Microtiming in music denotes a wide range of time-related phenomena that arise as a consequence of conflicting concepts of musical time. Music theory describes the organization of time in metered Western popular or art music using a few discrete, rationally related time duration categories (Hasty, 1997; London, 2004). The canonical notation of rhythm in Western music epitomizes this principle: the relation between the duration of different rhythmic values can be expressed as small-integer ratios. Given a specific tempo, a sequence of notes of the same rhythmic value (e.g., quarter notes) is thought to be isochronous. And notes written on the same metric position (e.g., chords) are supposed to begin synchronously. Performed music, however, plays in continuous physical time where musical events may happen at any moment. In performance, the occurrence of musical events shows considerable temporal freedom, and time intervals between events are variable. This fundamental discrepancy between theoretical, fixed, discrete duration categories and the flexible nature of music performance in continuous time broadly defines the domain of microtiming in metered Western music.

Microtiming phenomena are very diverse and differ across musical contexts. Some manifestations of microtiming are relatively large-scale, can easily be detected by the untrained ear, and have become characteristic for certain musical styles. The asymmetric subdivision of the beat, for example, is a frequent feature of both jazz (for an overview on the swing ratio literature, see Friberg and Sundström, 2002; Dittmar et al., 2015; Camara, 2016) and baroque music (Moelants, 2011). Further, expressive timing (i.e., local tempo variations) is a phenomenon widely observed in the performance of Western art music. It has been associated with phrase structure, harmonic and melodic development, and it is understood to be a major source of expressiveness in Western art music (Clarke, 1982; Cook, 1987; Repp, 1992, 1997, 1998b; Beran and Mazzola, 2000; Hong, 2003; Sundberg, 2003; Cheng and Chew, 2008; Senn et al., 2009, 2012; Dodson, 2011; MacRitchie, 2011; Benadon and Zanette, 2015).

A multitude of musical or contextual factors may be associated with microtiming phenomena. Tempo, for example, has been shown to be related with microtiming magnitude: Friberg and Sundström (2002) found that the swing ratio (i.e., the duration ratio between the long first and the short second swing eighth note) is negatively correlated with tempo. Moelants (2011) observed a comparable relationship for the baroque notes inégales, and Repp (1995) reported a similar tendency for the execution of expressive timing in Nineteenth century piano music: faster tempo implied less microtiming (see also Fraisse, 1956; Repp et al., 2002).

Bengtsson (1974) showed that the first quarter note of a Viennese Waltz measure tends to be longer than the second and third quarter notes. This can be associated with the dance movements: the basic Waltz step pattern begins with a long step, followed by two shorter ones. The microtemporally adapted beat durations help dancers to map their steps to the music more easily. Hence, the fact that the Waltz is used for dancing has shaped microtiming properties of the music.

Finally, the use of tempo rubato in the performance of Western art music piano repertoire has changed through performance history. Pianists of the early Twentieth century used ample rubato, but it fell out of favor during the second half of the century (Philip, 2004). Influential performers played a role (e.g., Glenn Gould and his recordings of works by J. S. Bach) but also new performance paradigms (such as the historically informed performance movement). In this case, the taste and aesthetics of the performers and of their audiences were contextual factors that modified the use of a microtiming-based performance technique like tempo rubato.

Within the same context, microtiming patterns might be so stable that they can even be cast into fixed performance rule systems (Beran and Mazzola, 2000; Friberg et al., 2006). Listeners' familiarity with such stable patterns may also affect their sensitivity to microtiming. Repp exemplified this in a striking way: he showed that listeners of Chopin's Etude op. 10, No. 3, had “obligatory expectations” with respect to the microtiming pattern, depending on phrase structure and an implicit rule system (Repp, 1998a).

The pioneers of technology-based timing analysis, Ingmar Bengtsson and Alf Gabrielsson, discussed the question to what extent small-scale microtiming phenomena are a meaningful part of the performance or just motor noise resulting from humans' limited capacity to realize a “quantized” music performance, i.e., a performance with perfect mechanical regularity (Gabrielsson, 1974; Bengtsson and Gabrielsson, 1977, 1980, see also Rasch, 1988). A large body of research on sensori-motor synchronization (for an overview of the tapping literature, see Repp, 2005; Repp and Su, 2013) studied the production side of this question, namely humans' timing precision when synchronizing body motion with acoustic stimuli. Some of these studies addressed the precision of expert drummers' performance (Fischinger, 2009; Fujii et al., 2011; Kilchenmann and Senn, 2011) and discussed methods to distinguish between unsystematic, random timing variations that are merely motor noise, and systematic, recurring variations that may be characteristic for a style and relevant for the effect of the music (Hellmer and Madison, 2015).

