrical unit. If the beat is the relevant metrical unit, these three possibilities are: 1) a note starts on a beat and therefore reinforces the meter, 2) a syncopation anticipates the beat and lasts through its onset and therefore disturbs the meter, and 3) all other events such as rests or ties that start on the beat provided no syncopation anticipates them. Two experiments showed that similarity between rhythms depends on both their temporal patterns of onsets and their families, which combined give a better account than edit distance – a metric of the distance apart of two strings of symbols. Two further experiments examined the errors that participants made in reproducing rhythms by tapping them. Errors more often yielded rhythms in the same family as the originals than rhythms in a different family.

We report two experiments exploring whether matched metrical and motivic structure facilitate the recognition of melodic patterns. Eight tonal melodies were composed from binary (four-note) or ternary (three-note) motivic patterns, and were each presented within a metrical context that either matched or mismatched the pattern. On each trial, participants heard patterns twice and performed a same-different task; in half the trials, one pitch in the second presentation was altered. Performance was analyzed using signal detection analyses of sensitivity and response bias. In Experiment 1, expert listeners showed greater sensitivity to pitch change when metrical context matched motivic pattern structure than when they conflicted (an effect of metrical encoding) and showed no response bias. Novice listeners, however, did not show an effect of metrical encoding, exhibiting lower sensitivity and a bias toward responding “same.” In a second experiment using only novices, each trial contained five presentations of the standard followed by one presentation of the comparison. Sensitivity to changes improved relative to Experiment 1: evidence for metrical encoding – in the form of reduced response bias when meter and motive matched – was found. Results support the metrical encoding hypothesis and suggest that the use of metrical encoding may develop with expertise.

Mirka (2009) has recently argued that the 18th-century metrical theories of Heinrich Christoph Koch can be revelatory for a reconstruction of contemporary ways of hearing Viennese high classicism. Koch’s claims revolve around interactions between the metrical placement of cadences and the articulation of specific beat levels, and these claims are most specific and testable for common time and 6/8. This paper reports two statistical surveys of works by Mozart that were designed to gauge the fit between the corpus and Koch’s theory. In the works examined, the theory was strongly supported for common time, strongly disconfirmed for 6/8, and weakly supported for the other meters encountered. It is argued that these results point toward caution regarding the use of Koch’s theories but not toward their outright rejection, and that unexpected statistical contrasts within the corpus indicate the need for a fine-grained approach to meter in music of the later 18th century.

Despite the plethora of research on the role of tonality and meter in music perception, there is little work on how these fundamental properties function together. The most basic question is whether the two hierarchical structures are correlated – that is, do metrically stable positions in the measure preferentially feature tonally stable pitches, and do tonally stable pitches occur more often than not at metrically stable locations? To answer this question, we analyzed a corpus of compositions by Bach, Mozart, Beethoven, and Chopin, tabulating the frequency of occurrence of each of the 12 pitch classes at all possible temporal positions in the bar. There was a reliable relation between the tonal and metric hierarchies, such that tonally stable pitch classes and metrically stable temporal positions co-occurred beyond their simple joint probability. Further, the pitch class distribution at stable metric temporal positions agreed more with the tonal hierarchy than at less metrically stable locations. This tonal-metric hierarchy was largely consistent across composers, time signatures, and modes. The existence, profile, and constancy of the tonal-metric hierarchy is relevant to several areas of music cognition research, including pitch-time integration, statistical learning, and global effects of tonality.

the normalized pairwise variability index (npvi) , originally developed for the analysis of speech prosody, has been shown to be a useful tool in the analysis of the rhythmic variability present in individual melodies and melodic corpuses (Patel & Daniele, 2003a; Huron & Ollen, 2003; Patel, Iverson, & Rosenberg, 2006). Here we suggest a number of rhythmic refinements for the application of the nPVI in musical contexts. These include (a) applying the nPVI metric to higher levels of rhythmic structure, (b) taking metrical structure (duple versus triple) into account, and (c) using alternative codings for surface durations. A reanalysis of the data from Patel & Daniele (2003a) is given as a demonstration of the utility of these refinements for the analysis of musical styles and repertoires; other possible refinements are discussed.

in this study we examine a rhythmic pattern known as the Scotch Snap (SS): a sixteenth-note on the beat followed by a dotted eighth-note. A musical corpus analysis shows that the SS is common in both Scottish and English songs, but virtually nonexistent in German and Italian songs. We explore possible linguistic correlates for this phenomenon. Our reasoning is that languages in which stressed syllables are often short might tend to favor the SS pattern. The traditional distinction between long and short vowels correlates partly with the SS pattern across languages, but not completely. (German allows short stressed vowels, but the SS pattern is not common in German music.) We then examine the duration of stressed syllables in four modern speech corpora: one British English, one German, and two Italian. British English shows a much higher proportion of very short stressed syllables (less than 100 ms) than the other two languages. Four vowels account for a large proportion of very short stressed syllables in British English, and also constitute a large proportion of SS tokens in our English musical corpus. This is the first study known to us that establishes a correlation between speech rhythms in languages and musical rhythms in the songs of those languages.

when finger taps are synchronized with an isochronous click, it is known that tap-click asynchrony and its variability increase with the interonset interval (IOI). It remains unclear whether these results are due to the IOI or the intertap interval (ITI) duration. The present study examines how these two factors influence tapping performance by altering the tap-click ratio (i.e., 1: n tapping). It has been shown that holding the ITI constant while decreasing the IOI—so that extra clicks subdivide each tap—results in a reduction of tapping variability, described as a subdivision benefit (Repp, 2003). Two questions remain: Does asynchrony and variability increase with the ITI while holding the IOI constant? Does asynchrony decrease with the IOI while holding ITI constant? Using linear regression, both asynchrony and variability decreased with the IOI, with little additional effect of ITI. In contrast, when using ITI as a predictor, the contribution of IOI was significant, suggesting that IOI is the main determinant of tapping performance. In addition, an ANOVA revealed a disadvantage for 1:3 tapping, supporting a categorical distinction between duple and triple meters since 1: n tapping can engender the subjective feel of different metric structures.

