The right inferior frontal gyrus processes nested non-local dependencies in music

Complex auditory sequences known as music have often been described as hierarchically structured. This permits the existence of non-local dependencies, which relate elements of a sequence beyond their temporal sequential order. Previous studies in music have reported differential activity in the inferior frontal gyrus (IFG) when comparing regular and irregular chord-transitions based on theories in Western tonal harmony. However, it is unclear if the observed activity reflects the interpretation of hierarchical structure as the effects are confounded by local irregularity. Using functional magnetic resonance imaging (fMRI), we found that violations to non-local dependencies in nested sequences of three-tone musical motifs in musicians elicited increased activity in the right IFG. This is in contrast to similar studies in language which typically report the left IFG in processing grammatical syntax. Effects of increasing auditory working demands are moreover reflected by distributed activity in frontal and parietal regions. Our study therefore demonstrates the role of the right IFG in processing non-local dependencies in music, and suggests that hierarchical processing in different cognitive domains relies on similar mechanisms that are subserved by domain-selective neuronal subpopulations.

3 grammaticality of at least 9 out of 10 test sequences in two consecutive blocks. Participants who reached level four were invited to the scanning session. The experiment was over if the participant did not progress after 20 blocks. Each block started with a visual instruction (3 s) to attend to the training sequences. A trial began by displaying the sequence number (1.2 s), followed by the playback of a grammatical sound sequence and the replacement of the text by a fixation cross at the centre of the screen. Afterwards, another visual instruction was given (3 s) to judge the grammaticality of 10 subsequent test sequences, of which 5 were ungrammatical. Grammaticality of the test sequences was pseudo-randomised, such that there could only be at most two successive presentations of sequences with identical grammaticality, and the two types of violations for ungrammatical sequences were roughly balanced. Following a fixation cross (1.2 s) and the ensuing stimulus, participants were given a time window (3 s) to respond to a question (Did the sequence correspond to the rule?) by selecting either Yes (left arrow key) or No (right arrow key) on a computer keyboard. Key assignment was counterbalanced between participants. Visual feedback in the form of a smiley or sad emoticon was given (1.2 s), followed by a pause (0.75 s) and the next trial ensued.
To acquaint participants with the new response format (where the position of the grammatical response was now variable), participants heard 10 grammatical sequences with ZERO-, ONE-, and TWO-LoE and practiced the task on 30 new sequences prior to fMRI scanning.

Correlation of behavioural data
We also correlated our behavioural results with the number of days apart between sessions, reverse digit span (using PEBL 0.14 1 ), general musical sophistication, and the number of years of training in participants' most experienced instrument using Pearson's correlation.
These participant-characteristics constituted the family for which we applied Holm's method 2 to correct for multiple comparisons.

Supplementary Discussion
Grammaticality processing: dorsolateral PFC and pre-SMA As opposed to the functional activity of the right IFG (see main discussion), the current literature suggests that the involvement of the dorsolateral prefrontal cortex (dlPFC), presupplementary motor area (pre-SMA), and the anterior insular cortex (AIC) in grammaticality may rather be due to their complementary roles in cognitive control (cf. Cole and Schneider, 2007). Cognitive control processes dynamically assign mental resources to modify and control behaviour according to one's goals and intentions 4,5 . In the context of the present experiment, the dlPFC and pre-SMA may respectively supplement violation detection by enabling participants to (1) actively maintain task-relevant information, and (2) prepare and initiate the appropriate motor response. As in the main discussion, cognitive control signals generated by the dlPFC are said to activate representations of the incoming motifs, which can then be compared to determine whether the nested dependencies have been correctly resolved.
Second, pre-SMA activity has been implicated in the integration of sequential information in speech and music 6,7 , but also in other domains 8 , into higher-order schemas. Alternatively the pre-SMA could reflect the different brain states pertaining to the two grammaticality conditions in preparation for the subsequent behavioural response, as shown through its implication in the timing of self-initiated motor responses 9 and the maintenance of abstract contingencies in preparation for the selection of concrete motor responses [10][11][12] . Importantly, pre-SMA activity cannot reflect the actual motor response, as the position of the correct finger response was pseudo-randomly assigned across trials.
Grammaticality processing: middle temporal gyrus 6 The increased activity in the right posterior middle temporal gyrus (MTG) for ungrammatical against grammatical nested sequences is possibly due to the processing of meaning information. Although the observed co-activation of the MTG and the IFG echoes previous studies on violations to tonal harmony 13 and musical expectancy 14,15 , the MTG has typically been associated with the processing and storage of semantic information in music [16][17][18] and language [19][20][21][22] . On one hand, participants may have attributed semantic information to the nested sequences by assigning a unique internal representation for each motif to reliably discriminate between grammatical and ungrammatical sequences. On the other hand, music theorists (e.g. Meyer 23 ) have traditionally argued that musical meaning arises from the interplay of tension and relaxation across multiple levels of musical structure. Grammatical and ungrammatical nested sequences in the current experiment may have thus conveyed different musical meaning information through their respective fulfilment and deviation of predictions, as suggested from their behavioural data. The likelihood that the processing of nested hierarchical dependencies in music involves the dynamic integration of syntactic information in the IFG with semantic information in the MFG is increased by evidence on the regions' strong structural and functional tractography 24 .

Grammaticality processing: ventromedial prefrontal cortex
The ventromedial prefrontal cortex (vmPFC) was the only region that showed increased BOLD response to grammatical nested musical sequences compared to ungrammatical.
While this finding was unexpected, the vmPFC has been proposed to be involved in decisionmaking by encoding and updating the value of alternative outcomes [25][26][27] . We thus speculate that increased vmPFC activity for grammatical sequences reflects the confirmation reward received when the incoming motifs match participants' predictions.