Anna Fiveash
email: anna.fiveash@inserm.fr

Nathalie Bedoin

Philippe Lalitte

Barbara Tillmann

Rhythmic priming of grammaticality judgments in children: Duration matters

Keywords: rhythm, music, language, speech, reading age, temporal attention

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Accumulating evidence suggests that the neural mechanisms underlying temporal processing and temporal attention are similar for music and speech rhythm [START_REF] Fujii | The role of rhythm in speech and language rehabilitation: The SEP hypothesis[END_REF][START_REF] Tierney | Auditory-motor entrainment and phonological skills: Precise auditory timing hypothesis (PATH)[END_REF]. Rhythm in music is generally regular and stable, providing a highly predictive rhythmic context [START_REF] London | Hearing in time: Psychological aspects of musical meter[END_REF][START_REF] Mcauley | Tempo and rhythm[END_REF]. Rhythm in speech is less regular, but still facilitates temporal prediction of upcoming elements, especially in relation to stress prominence of accented and unaccented syllables [START_REF] Arvaniti | Rhythm, timing and the timing of rhythm[END_REF][START_REF] Pitt | The use of rhythm in attending to speech[END_REF]). An influential theory explaining how the brain tracks music and speech rhythms is based on dynamic attending. The dynamic attending theory (DAT) suggests that external stimuli with rhythmic regularities are represented in the brain via the entrainment of endogenous neural oscillations at multiple hierarchical levels. This synchronization facilitates temporal prediction of upcoming events, notably by enhancing temporal attention to expected points in time [START_REF] Jones | Time, our lost dimension: Toward a new theory of perception, attention, and memory[END_REF][START_REF] Jones | Musical time[END_REF][START_REF] Jones | Time will tell[END_REF][START_REF] Jones | Dynamic attending and responses to time[END_REF]. As both music and speech appear to be tracked in the brain via similar neural mechanisms, research has begun to exploit the strongly regular temporal structure of music to enhance the processing of the less regular speech signal. The current study investigates this issue by focusing on whether regular rhythmic primes can influence syntactic processing of speech in children.

Research has shown that music and language share cognitive resources for structural integration (Fiveash, McArthur, et al., 2018;Fiveash, Thompson, et al., 2018;[START_REF] Fiveash | Music and language: Do they draw on similar syntactic working memory resources?[END_REF][START_REF] Patel | Music, language, and the brain[END_REF][START_REF] Slevc | Making psycholinguistics musical: Selfpaced reading time evidence for shared processing of linguistic and musical syntax[END_REF], and relations have been observed between music rhythm and language grammar processing capacities [START_REF] Gordon | Perspectives on the rhythm-grammar link and its implications for typical and atypical language development[END_REF]. For example, [START_REF] Gordon | Musical rhythm discrimination explains individual differences in grammar skills in children[END_REF] found that rhythm perception skills were related to grammatical production skills in typically developing six-year-old children. Further, 10-11 year old children with music training showed an early left anterior negativity (ELAN) response to violations of language structure (grammatical errors), whereas this response was not observed in the children who were not musically trained, likely because their automatic language syntax skills were still developing [START_REF] Jentschke | Musical training modulates the development of syntax processing in children[END_REF]. In addition to long-term benefits of music rhythm on language processing (see [START_REF] Schön | Short-and long-term rhythmic interventions: Perspectives for language rehabilitation[END_REF], short-term effects have been investigated within the rhythmic priming paradigm, focusing specifically on whether regular rhythmic primes can facilitate subsequent grammaticality judgments in speech [START_REF] Canette | Rhythmic and textural musical sequences influence differently syntax and semantic processing in children[END_REF][START_REF] Canette | Rhythmic and textural musical sequences differently influence syntax and semantic processing in children[END_REF][START_REF] Chern | New evidence of a rhythmic priming effect that enhances grammaticality judgments in children[END_REF][START_REF] Przybylski | Rhythmic auditory stimulation influences syntactic processing in children with developmental language disorders[END_REF].

