1,2 & Jessica A. Grahn1-3

Canada

Humans perceive a pulse, or beat, underlying musical rhythm. Beat strength correlates with activity in the basal ganglia and SMA, suggesting these regions support beat perception. However, the basal ganglia and SMA make up a general timing network active during rhythm and timing perception, regardless of beat. Therefore, activity in these regions may represent basic rhythmic features, in addition to beat. Using RSA, we characterized the neural representation of rhythm in the basal ganglia, SMA, and across the whole brain. During fMRI, participants heard 12 rhythms – 4 strong-beat, 4 weak-beat, and 4 non-beat. Multi-voxel activity patterns for each rhythm, and for the mean of each condition, were tested for uniqueness. Activity patterns in beatsensitive regions should alter as a function of beat strength, eliciting greater dissimilarities between rhythms with different beat strength than between rhythms with similar beat strength. Indeed, mean activity patterns in the putamen and SMA were significantly dissimilar for strongbeat and non-beat conditions, and dissimilarity between activity patterns across all 12 rhythms correlated with beat strength models, not basic rhythmic features. Whole-brain analyses also identified beat-sensitivity in the IFG, and inferior parietal cortex. These findings build upon univariate work suggesting that motor and association regions are beat-sensitive.

A network of regions involved in rhythm and beat perception has been well-established across various fMRI experiments. Both monophonic rhythms (Grahn & Brett, 2007) and melodic rhythms (Matthews et al., 2020) are reliably associated with activity in the bilateral auditory cortex, insula, supplementary motor area (SMA), premotor cortex, basal ganglia, and cerebellum (Kasdan et al., 2022). Rhythms with a clear beat are typically associated with greater activity in the SMA and basal ganglia, suggesting a role in beat perception (Chen et al., 2008b, 2008a; Grahn & Brett, 2007; Matthews et al., 2020). However, most previous studies conduct univariate analyses, which detect regional activity changes that are averaged across voxels, but overlook fine-grained patterns of activation across voxels, which may encode or ‘represent’ stimulus features (Mur et al., 2009). Examining the neural representation may be especially important for studies of beat perception, as the basal ganglia and SMA also exhibit above-baseline univariate activity during perception of rhythms without a beat (though less than when a beat is present). This above-baseline activity suggests these areas are involved in rhythm perception more generally, which means that beat-sensitive regions may also encode rhythmic features (e.g., tempo, number of onsets). We specifically tested whether previously identified beat-sensitive regions encode only the presence or absence of beat (i.e., all strong-beat rhythms elicit similar patterns of response; Figure 1D), or if beat is represented in addition to rhythmic features (Figure 1F). Even more importantly, MVPA can discover regions in which the fine-grained patterns show clear beat sensitivity that is obscured by the averaging of univariate approaches. We therefore used MVPA to identify rhythm and beat-encoding regions across the whole brain that may have been overlooked by less-sensitive univariate analyses.

activity in each voxel. Small circles represent individual rhythms, larger clouds show mean groupings. A-C) Shows the importance of testing both item-wise and condition-wise activity patterns, which may be represented in multiple orientations. A) Highly-dissimilar item-wise distances, with no dissimilarity between condition-wise patterns. A region with this orientation is beat-sensitive at the item level, but not the condition level – strong-beat rhythms have highly correlated patterns, but each weak-beat rhythm has a unique activity pattern. B) Highlydissimilar condition-wise activity patterns, with some overlap between item-wise patterns. A region with this orientation is beat sensitive on average, but is not highly sensitive at the itemlevel. C) Highly-dissimilar condition-wise and item-wise activity patterns. A region with this orientation is highly sensitive to the beat, and activates in distinct patterns for rhythms of

different beat strength. Similar beat-strength rhythms elicit similar activity patterns. D-F) Shows the importance of testing between-condition distances against within-condition distances. Between-condition distances (dashed lines) connect blue (Strong-beat) and red (Weak-beat) conditions to each other. Within-condition distances (solid lines) connect only red, or only blue, dots to each other. In all 3 panels, significant between-condition distances would be found: average distances between blue and red dots would be greater than 0. However, beat encoding is only present in D and F, as the between-condition distances are greater than the within-condition distances, on average. E) A region that activates in a unique pattern for each rhythm, and does not represent the beat; Between-condition distances are equal to the within-condition distances.

Reports across several cognitive domains show that univariate activity does not necessarily reflect neural encoding of features within a region (Berlot et al., 2020; Popov et al., 2018; Wiestler & Diedrichsen, 2013). Univariate analyses average the overall magnitude of signal across voxels in a region, and ask whether there is more or less signal for a task, or between experimental conditions: A brain region with above-baseline signal is likely to be involved in a task, and a region that has greater signal in a certain experimental condition is interpreted as being more involved in that condition. However, univariate analyses overlook slight activation variability across multiple voxels: These relatively small signal changes across multiple voxels may combine to create reliable spatially-distributed activity patterns that encode more specific features (Weaverdyck et al., 2020), such as differences in beat strength between two rhythms. In visual perception, distinct activation patterns are found between categories of pictures (e.g., faces, animals, and objects), even when the maximally-active voxels (i.e., those that would drive univariate findings) for the categories are removed (Haxby et al., 2001). In