The perception of microtiming has also been studied: a substantial body of work discusses the precision of human timing discrimination with respect to auditory stimuli (Michon, 1964; Fraisse, 1967; Nordmark, 1968; Abel, 1972; Lunney, 1974; Halpern and Darwin, 1982; Hibi, 1983; Nakajima, 1987; Hirsh et al., 1990; Nakajima et al., 1992; Drake and Botte, 1993; Hoopen et al., 1995; Sasaki et al., 1998; Ehrlé and Samson, 2005; Thomas, 2007). In their influential study, Friberg and Sundberg (1995) found that the Just Noticeable Difference (JND) for microtiming deviations in a monotonic, isochronous sequence was approximately constant at an absolute value of 6 ms for inter-onset-intervals (IOIs) smaller than 240 ms. The JND remained stable at roughly 2.5% of the IOI when the interval was in the range 240–1,000 ms. Hence, above the 6 ms threshold, listeners' sensitivity to microtiming deviations appears to follow Weber-Fechner's law. JND research investigated listeners' time discrimination in a laboratory setting that is optimized for the detection of minimal deviations. In everyday listening situations, however, performed music is usually more complex than the lab stimuli, and listeners' threshold for detecting microtiming deviations in a regular listening context is likely to differ from the JND's.

In recent years, the impact of microtiming on the groove phenomenon has been a major research topic. Relevant papers in music psychology define groove as an enjoyable inner urge to synchronize body movement with the beat of the music (Janata et al., 2012; Witek et al., 2014). This shifts the focus from the perceptual detectability or noticeability of microtiming to bodily entrainment and emotional responses.

The hypothesis that microtiming is essential for triggering groove originated in Charles Keil's Theory of Participatory Discrepancies or PD Theory (Keil, 1987, 1995, 2010). It has considerable support among musicians (Berliner, 1994; Monson, 1996; Doffman, 2008). The empirical evidence concerning the relevance of microtiming for groove, however, has been inconclusive so far: some studies found no evidence that microtiming influences groove (Butterfield, 2010; Madison et al., 2011; Madison and Sioros, 2014), others found that microtiming is detrimental to groove (Davies et al., 2013; Frühauf et al., 2013; Matsushita and Nomura, 2016); yet others found that microtiming patterns arising in competent performance do not affect groove negatively, but if the patterns are exaggerated in magnitude, the groove experience decreases (Kilchenmann and Senn, 2015; Senn et al., 2016). Finally, Hofmann et al. (2017) suggested that listeners preferred tightened microtiming patterns to the microtiming magnitude of the originally performed music.

How can we explain the discrepancies between these empirical results? Previous research has primarily focused on the magnitude of microtiming deviations. The patterning of the microtiming deviations have received little attention up to now. This paper presents three small studies that aim at exemplifying how patterning aspects may impact listeners' emotional responses to microtiming.

Study A compares the groove-related effects of two laboratory-generated methods for systematically introducing fixed microtiming deviations into quantized music. The two manipulations affect entire instrumental parts or voices (i.e., layers of the musical fabric that are characterized by specific timbres) differently: the Shift manipulation displaces parts that are played by different musicians against each other by a certain time offset (between musicians). The Disturbance manipulation displaces voices against each other that are played by the same musician (within musician).

Butterfield (2010) used the Shift method: he worked with standard-practice jazz rhythm section examples (bass and drums). He displaced the drum tracks and the bass track relative to each other by either anticipating the bass onsets by 10, 20, or 30 ms relative to the drums (bass lead) or by conversely anticipating the drum onsets by 10, 20, or 30 ms (drums lead) relative to the bass. Butterfield found that this kind of manipulation had little effect on listeners.