the present study models listeners' tactus choices relative to the metric structure of fully musical excerpts using data from a tapping experiment. Viewed from the standpoint of metric structure, tactus was ambiguous between individuals and within excerpts, providing no evidence that this behavior has a global basis in tempo or in a subdivision benefit. Tactus was more consistent within individuals, however, when viewed as following from one of three basic strategies: (1) tapping with a subdivided pulse, (2) tapping with the fastest consistent pulse in the music (a pulse with no consistent subdivision), or (3) using a mixture of these two strategies based on inconsistent rhythmic activity at the musical surface. Music training correlated positively with the first of these strategies. Since individual listeners engage with musical meter in different ways, ambiguity of tactus should be an expected feature of any audience's response to metrical music.

Listening to music often is associated with spontaneous body movements frequently synchronized with its periodic structure. The notion of embodied cognition assumes that intelligent behavior does not emerge from mere passive perception, but requires goal-directed interactions between the organism and its environment. According to this view, one could postulate that we may use our bodily movements to help parse the metric structure of music. The aim of this study was to investigate how pulsations on different metrical levels manifest in music-induced movement. Musicians were presented with a piece of instrumental music in 4/4 time, played at four different tempi ranging from 92 to 138 bpm. Participants were instructed to move to the music, and their movements were recorded with a high quality optical motion capture system. Subsequently, signal processing methods and principal components analysis were applied to extract movement primitives synchronized with different metrical levels. We found differences between metric levels in terms of the prevalence of synchronized eigenmovements. For instance, mediolateral movements of arms were found to be frequently synchronized with the tactus level pulse, while rotation and lateral flexion of the upper torso were commonly found to exhibit periods of two and four beats, respectively. The results imply that periodicities on several metric levels are simultaneously present in music-induced movement. This could suggest that the metric structure of music is encoded in these movements.

THIS STUDY EXPLORES WAYS OF MODELING the compositional processes involved in common-practice rhythm (as represented by European classical music and folk music). Six probabilistic models of rhythm were evaluated using the method of cross-entropy: according to this method, the best model is the one that assigns the highest probability to the data. Two corpora were used: a corpus of European folk songs (the Essen Folksong Collection) and a corpus of Mozart and Haydn string quartets. The model achieving lowest cross-entropy was the First-Order Metrical Duration Model , which chooses a metrical position for each note conditional on the position of the previous note. Second best was the Hierarchical Position Model , which decides at each beat whether or not to generate a note there, conditional on the note status of neighboring strong beats (i.e., whether or not they contain notes).When complexity (number of parameters) is also considered, it is argued that the Hierarchical Position Model is preferable overall.

WHEN A MELODY BEGINS WITH AN ANACRUSIS, (i.e.,"pick up" notes), rhythm and meter are out of phase. Three experiments were conducted to investigate the interactions between structural (rhythm and pitch) and performance (articulation and tempo) factors on the perception of anacruses. The independent variables were rhythmic figure, initial melodic direction, initial melodic interval, implied harmony, articulation, and tempo. Participants tapped "every other beat" to melodies composed for each experiment; the phase-alignment of taps with the stimulus was the dependent measure of anacrustic vs. non-anacrustic perception. Experiment 1 found a strong main effect for rhythmic figure and an interaction between rhythmic figure and tempo. Experiment 2 showed that as tempo increased there was a systematic shift toward anacrustic perception of some melodies. Experiment 3 found that in a rhythmically impoverished context, pitch-based structural factors had only a weak effect on the perception of anacrusis.

DEBELLIS (2009) ARGUES THAT INTROSPECTIONIST music theory, as represented in my book The Cognition of Basic Musical Structures ( CBMS ; Temperley, 2001), makes an ungrounded assumption that the intuitions of the author are shared by other theorists and by experienced listeners generally. But this inductive leap is motivated by experimental and corpus evidence showing that, with regard to basic structures such as meter, listeners largely do hear things in the same way; and this assumption is confirmed in CBMS by corpus tests in which my analyses are compared to those of other listeners. DeBellis suggests that what I was doing in CBMS was not accessing unconscious representations, but rather bringing new representations into existence. But this implies either that experienced listeners in general do not represent meter at all, or that they arrive at metrical analyses by a pre-theoretic process that is not available to music theorists; neither of these options is plausible.

This article introduces a new method for detecting long-timescale structure in music. We describe a way to compute autocorrelation such that the distribution of energy in phase space is preserved in a matrix. The resulting Autocorrelation Phase Matrix (APM) is useful for several tasks involving metrical structure. In this article we describe the details of calculating the APM. We then show how phase-related regularities from music are stored in the APM and present two ways to recover these regularities. The simpler approach uses variance or entropy calculated on the distribution of information in the APM. The more complex approach explicitly searches through the phase and lag space of the APM to predict meter and tempo in parallel. We compare these approaches against standard autocorrelation for the task of tempo prediction on a relatively large database of annotated digital audio files. We demonstrate that better tempo prediction is achieved by exploiting the phase-related information in the APM.We argue that the APM is an effective data structure for tempo prediction and related applications, such as real-time beat induction and music analysis.