Hoddinott & Grahn 6 some cases, uninformative univariate outcomes have been better characterized using multivariate pattern analysis (MVPA). For example, when learning motor sequences, average regional activity may increase or decrease across training, but multivariate activity patterns for each motor sequence become more distinct from each other, suggesting the neural representation of trained motor sequences is strengthened (Wiestler & Diedrichsen, 2013). In all cases, univariate analysis is an appropriate tool for identifying regions involved in a task, however, MVPA is better equipped to characterize how information is represented in an involved region (Mur et al., 2009). Although several neuroimaging studies have shown motor region involvement during rhythm and beat perception, to date none have examined how rhythms are represented in regional activity patterns. For example, certain brain areas may be sensitive only to the presence or absence of a beat, or they may also encode additional rhythmic features.

One method to characterize neural representations in fMRI is representational similarity analysis (RSA). RSA operates under the assumption that neurons, and more widely neuronal populations, are tuned to specific stimulus features. For example, a neuron in the visual system may fire rapidly for horizontal lines, but returns to baseline for vertical lines, showing specific tuning to line orientation (Albright, 1984), whereas a neuron in the auditory cortex may fire specifically for sound frequencies near 440Hz, but not for sounds at other frequencies (Bendor & Wang, 2005). To communicate information downstream, any ‘tuned’ region must output activity in a manner that is consistent and sufficiently distinct to be decoded by the region receiving activity as input. In this way, a region tuned to a stimulus will exhibit an activity pattern unique to that stimulus, and the activity pattern should be sufficiently discriminable from patterns associated with other stimuli. Compared to single-neuron recordings, fMRI has a coarser spatial resolution, but it can still show differences in the tuning of large populations of neurons to a task,

stimulus, or a combination of stimulus features. Thus, RSA poses that encoding can be measured by the relative dissimilarity (i.e., the ‘decodability’) between activity patterns for any stimulus that differs along the encoded feature (Kriegeskorte et al., 2008). For example, a region that encodes beat strength may exhibit dissimilar activity patterns in response to rhythms that have a strong beat versus no beat, but similar patterns for different rhythms with similar beat strength. Therefore, RSA can measure the relative dissimilarity between multi-voxel activity patterns associated with individual rhythms and determine how stimulus features (such as beat strength) are represented across different regions of the rhythm perception network.

Evidence outside of music neuroscience suggests that regions related to rhythm perception may encode temporal features, even beyond the auditory modality. In motor sequencing studies, premotor cortices and the SMA exhibit distinct activation patterns for learned finger-press sequences. Importantly, the timing and the spatial features (i.e., the order of finger presses) of the sequences are independently represented in the SMA and premotor cortex – decoders trained on either timing or spatial features of motor sequences successfully classified activity patterns in SMA and premotor cortex (Kornysheva & Diedrichsen, 2014). Moreover, the SMA encodes temporal intervals in a ‘chronotopic map’ such that relative durations between visual stimuli activate small, distinct topographic regions across the cortex (Protopapa et al., 2019), akin to the ‘tonotopic’ maps of pitches in auditory cortex (Humphries et al., 2010). The SMA also encodes metronome-synchronized tapping tempo via the firing rate patterns of neuronal populations in non-human primates (Gámez et al., 2019), suggesting the patterns of activity in the SMA are sensitive to temporal information at the neuronal population level. Because the SMA and premotor cortices are sensitive to temporal information across many tasks and modalities, these motor regions are likely responsible for encoding acoustic rhythms,

Hoddinott & Grahn 8 regardless of beat presence. Indeed, in one rhythm perception study, a linear classifier accurately identified which rhythm was played to participants based on SMA or premotor cortex activity patterns (Notter et al., 2019). The classifier was trained and tested on fMRI data from participants listening to two short rhythms and a metronome. The training data set was played at different tempi from the test set, suggesting that the rhythmic pattern itself (i.e., the relative timing of notes, not their absolute durations) was encoded in SMA and premotor cortex activity patterns (Notter et al., 2019). This evidence suggests the SMA and premotor cortices activate in different multi-voxel patterns for different rhythms, regardless of tempo. However, both rhythms used in the previous experiment were metric, and could elicit the feeling of a beat. Thus, it is not clear whether the SMA or premotor cortex only encode strong-beat rhythms, or if any rhythm, including irregular non-beat rhythms, elicits unique activation patterns in these regions. Based on previous univariate work, the SMA and premotor cortex have above-baseline activity for all rhythms, regardless of the beat, suggesting that individual rhythms may be encoded in these regions, regardless of beat strength. However, the SMA does appear beat-sensitive, with greater overall activity for rhythms with a strong-beat, compared to weak- or non-beat rhythms (Grahn & Brett, 2007). However, as detailed above, univariate activity does not reveal how information is represented in a region. Thus, more evidence is needed to characterize the neural representation of rhythm and beat in the human brain to determine whether regions in the rhythm perception network alter activity patterns based on beat strength, or other rhythmic features.