The rhythmic priming paradigm draws on the premise of DAT that oscillatory neural activity is entrained to temporal regularities in the environment, and actively supports the distribution of attention in time via temporal predictions. Neural entrainment is therefore suggested to reflect more than a mere accumulation of separate passive responses to acoustic energy in external stimuli (Large, 2008;[START_REF] Tal | Neural entrainment to the beat: The "missing-pulse" phenomenon[END_REF]. In line with oscillator dynamics [START_REF] Large | The dynamics of attending: How people track time-varying events[END_REF], the entrained neural oscillations are proactive, self-sustaining, and can continue even when the external stimulus has stopped. The continuation of self-sustaining oscillations triggered by a rhythmic context results in the hypothesis that a transient rhythmic prime can influence subsequent perception. Indeed, studies testing predictions of the DAT have shown that attention is enhanced at specific points in time when an event is expected to occur based on a prior entrained sequence (e.g., [START_REF] Barnes | Expectancy, attention, and time[END_REF][START_REF] Jones | Evidence for rhythmic attention[END_REF][START_REF] Large | The dynamics of attending: How people track time-varying events[END_REF]. The effect of sustained neural oscillations and temporal attention to the subsequent processing of speech stimuli has been tested using either a one-to-one mapping of a prime (or cue) matched to one specific sentence that follows, or a more global priming approach. The oneto-one mapping approach has shown enhanced processing of phonemes [START_REF] Cason | Bridging music and speech rhythm: Rhythmic priming and audio-motor training affect speech perception[END_REF][START_REF] Cason | Rhythmic priming enhances the phonological processing of speech[END_REF] and words [START_REF] Gould | The beat goes on: The effect of rhythm on reading aloud[END_REF][START_REF] Gould | Examining the neuroanatomical and the behavioural basis of the effect of basic rhythm on reading aloud[END_REF], and even enhanced neural entrainment to the following sentence [START_REF] Falk | Tuning neural phase entrainment to speech[END_REF][START_REF] Gordon | Words and melody are intertwined in perception of sung words: EEG and behavioral evidence[END_REF]. The focus of the more global rhythmic priming paradigms, including the one presented here, has been on morpho-syntactic processing following regular rhythmic primes (in comparison to different baseline conditions).

In global rhythmic priming paradigms, participants are presented with longer rhythmic primes followed by a set of naturally spoken sentences. Regular rhythmic primes are assumed to entrain brain oscillations globally at the beat level (and related hierarchical meter levels). This entrainment then favors a state of enhanced activation, which boosts subsequent sentence processing by the promotion of an attentional temporal window consistent with linguistic units in the naturally spoken speech signal. Early studies using long rhythmic primes (three-minutes) in patient populations have shown benefits to subsequent grammatical speech processing. Rhythmic primes restored the P600 component to syntactic violations in patients with basal ganglia lesions [START_REF] Kotz | The basal ganglia are receptive to rhythmic compensation during auditory syntactic processing: ERP patient data[END_REF] who have been previously reported to not show this component [START_REF] Frisch | Why the P600 is not just a P300: The role of the basal ganglia[END_REF][START_REF] Kotz | Syntactic language processing: ERP lesion data on the role of the basal ganglia[END_REF]. Similarly, rhythmic march primes restored the P600 to subsequently presented sentences in a patient with Parkinson's disease [START_REF] Kotz | Can rhythmic auditory cuing remediate language-related deficits in Parkinson's disease?[END_REF].

Based on the promising results of rhythmic priming in adults, studies began to investigate whether rhythmic priming also enhanced grammaticality judgments in children who are still developing their syntactic processing skills, using shorter primes and shorter blocks of sentences. [START_REF] Przybylski | Rhythmic auditory stimulation influences syntactic processing in children with developmental language disorders[END_REF] presented regular and irregular 32-second primes, each followed by six grammatically correct and incorrect sentences to French children with developmental language disorder (DLD; previously named specific language impairment, see [START_REF] Bishop | Phase 2 of CATALISE: A multinational and multidisciplinary Delphi consensus study of problems with language development: Terminology[END_REF], children with dyslexia, and their chronological and reading age matched controls. All groups showed enhanced sensitivity to syntactic violations after a regular compared to an irregular rhythmic prime, and this effect was particularly strong for DLD children. To investigate whether this effect was based on a facilitative influence of the regular primes and not simply a detrimental effect of the irregular primes, [START_REF] Bedoin | Temporally regular musical primes facilitate subsequent syntax processing in children with specific language impairment[END_REF] presented DLD children and age-matched controls with the same 32second regular prime compared to an environmental sound scene without temporal regularities.

Grammaticality judgments were improved after the regular primes, suggesting that the previously reported relative facilitation (comparing regular to irregular primes) effect is at least partly due to the boosting effect of the regular prime. Rhythmic priming has also been observed in different languages and within training paradigms (all using ~30-second primes followed by six sentences or short tasks). Recent research using the same primes as in [START_REF] Przybylski | Rhythmic auditory stimulation influences syntactic processing in children with developmental language disorders[END_REF] has replicated the rhythmic priming effect in English [START_REF] Chern | New evidence of a rhythmic priming effect that enhances grammaticality judgments in children[END_REF] and Hungarian (Ladányi et al., submitted) children. Chern et al. (2018) included two nonlinguistic control tasks (math and visuospatial) and Ladányi et al.