Frühauf et al. (2013) took the Disturbance approach: they used a generic rock/pop drum pattern (eighth notes on the hi-hat, downbeats on the bass drum, and backbeats on the snare drum) and manipulated one layer within the drum track. They displaced either all bass drum or all snare drum sounds uniformly by −25, −15, 0, 15, or 25 ms, while keeping the remaining instruments in place. Frühauf et al. found a dose-response effect of the displacements on listeners' groove ratings: the perfectly quantized stimulus (0 ms displacement) obtained the highest groove ratings. Ratings decreased with larger displacements in either direction (early or late) and for either of the instruments. However, this effect was stronger when the snare drum was displaced instead of the bass drum, and when the displaced event onsets were early instead of late.

Matsushita and Nomura (2016) proceeded according to the Shift method. They used the same standard rock/pop drum pattern as Frühauf et al. (2013), but combined it with repeated eighth notes on a bass guitar. Compared to Butterfield (2010), they increased the magnitude of the time shift considerably: the bass voice was displaced by −62.50, −46.88, −31.25, 0, +31.25, +46.88, and +62.50 ms (negative numbers refer to bass lead, positive numbers to bass lag). They found that groove ratings were high for well synchronized stimuli, and declined with larger displacements in both bass lead and bass lag direction; these results were similar to those reported by Frühauf et al. (2013).

The goal of Study A is to replicate the main results of Butterfield (2010) and Frühauf et al. (2013) by applying both displacement methods to the swing and funk examples from Kilchenmann and Senn (2015). In particular, we try to verify, whether introducing a Disturbance microtiming pattern by displacing the snare drum layer against the other layers (the remaining drum tracks and the bass) affects the groove experience negatively (comparable to the effects found by Frühauf et al., 2013), and whether introducing a time Shift microtiming pattern between bass and drums has little or no effects on listeners (comparable to Butterfield, 2010).

In Senn et al. (2016) we reported that listeners' emotional responses were similar for swing and funk when the originally performed microtiming patterns were scaled by the same percentages. This was a surprising result, because the microtiming deviations (measured in milliseconds) of the swing performance were more largely spread than the deviations of the funk performance, and this difference was accentuated when the microtiming deviations were upscaled. Do listeners have an implicit knowledge which microtiming magnitudes are appropriate in each style? In Study B, instead of accepting such an essentialist explanation, we will try to identify moderating factors that bridge the differences, using the EAG response data from Senn et al. (2016).

Three different measures of microtiming magnitude will be defined: the Standard Timing Deviation (STD) estimates the mean microtiming deviation per note onset (a bass tone, a stroke on a drum etc.) in milliseconds using the Root Mean Squared Error method. The Tempo-adjusted Standard Timing Deviation measures mean deviation as a proportion of beat duration. And the Density-adjusted Standard Timing Deviation measures it as a proportion of the mean IOI between neighboring rhythmic events.

The two adjusted measures translate the core result of Friberg and Sundberg's (1995) experiment into the domain of more complex musical stimuli: for the monotonic, isochronous sequences of their experiment, a change of IOIs can equivalently be understood as a manipulation of tempo or of rhythmic density. For more complex musical objects, these two aspects need to be separated. A complex pattern might move at a slow tempo, but still be rhythmically dense, and vice versa.

The Tempo-adjusted STD implements tempo as a moderator variable (see Baron and Kenny, 1986; Cohen, 2003), which, in Western popular music, is represented by the periodicity of the beat. In contrast, the Density-adjusted STD considers how frequently a listener obtains any kind of rhythmic information. The two measures lead to different values when applied to this study's swing and funk stimuli: the swing example has higher tempo (150 bpm) than the funk example (100 bpm), hence the Tempo-adjusted STD augments the microtiming magnitude of the swing example relative to the funk example. But the rhythmic density of the swing example is smaller than the density of the funk example, because the smallest subdivision in swing are eighth notes, whereas the funk example has an underlying sixteenth note pulse. Hence Density-adjusted STD will accentuate the microtiming magnitude of the funk example relative to the swing example.

In a second step, we will analyse listeners' emotional responses to the swing and funk stimuli as a function of the three different microtiming measures. If any of the measures successfully aligns listeners' responses to microtiming in both the swing or the funk contexts, this measure potentially can be used to uniformly quantify microtiming across different musical situations, and the adjusting factor can be understood as a unifying moderator variable.