In this experiment, we characterized the neural representations of rhythm and beat perception using RSA and high-resolution 7-Tesla fMRI. In a single scanning session, participants completed 8 runs of a rhythm discrimination task. The rhythm discrimination task required listening to a short, ~3-second, rhythm twice, and then deciding if a third rhythm was

the same as or different from the previous two. We used a set of 12 unique rhythms taken from previous beat perception work (Grahn & Brett, 2007). Of the 12 rhythms, 4 had a strong beat, 4 had a weak beat, and 4 had no beat. Using classic univariate analysis, we predicted a replication of previous findings, with activation in motor and auditory regions during rhythm perception. We also predicted greater univariate activation in the basal ganglia and SMA for strong-beat rhythms compared to weak- and non-beat rhythms (Grahn & Brett, 2007). Using RSA, we predicted that univariately activated regions would exhibit highly dissimilar multivariate patterns between all rhythms. However, we also predicted that regions sensitive to the beat would show greater dissimilarity between strong-beat and weak- and non-beat rhythms, compared to withincondition dissimilarities (e.g., the dissimilarity between patterns for the 4 strong-beat rhythms). Univariate contrasts indeed replicated previous findings of motor and auditory activation when listening to rhythms, and greater activity in the basal ganglia for strong-beat rhythms compared to other conditions. Representational similarity analysis showed that motor and auditory regions encoded the different rhythms in multi-voxel activity patterns. However, the SMA and putamen appeared to have distinct activity patterns for rhythms differing in beat strength, with activity patterns becoming increasingly dissimilar as a function of beat strength, overall suggesting that the SMA and putamen are indeed sensitive to the beat.

as metal in the body or a history of claustrophobia. All participants were compensated for their time monetarily and procedures were approved by the Health Sciences Research Ethics Board at Western University.

To test for differences between musicians and non-musicians, the sample was divided into 2 groups using a mean split on years of music playing. The musician group had 11 participants with higher-than-average years of music playing (M = 11.82 years, SD = 2.32 years). The remaining 15 participants were included in the non-musician group, and reported lowerthan-average years of music playing (M = 2.39 years, SD = 1.94 years).

(Kriegeskorte et al., 2008). If activity patterns for two stimuli are highly dissimilar, that brain region likely encodes information contained in those stimuli, and it may especially ‘tune’ to the differences in features between those stimuli, such as the strength of the beat. Thus, we were interested in how distinct, or dissimilar, activity patterns were between beat strength conditions both at the individual rhythm level, and at the mean activity level for each condition. Alternatively, rhythm-encoding regions may not tune to beat strength, and may have unique activity patterns both within and between beat strength conditions. To accurately characterize the representational structure of activity patterns within a region, we performed MVPA on the itemwise activity patterns – examining pattern dissimilarities between each pair of the 12 rhythms – and on the mean activity patterns between conditions – examining pattern dissimilarities collapsed across rhythms of the same beat strength. Mean pattern dissimilarity is a necessary complement to interpret the between-condition dissimilarities of the item-wise analysis, which may be driven by more dispersed patterns surrounding an overlapping mean pattern between conditions (i.e., Figure 1B). Essentially, the mean activity pattern for two conditions may be highly similar (overlapping), but large dissimilarities between item-specific patterns can still exist, falsely inflating dissimilarities between conditions and appearing to be beat-sensitive. For our purposes, mean pattern dissimilarity suggests a region encodes beat strength, but does not test whether other features of the rhythms are encoded.

Item-Wise General Linear Model. For the item-wise multivariate analysis, a first-level general linear model (GLM) was implemented independently from the univariate GLM. For each session, independent regressors were entered for each of the 12 rhythms and aligned to the onset and duration for the first and second presentations in each trial. As in the univariate GLM, the target rhythm, button response, and 6 movement regressors were also entered. All trial regressors

were created using an on-off boxcar method convolved with a canonical hemodynamic response function. This analysis resulted in eight baseline-corrected (beta) images for each rhythm (one per session), for a total of 96 images.

Condition-Wise General Linear Model. The condition-wise multivariate analysis was performed identically to the item-wise analysis, except for the regressors entered into the first-level GLM. Here, an independent regressor was entered for each of the 3 beat strength conditions, aligned to the onset and duration for the first and second presentations in each trial. As in the univariate GLM, the target rhythm, button response, and 6 movement regressors were also entered. All trial regressors were created using an on-off boxcar method convolved with a canonical hemodynamic response function. This analysis resulted in eight baseline-corrected (beta) images for each beat strength condition (i.e. 3 condition-mean images for each of 8 runs), for a total of 24 images. The condition-wise GLM was therefore identical to the univariate GLM, except that it was performed on unsmoothed native-space functional images.

Representational Similarity Analysis. To characterize the neural representations of rhythm, we used representational similarity analysis (RSA), a technique that tests for the encoding specificity of regional activity by comparing the dissimilarity between multivariate activity patterns elicited by each stimulus (Kriegeskorte et al., 2008). We were interested in how distinct, or dissimilar, patterns were between individual rhythms, as well as between beat-strength conditions.

patterns, rather than a discretized classification accuracy, and is therefore informative about how much dissimilarity exists between activity patterns. To calculate the crossnobis distance, each stimulus was assigned a BOLD activity pattern consisting of beta weights from the first-level GLM for each voxel within an ROI or searchlight (see below). For each of the 8 imaging runs, the activity patterns were multivariate noise normalized using the variance-covariance matrix of the first-level GLM residuals (Walther et al., 2016). Multivariate noise normalization downweighs the contribution of voxels relative to their residual variance (variance-covariance diagonal) and its correlational structure with other voxels included in the matrix (variancecovariance off diagonal). Because noise can be unique to each run, multivariate noise normalization was performed for each of the 8 functional runs independently.

Noise-normalized activity patterns were cross-validated using a leave-one-run-out approach. To cross-validate, distances between activity patterns were averaged across all but one imaging run. The distance was also calculated between activity patterns for the left-out run. Next, the inner product of the run-averaged distance and the left-out run distance vectors was calculated. The inner product reveals the consistency and magnitude of the two distance vectors, with 0 meaning no dissimilarity, and a possibility for negative distance if the vectors are in different spatial orientations – suggesting the dissimilarity is highly inconsistent across runs. The cross-validation steps are repeated by switching the left-out run on each iteration until all 8 runs were left out. The average of the 8 resulting inner products for each stimulus pair was taken as the cross-validated distance. Thus, each ROI and searchlight center exhibited 66 crossnobis distances per scanning session. Multivariate pattern analysis was performed in Matlab using the rsa toolbox (Nili et al., 2014), pcm toolbox (Diedrichsen et al., 2018), and custom code.

Region of Interest (ROI) Definition. Left and Right pallidum, putamen, caudate, and SMA were the regions of interest. Binary masks were created in MNI space using anatomically-defined regions from the AAL3 atlas (Rolls et al., 2020). Masks were then warped from MNI space to each subject’s native space using SPM12 deformation tool and the inverse of the affine transformation matrix generated from the normalization step (see preprocessing). All nativespace ROIs were visually inspected for accuracy.

Whole-Brain Volumetric Searchlight. To examine activity patterns across the whole brain, a volumetric searchlight was employed to test pattern dissimilarities in overlapping small spherical ROIs. The volumetric searchlight considered data from small spheres of 160 voxels across each subject’s whole brain in native space. Each voxel in the functional mask was used as a searchlight center. For each searchlight center, the nearest 160 voxels were considered for the activity pattern calculation. If a minimum of 160 voxels were not present in a sphere surrounding the searchlight center (e.g., on the edges of the functional mask), voxels nearest to the center (calculated by Euclidean distance, up to a maximum 30mm radius) were added to the searchlight until ~160 voxels were present. For each searchlight, multivariate noise normalization and dissimilarity metrics were applied. Thus, this technique returned 66 pairwise distances for each searchlight center across the whole brain.

For group-level analysis of the whole-brain searchlight, all averaging of the crossnobis distances (see results) was performed in native-space, creating whole-brain average crossnobis distance maps for each subject. Average crossnobis distances more than 4 times the interquartile range were removed from the wholebrain maps for each subject. The average crossnobis distance maps were then warped to MNI space for group-level testing. For the feature-encoding analysis (see below), a group-level map of possible beat-encoding regions was reverse-warped from MNI

score (C-Score) model from Povel & Essens (1985). Counterevidence scores were calculated for each rhythm using a 4/4 meter. Unlike the hierarchical beat strength model, the C-Score model takes into account the beat strength of each individual rhythm.

Using Pearson’s r, the 9 models were correlated with neural RDMs for each subject and ROI. Thus, a distribution of 26 r-values was created for each model and ROI. To establish the expected correlation value of a successful model, we calculated upper- and lower-bounds of the noise ceiling independently for each ROI. Noise ceilings estimate the range within which the true explanatory model (i.e., a perfect model containing all features encoded by a region) can be expected to relate to the data, given the inter-subject variability in the sample (Lage-Castellanos et al., 2019). Thus, representational models that have correlations within the noise ceiling are likely to be an accurate estimate of the true representational structure of a region. Noise ceilings were created using a leave-one-subject-out approach (Nili et al., 2014). For the lower bound, each subject’s neural RDM was correlated with the group-averaged RDM with that subject left out. The left-out subject was rotated until all subjects had been left out once. The lower-bound of the noise ceiling is the average of each subject’s correlation with the group. The noise-ceiling upper-bound is calculated in the same way as the lower-bound, except that the “left-out” subject is still included in the group-averaged RDM, increasing the correlation between each subject and the group RDM.

model was not significantly more correlated than the Non Beat (t(25) = 1.67, p = .11) or Beat Hierarchy (t(25) = .91, p = .37) models in the right SMA. Thus, in left and right SMA, the CScore model best explains the neural RDMs, suggesting that the SMA encodes beat strength on a rhythm-by-rhythm basis, beyond that explained by basic rhythm features or categorical beat strength.