The previous section presented some evidence that the Density-adjusted Standard Timing Deviation aligns listener responses to microtiming deviations across different musical contexts. This alleged invariance is not more than a claim at this point. But if confirmed by further research, it might provide a welcome common ground for the comparison of microtiming effects arising in different situations and contexts.

In Study C, we probe into the potential of such comparisons: we hypothesize that listeners respond differently to the invariant, lab-generated Shift and Disturbance patterns (Study A) compared to the variable microtiming pattern that arose in the original Performances (Study B). The rationale behind this claim is that we expect listeners to be more accustomed to Performance microtiming patterns than to Shift and Disturbance patterns. And we also hypothesize that Expert listeners react more strongly to microtiming deviations, compared to Non-Expert listeners, due to the Experts' training and refined auditory perception. In order to test these hypotheses, we will fit regression models to listeners' EAG ratings, using the Density-adjusted STD as a common predictor variable.

This paper's Study A replicated results from previous research. It showed that, on one hand, the mutual displacement of the bass track against the drums track by a magnitude up to 24 ms (Shift) did not have a significant effect on listeners' groove experiences (thus solidifying the main result of Butterfield, 2010). On the other hand, the study showed that displacing the snare drum track alone against the other tracks (Disturbance) affected listeners' groove experience negatively (thus it confirmed a core finding of Frühauf et al., 2013). Overall, we could confirm that not only the magnitude of microtiming deviations seems to matter, but also which layers of a musical fabric were affected: displacements between instrumental parts played by the same musician had a negative effect, whereas displacements between parts played by different musicians had no effect.

The effect of the Disturbance manipulation measured in Study A was considerably smaller than the effect found by Frühauf et al. (2013). This may have had several reasons: firstly, Study A had a flaw in the experimental setup that invalidated the responses to the quantized stimuli. This loss of data affected the statistical power of the experiment adversely. Secondly, the musical patterns of the stimuli in Study A differed considerably from those in Frühauf et al. (2013). The latter used a simple, straightforward rock music drum pattern, in which the snare drum played the quintessential backbeat and nothing else. In the present paper, both the swing and funk stimuli present a more complicated pattern, where the snare drum may appear on different, more or less metrically important positions. Attention research claims that irregular signals are easier to detect, when they are perceived against a regular background (Scerbo et al., 1986; Bregman, 1999; Parasuraman, 2000; Helton et al., 2005; Dalton et al., 2007; Winkler et al., 2009), compared to an irregular background. The pattern presented in Frühauf et al. (2013) represents a regular background, whereas the music used in this paper's Study A are rhythmically far more complicated and irregular, and this might have affected both the detectability and emotional impact of the microtiming displacements.

Study B explored different ways of measuring the magnitude of microtiming deviations in music. Using data from an earlier study (Senn et al., 2016), it showed that emotional listener reactions aligned with each other across two select musical styles (Funk and Swing), when microtiming magnitude was measured as a proportion of the mean IOI, and rhythmic density is accounted for as a moderating factor. The result suggests that the Density-adjusted STD is potentially better suited than the simple STD or the Tempo-adjusted STD to measure and compare the magnitude of microtiming phenomena across a variety of musical situations. This finding resonates with results from research on just-noticeable differences in auditory perception (Friberg and Sundberg, 1995), sensori-motor synchronization (Madison, 2014) and attentional dynamics (Jones et al., 2006). Further studies are necessary to establish whether the result expands to other musical contexts beyond the two situations investigated in this paper.

Finally, Study C probed into the effects of different microtiming patterns on listeners' emotional response, using the Density-adjusted STD as common measure of microtiming magnitude. This inquiry yielded one marginal result only: it showed that music expert listeners reacted with more Irritation when the snare drum was displaced against a quantized background, compared to the widely distributed microtiming patterns present in the originally recorded performances. A collateral result is perhaps of greater importance: Study C showed that the artificially introduced microtiming deviations (Shift, Disturbance) were of far smaller magnitude than the displacements found in the original performances. This suggests that, in future research, the magnitudes of lab-created and performance-generated microtiming patterns need to be matched in order to be comparable.