Model RDM correlations were also calculated in the left and right putamen, which appeared beat sensitive in previous analyses. Similar to the SMA, the C-Score model was the winning model in the left and right putamen (Figure 2). However, because the noise ceiling crosses r = 0 (suggesting high inter-subject variability), we did not statistically test the strength of this model compared to others.

condition > 0] searchlights. Heat map indicates strength of the t-test, indicating areas that encode rhythmic features. Insets: Group mean and standard error of Pearson correlations for each representational model. White, light grey, and dark grey bars represent basic features, conditionspecific, and beat strength models, respectively. Left and right supramarginal gyri (SMG), premotor cortex (PMC), inferior parietal lobe (IPL), and inferior frontal gyri (IFG) were most correlated with models of beat strength. Cerebellum lobule VI (*n = 25) was most correlated with the tempo, Strong-beat, and beat hierarchy models. Cerebellum lobule VIII (*n = 19) was most correlated with the Non-beat model. Several regions in the temporal lobe did not have a successful model fit (not shown).

L Precentral Gyrus 9 Strong-beat, Non-beat, Beat Beat Hierarchy

Hierarchy, C-Score SMA 6 Beat Hierarchy, C-Score C-Score .11 R Parahippocampal Gyrus 8 Onsets, Non-beat Onsets .048 R Inferior Frontal Operculum 1 Strong-beat, Non-beat, Beat Beat Hierarchy .085

Hierarchy, C-Score R Inferior Frontal Triangularis 1 Non-beat, Beat Hierarchy, C-Score C-Score .073 R Inferior Frontal Orbital Cortex 1 Strong-beat, Beat Hierarchy, C-Score C-Score .086 R Precentral Gyrus 1 Beat Hierarchy, C-Score Beat Hierarchy .098 R Insular Cortex 1 Tempo, Beat Hierarchy, C-Score C-Score .067 R Superior Temporal Pole 1 Onsets, Tempo, Strong-beat, Beat Tempo .061

Hierarchy, C-Score R Middle Temporal Gyrus* 1 Strong-beat, Beat Hierarchy, C-Score C-Score .096 R Supramarginal Cortex 1 Non-beat, Beat Hierarchy, C-Score C-Score .083 L Inferior Frontal Triangularis 2 Non-beat, C-Score C-Score .078 L Inferior Frontal Operculum 2 C-Score C-Score .070 L Postcentral Gyrus 2 C-Score C-Score .12 L Inferior Parietal Lobe 2 C-Score C-Score .083 L Supramarginal Gyrus 2 C-Score C-Score .10 R Fusiform Gyrus 3 Non-beat Non-beat .047 R Cerebellum Lobule VI* 3 Tempo, Strong-beat, Beat Hierarchy Tempo .039 R Cerebellum Lobule VIII* 3 Non-beat Non-beat .085 R Primary Visual Cortex 7 Non-beat Non-beat .029 Note: Regions with a noise ceiling crossing 0, or with no model breaching the lower bound of the noise ceiling are not reported. *Regions with missing data: Middle temporal gyrus (n = 24), cerebellum lobule Mean

Fit (Mr) .10 VI (n = 25), cerebellum lobule VIII (n = 19).

In motor areas, significant searchlights were found in left and right premotor cortices (precentral gyri and left postcentral gyrus), and in the SMA. In the left premotor cortex (precentral gyrus), the Strong Beat, Non Beat, Beat Hierarchy, and C-Score models breached the lower bound of the noise ceiling, suggesting the left premotor cortex is sensitive to beat strength. Paired sample t-tests between each of these models revealed no differences between these models (p’s > .053). In the left postcentral gyrus, only the C-Score model breached the noise ceiling. In the right premotor cortex, (precentral gyrus), the Beat Hierarchy and C-Score models SD .15 .19 .12 .14 .19 .13 .18 .13 .15 .13 .17 .22 .20 .19 .20 .20 .13 .14 .16 .16

breached the noise ceiling. Comparisons between these models revealed no significant difference (p = .68). In the SMA, similar to the a priori SMA ROI, the Beat Hierarchy and C-score models breached the noise ceiling, but were not significantly different from each other, (p = .60).

The right inferior frontal gyrus was parcellated into the operculum, triangularis, and orbital cortex. In the right inferior frontal operculum, the Strong Beat, Non Beat, Beat Hierarchy, and C-Score models all breached the noise ceiling. Comparisons between these models revealed no significant differences (p’s > .14). In the right inferior frontal triangularis, Non Beat, Beat Hierarchy, and C-Score models all breached the noise ceiling. Comparisons between models revealed no significant differences between mean correlations of these three models (p’s > .58). In the right inferior frontal orbital cortex, Strong Beat, Beat Hierarchy, and C-Score models all breached the noise ceiling. Comparisons between models revealed that the mean correlation of the C-Score model was marginally greater than the Strong Beat model (t(25) = 1.81, p = .08). No other significant differences were detected (p’s > .11). In the left hemisphere, the inferior frontal gyrus only covered the triangularis and operculum. In the left inferior frontal triangularis, the Non Beat and C-Score models breached the noise ceiling. Comparisons between models revealed no significant differences between models (p = .87). In the left inferior frontal operculum, only the C-Score model breached the noise ceiling. Overall, this suggests that the right and left inferior frontal gyri encode beat strength, possibly on the individual rhythm level. In the right insular cortex, Tempo, Beat Hierarchy, and C-Score models breached the noise ceiling. Comparisons between these models revealed no significant differences between models (p’s > .56)

The temporal lobe had significant searchlights throughout auditory cortices, but many did not have a model of good fit. However, the right superior temporal pole, and the right middle

Hoddinott & Grahn 37 temporal gyrus were correlated with feature-encoding models. In the right superior temporal pole, the Onsets, Tempo, Strong Beat, Beat Hierarchy, and C-Score models breached the noise ceiling. Comparisons across these models revealed no significant differences (p’s > .28). In the right middle temporal gyrus, the Strong Beat, Beat Hieararchy, and C-Score models breached the noise ceiling. Comparisons across these models revealed no significant differences between models (p’s > .13). In the right parahippocampal gyrus, the Onsets model and Non Beat model breached the noise ceiling, but were not significantly different (t(25) = .50, p = .62).

In the left inferior parietal lobe, dorsal to the supramarginal gyrus, only the C-Score model breached the noise ceiling, suggesting the inferior parietal lobe encodes beat strength at the individual rhythm level. In the left supramarginal gyrus, only the C-Score model breached the noise ceiling. In the right supramarginal gyrus, the Non Beat, Beat Hierarchy, and C-Score models breached the noise ceiling. Comparisons across these models revealed no significant differences between models (p’s > .32).

In the right cerebellum, lobules VI and VIII had significant searchlights. In right lobule VI, the Tempo, Strong Beat, and Beat Hierarchy models breached the noise ceiling. Comparisons across these models revealed no significant differences between model fits (p’s > .79). In right lobule VIII, only the Non Beat model breached the noise ceiling. This suggests that lobule VIII encodes non-beat rhythms differently from all other rhythms.

In the right primary visual cortex and right fusiform gyrus, only the Non Beat model breached the noise ceiling.

difficult to interpret through the lens of previous univariate work – as the current study used a more repetitive task design, and an MRI scanner with greater field strength (7 T vs. 3 T), which can impact signal-to-noise ratios (Triantafyllou et al., 2005). Despite null effects in the caudate and pallidum, the current study builds on previous univariate findings (Grahn & Brett, 2007; Chen et al. 2008a; 2008b): It is the first to show that the SMA and putamen encode rhythms via multi-voxel activity patterns, and that these patterns are dictated by beat strength – individual rhythms elicit unique activity patterns, and the magnitude of dissimilarity between activity patterns matches the relative differences in beat strength between rhythms.

In addition to anatomically defined ROIs for the SMA and basal ganglia, rhythm- and beat-encoding regions across the brain were identified using a whole-brain searchlight. Rhythmencoding regions are those that activate in unique activity patterns for each individual rhythm, regardless of beat strength (detected by within-condition dissimilarity). Beat-encoding regions have highly dissimilar activity patterns between beat strength conditions, but not necessarily within a beat strength condition. The item-wise activity patterns revealed that rhythms are encoded in auditory and motor regions across the brain. Significant within-condition distances were found in the left and right inferior frontal gyrus, premotor cortex, temporal pole, superior temporal gyrus, medial temporal lobe, medial temporal gyrus, and cerebellum. These regions align well with the univariate activation both here (in the all Rhythms > rest contrast), and in previous work (Chen et al., 2006, 2008b, 2008a; Grahn & Brett, 2007; Grahn & McAuley, 2009; Grahn & Rowe, 2009; Grahn & Schuit, 2012; Hoddinott et al., 2021; Kung et al., 2013; Matthews et al., 2020). As expected, between-condition distances, which may reflect sensitivity to the beat, revealed encoding in areas overlapping with the individual rhythm-encoding areas.

Left and right inferior frontal gyri, medial frontal gyri, SMA, premotor cortices, left insula, left

Hoddinott & Grahn 40 and right auditory cortex, left inferior parietal lobe, and the right cerebellum activated in patterns that were significantly dissimilar between beat strength conditions. To test whether any of the individual rhythm-encoding regions were more sensitive to beat strength than individual rhythms (which would elicit large within- and between-condition distances), the between-condition distances were tested against the within-condition distances. No regions were identified as more sensitive to strong-beat vs. weak-beat rhythms than to individual rhythms. However, at a more liberal statistical threshold (p < .001), in the left and right SMA, left and right inferior frontal gyri, left post-central gyrus, left and right precentral gyrus, left putamen, left superior temporal gyrus, left inferior parietal lobe, and the left paracentral lobule, distances between strong-beat and non-beat rhythms were greater than distances within strong-beat and non-beat conditions. That is, activity patterns in some a priori regions of interest, including SMA, and in other wholebrain identified regions, such as premotor cortex and parietal regions, were more sensitive to the differences in beat strength than simply individual rhythms, or differences in rhythmic features that were controlled across beat strength conditions (i.e., the within-condition distances).