Overlooking the corpus of groove studies concerned with microtiming, we may summarize that this branch of research has surprisingly few results to show for its efforts. This is what we know so far: stimuli with quantized timing receive high groove ratings, at least in the context of an experiment. We also know that groove ratings deteriorate, as microtiming deviations are expanded (Davies et al., 2013; Frühauf et al., 2013; Matsushita and Nomura, 2016; Senn et al., 2016). We further obtained some evidence that the groove ratings of stimuli with microtiming that arises in professional performance are on par with those elicited by stimuli with quantized timing (Senn et al., 2016) and that it is not necessarily the quantized stimuli that motivate the most intense body movement in listeners (Kilchenmann and Senn, 2015). Finally, Hofmann et al. (2017) suggested that tight microtiming patterns are preferred by listeners, compared to larger microtiming magnitudes.

These results offer little support to the claim of the Theory of Participatory Discrepancies that microtiming deviations are essential for groove. Rather, it led scholars to the opposite conclusion, namely that music should be played with as little microtiming as possible in order to have high groove—this opinion has been most prominently voiced by Merker (2014). This conclusion, however, is at odds with the firm belief of many musicians that microtemporal aspects are crucial for groove (Berliner, 1994; Monson, 1996; Doffman, 2008) and with the findings of Hove et al. (2007) that the presence of certain kinds of microtiming improves rhythmic precision in musicians.

In a recent article, Witek pointed out with respect to microtiming that “it seems to matter greatly how these rhythmic nuances are implemented,” and she observed that “the conditions under which microtiming is effective have been difficult to recreate in a laboratory setting” (Witek, 2016, p. 16, emphasis in the original). Taking into account relevant moderating factors bridging between “conditions” and using patterns from expert performance in empirical research may allow to reach beyond the lab situation and better capture the groove phenomenon. Up to now, most experimental studies investigated the effect fixed microtiming patterns, and manipulated them by scaling the magnitude of the deviations. But the effect of systematically varying the patterning of microtiming deviations while retaining the magnitude of the deviations has not yet been sufficiently approached. The methodological advantage of varying magnitude as an experimental variable consists in the fact that, being a quantity, magnitude can be manipulated along one single dimension. Varying patterns is inherently multidimensional, and it is difficult to imagine how systematic manipulations can be achieved.

Another yet unchartered territory in groove studies is related to the variability of microtiming patterns across the time of a performance. In the past, average microtiming variation profiles have been extracted from performed music (see examples in Fujii et al., 2011; Kilchenmann and Senn, 2011, 2015; Naveda et al., 2011; Hellmer and Madison, 2015; Hofmann et al., 2017). These patterns may well represent a systematic aspect of microtiming in a certain style or context. But they do not take the procedural aspect of music performance into account: the development of the music in time and the rhythmic interaction between players. According to Keil (1966, 1987, 1995, 2010) this procedural aspect is of great importance. Large's and Jones' Theory of Dynamic Attending (Large and Jones, 1999; Jones et al., 2006) might provide a solid conceptual basis for tackling process-related aspects of musical performance.

In recent years, research has moved on to discuss other musical aspects that promise to be relevant for groove, besides microtiming. Beat salience, event density and pulse clarity have been identified as possible sources for (or at least correlates of) groove (Madison et al., 2011; Stupacher et al., 2016). Several studies have shown that syncopation is associated with the experience of groove (Madison and Sioros, 2014; Sioros et al., 2014; Witek et al., 2014) and with body movement (Witek et al., 2017). The groove qualities of rhythmic patterns have also been discussed, albeit not yet empirically (Zbikowski, 2004; Danielsen, 2006; Witek, 2016). The diversification of groove studies, to include other factors than microtiming, is a fruitful and necessary development. There is currently no shared doctrine among scholars whether microtiming is relevant or not, but everybody will agree that microtiming cannot be the only relevant aspect for groove, and that there are innumerable other routes to explore.

This study was carried out in accordance with the recommendations of the Ethics Commission of the Canton of Lucerne. All subjects gave written informed consent in accordance with the Declaration of Helsinki. The protocol was approved by the Ethics Committee of the Canton of Lucerne.

Conceived and designed the experiments, wrote the paper, and designed the EAG questionnaire: OS, LK, RvG, and CB. Conducted the studio recording session and performed the experiments: LK. Validated the EAG questionnaire: RvG. Analyzed the data: OS.