Finally, to determine whether regions identified in the searchlight encode beat strength or basic rhythm features, we performed the feature-encoding model analysis to the searchlights in regions with [between condition distances > 0]. Activity patterns in the left and right premotor cortex were most correlated with beat strength models, including the Beat Hierarchy model in the left premotor cortex, and the C-Score model in the right premotor cortex. Searchlights in the SMA reflected what we found in the a priori SMA ROIs: activity patterns correlated most with the C-Score model of beat strength. Left and right inferior frontal gyri activity also correlated with beat strength models, including the C-Score and beat hierarchy models. Altogether, the left and right premotor cortex, SMA, and inferior frontal gyri all correlated most with models of beat

Hoddinott & Grahn 41 strength, suggesting these regions are sensitive to the differences in beat strength between rhythms. Activity patterns in the left and right supramarginal gyrus were also most correlated with models of beat strength, specifically the C-Score model. In the temporal lobe, many regions had no winning model. Early auditory cortical regions, such as Heschl’s gyrus, may encode each sound with a unique activity pattern, and may not distinguish rhythms along the features for which we made distinct models. Activity patterns in the right superior temporal pole correlated with multiple models, including the Onsets, Tempo, Strong-beat, Beat Hierarchy, and C-Score models, though numerically the tempo model was the model of best fit. This is perhaps indicative of auditory regions encoding many basic and non-basic stimulus features. Similarly, activity in the right insula was correlated with the Tempo, Beat Hierarchy, and C-Score models, though C-Scores were the model of best fit.

Here, we identified the SMA, putamen, right premotor cortex, inferior frontal gyri, supramarginal gyri, and left inferior parietal lobe as beat-strength encoding regions, each of which fit well with previous univariate work in rhythm and beat perception. Previous studies report an identical rhythm listening network as reported here: Left and right auditory cortices, SMA, basal ganglia, premotor cortices, and cerebellum all activate during rhythm listening (Grahn & Brett, 2007; Chen et al., 2008a; 2008b), and report univariate activation of the SMA and putamen correlated with beat strength – strong-beat rhythms elicit greater overall activity than weak- and non-beat rhythms (Grahn & Brett, 2007). These findings were replicated with our data, except for the effect of beat strength in the SMA – no differences were found univariately between beat strength conditions, however, our data revealed multivariate encoding of beat strength in the SMA. The lack of a univariate effect of beat strength in the SMA may be due to the high level of stimulus repetition in the current study. Crossnobis distance calculation requires

Hoddinott & Grahn 42 many presentations of stimuli across fMRI runs. Therefore, to maximize signal-to-noise, only 12 rhythms were used here, compared to previous studies that used 90 unique rhythms (30 from each beat strength condition). Thus, particularly by the end of the experiment, participants may have recognized the rhythms, and had an attenuated univariate response in the SMA. This explanation is likely, as multivariate pattern analyses are known to be resilient to broad changes in univariate activation (Haxby et al., 2001; Weaverdyck et al., 2020), and despite a lack of univariate differences between beat strength conditions, the multivariate analysis still revealed SMA activity to be sensitive to the beat, as the magnitude of activity pattern dissimilarity correlated with differences in beat strength between individual rhythms.

The inferior frontal cortex had significant between-condition distances and appeared to encode beat strength. This finding aligns well with previous univariate work that used the same beat strength conditions, and reported greater activation in overlapping coordinates in the inferior frontal gyrus for strong-beat rhythms compared to weak- and non-beat rhythms (Grahn & Brett, 2007), perhaps revealing a beat-sensitive region that has not been thoroughly explored in rhythm perception. Outside of rhythm perception work, studies using naturalistic music have shown that the inferior frontal gyrus is more active when people listen to music, compared to amusical control conditions (Levitin & Menon, 2003), a contrast that may also reveal areas active for beat vs. no-beat stimuli. The inferior frontal gyrus also activates when there is rhythmic tension in music, and when subjects are tapping a steady beat during a rhythm with high counter-evidence for that beat (Vuust et al., 2006, 2011). Rhythmic tension fits well with the current finding that activity patterns in the inferior frontal gyrus correlates with beat strength. However, frontal regions are also involved in attention, both in music perception (Janata et al., 2002) and nonmusical domains (e.g., Cazzoli et al., 2021). Attention-related activation of the inferior frontal

gyrus may be an alternative explanation of the correlation with C-Score models in the current study, and with rhythmic tension found in previous studies: Rhythms with a weak or no beat, and/or with high rhythmic tension, may require increased attention to perform the task. Future studies may better understand rhythm encoding in frontal regions by manipulating beat strength, attention, and rhythmic tension orthogonally.

Representations of rhythm in the left and right inferior parietal lobes were most correlated with the beat strength counterevidence score model, compared to other models. The left and right supramarginal gyri (SMG) had significant between-condition distances, and neural representations were most correlated with models of beat strength. The supramarginal gyrus has been reported active for rhythm perception compared to silence, and for highly complex compared to simpler rhythms (Kasdan et al., 2022). One study reported that SMG activity is lateralized, with the left SMG responding to changes in pitch, and the right SMG responding to rhythm (Schaal et al., 2017), though there is also evidence that musicians recruit the right SMG for pitch recognition tasks (Schaal et al., 2015). Here, we did not manipulate pitch, and we found that SMG encoding was related to beat strength in both hemispheres. The SMG may encode sequential order. One TMS study reported that downregulation of the left SMG increased participants’ reporting of memorized verbal and visual sequences in the incorrect order, but did not increase the total number of errors compared to a sham condition, with no stimulation (Guidali et al., 2019). This suggests the SMG is necessary to encode the order of sequential stimuli, such as a list of letters, but not the content – which letters were in the list. However, if the supramarginal gyrus only encodes sequential order, one would expect similar encoding of all rhythms in the current study – each rhythm had a unique order of intervals. Instead, we found

that left and right supramarginal correlated most with counterevidence score models of beat perception.

Though beat-sensitivity was found bilaterally in the SMG, in the left hemisphere only, the between-conditions cluster extended dorsally from the SMG, crossing the intra-parietal sulcus and then medially into the inferior parietal lobe. Similar to the SMG, representations of rhythm in the ventral left inferior parietal lobe were most correlated with the beat strength counterevidence score model. Theoretical models of beat perception predict the inferior parietal lobe to play a role (Patel & Iversen, 2014). Specifically, the parietal lobe’s position in the dorsal auditory stream makes it a good candidate for crosstalk between auditory and motor regions. It has been proposed that the parietal lobe encodes rhythmic information, and may facilitate motor predictions of upcoming acoustic events, as predicted by the Action Simulation for Auditory Prediction (ASAP) hypothesis (Patel & Iversen, 2014), as well as recent motor physiological explanations for the role of the motor system in beat perception (Cannon & Patel, 2021). Empirical evidence also suggests a role for the parietal cortex in beat perception – downregulation of left posterior parietal cortex with transcranial magnetic stimulation (TMS) disrupts beat-based timing, but not absolute interval timing, suggesting left parietal cortex plays a role in beat-related behavior (Ross et al., 2018). Because the current task did not require explicitlytimed motor responses, our findings expand on previous brain stimulation experiments by showing that parietal cortex activity correlates with beat strength in rhythms during perception without action.

The regions we found that encoded rhythm, but were not sensitive to the beat, also align with previous research. The cerebellum is commonly found to be active in rhythm and timing

Hoddinott & Grahn 45 perception, encoding the absolute duration of intervals (Grube et al., 2010; Teki et al., 2011) as opposed to the relative duration between two intervals (e.g., encoding intervals in a rhythm relative to the underlying beat interval). Indeed, TMS stimulation of the cerebellum affects estimation of single-interval durations in tasks requiring absolute interval encoding (Lee et al., 2007). Our finding that the cerebellum lobule VI represents rhythms according to their overall tempo aligns well with an absolute timing process: Rhythms of different tempi must also have intervals of different absolute duration. It then makes sense that cerebellar activity patterns are highly dissimilar from each other when rhythms are made up of intervals that have different absolute durations. In cerebellum lobule VIII, we found that activity patterns differentiated nonbeat rhythms from all other rhythms (the Non-beat condition-specific model). This may also be explained by absolute timing in the cerebellum – the non-beat condition was the only condition in which rhythms included non-integer ratios. These non-integer ratios are impossible to encode relative to other durations, such as a beat or by subdividing longer intervals in the same rhythm. Thus, to encode non-beat rhythms absolute timing must be used. Cerebellum lobule VIII correlated most with the Non-beat condition specific model, which may indicate activation for rhythms that require absolute timing strategies.

Many searchlights throughout the auditory cortex represented individual rhythms. Bilateral STG, Heschl’s gyrus, temporal poles, and other auditory regions revealed significantly dissimilar activity patterns across rhythms. However, we were not able to create a sufficient model to explain which features of the rhythms were represented in the auditory cortex. Auditory areas may encode many features of the rhythms and sounds, so many that we cannot create a single model to capture this representation. Notably, the noise ceiling in auditory cortex is quite high, and does not show large variability between subjects – the upper and lower bounds are

Hoddinott & Grahn 46 relatively narrow. This suggests that even though our models do not sufficiently explain the representations of rhythm in the auditory cortex, activity patterns are quite reliable across subjects. More work is needed to reveal how rhythmic acoustic stimuli are represented in auditory cortex. Future studies may consider using larger, feature-rich stimulus sets, as opposed to the highly-controlled rhythms used in the current experiment. For example, some work has been performed using naturalistic music and speech (Norman-Haignere et al., 2015), but more can be done to specifically target beat strength using naturalistic music.

In conclusion, this experiment is the first to show that the SMA and putamen activate in highly distinguishable multi-voxel patterns for rhythms of different beat strength. The greater the difference in beat strength between two rhythms, the more dissimilar the activity patterns are for each of the rhythms. Through exploratory analyses, we also found that beat strength is represented in this same fashion in the left inferior parietal lobe, and in the right premotor cortex, though to a weaker degree relative to the SMA and putamen. Lastly, cerebellum activity patterns were altered most by tempo, suggesting the cerebellum may be tuned to overall rate of rhythms.

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