(under preparation) included a picture naming and a non-verbal stroop task. In both studies, a benefit of the regular prime was observed only for grammaticality judgments, and not for the control tasks, suggesting that the regular prime had a specific benefit on subsequent sentence processing, and was not merely a general effect of enhanced arousal. Rhythmic primes have also been implemented within morphosyntax training sessions proposed to cochlear implanted deaf children to investigate whether presenting a regular rhythmic prime (~30 seconds) compared to an environmental sound baseline before sets of training items enhanced the long-term benefits of training [START_REF] Bedoin | Boosting syntax training with temporally regular musical primes in children with cochlear implants[END_REF]. A larger improvement in performance for grammaticality judgments and non-word repetition was recorded in post-training sessions when morphosyntactic exercises had been preceded by rhythmic primes rather than baseline primes. These results suggest that rhythmic priming in the short-term context of morphosyntactic exercises could also have beneficial long-term effects on language processing. Rhythmic priming therefore appears to be a valuable tool to enhance grammaticality judgments in speech, and rhythmic primes of approximately 30-seconds appear to work well in this context.

To understand the strengths and limits of the priming effect, one question is how long the prime needs to be for the entrainment and synchronization of neural oscillations to sustain and facilitate subsequent language processing. Notably, the rhythmic primes used in previous studies have all been at least 30-seconds long. Three-minute rhythmic primes appeared to benefit the subsequent processing of 24 [START_REF] Kotz | The basal ganglia are receptive to rhythmic compensation during auditory syntactic processing: ERP patient data[END_REF] and 48 [START_REF] Kotz | Can rhythmic auditory cuing remediate language-related deficits in Parkinson's disease?[END_REF] sentences in adult patients. The other rhythmic priming studies outlined above have all used 32-second rhythmic primes followed by six sentences in children aged approximately between 6-10 years [START_REF] Bedoin | Temporally regular musical primes facilitate subsequent syntax processing in children with specific language impairment[END_REF][START_REF] Chern | New evidence of a rhythmic priming effect that enhances grammaticality judgments in children[END_REF]Ladányi et al., submitted;[START_REF] Przybylski | Rhythmic auditory stimulation influences syntactic processing in children with developmental language disorders[END_REF]. It is therefore unknown whether shorter rhythmic primes could also facilitate grammaticality judgments in sentence processing, and whether the length of the primes and their potential benefit might depend on children's chronological age or reading age.

The present study was designed with two main aims. The first aim was to replicate previous rhythmic priming effects with 32-second primes, and to investigate whether shorter prime lengths can also influence subsequent grammaticality judgments. Participants were presented with 8-second and 16-second rhythmic primes in Experiment 1, and 16-second and 32second rhythmic primes in Experiment 2. In both experiments, rhythmic primes (regular or irregular) were followed by six sentences (grammatical or ungrammatical) as in previous rhythmic priming experiments (e.g., [START_REF] Przybylski | Rhythmic auditory stimulation influences syntactic processing in children with developmental language disorders[END_REF]. We aimed to replicate the benefit of the regular rhythmic prime for 32-second primes, and to test whether this benefit extended at least to the 16-second primes or even the 8-second primes.

Our second aim was a first attempt to address whether the sensitivity to rhythmic primes might depend on chronological and reading age. Based on previous age ranges in similar research, we tested children from seven to nine years of age, as children in this age range are still developing their syntactic processing skills [START_REF] Friederici | The neural basis of language development and its impairment[END_REF][START_REF] Hahne | Brain signatures of syntactic and semantic processes during children's language development[END_REF]). We assessed each child's reading age (RA) based on a RA measure administered after the experiment, and recorded their chronological age (CA). We predicted that older children and children with a higher RA would benefit more strongly from the prime regularity, resulting in enhanced grammaticality judgments after regular compared to irregular primes. This prediction is based on evidence that rhythmic processing skills improve with age [START_REF] Bonacina | How rhythmic skills relate and develop in school-age children[END_REF][START_REF] Drake | The development of rhythmic attending in auditory sequences: Attunement, referent period, focal attending[END_REF][START_REF] Ireland | Rhythm and melody tasks for schoolaged children with and without musical training: Age-equivalent scores and reliability[END_REF][START_REF] Mcauley | The time of our lives: Life span development of timing and event tracking[END_REF], and documented links between reading skills and rhythmic processing skills [START_REF] Bekius | The beat to read: A cross-lingual link between rhythmic regularity perception and reading skill[END_REF][START_REF] Dellatolas | Rhythm reproduction in kindergarten, reading performance at second grade, and developmental dyslexia theories[END_REF][START_REF] Moreno | Musical training influences linguistic abilities in 8-year-old children: More evidence for brain plasticity[END_REF][START_REF] Taub | The effects of training in timing and rhythm on reading achievement[END_REF].

We ran two separate experiments for the following reasons: First, shorter experiments (approximately 20 minutes) were preferable to maintain attention within the current age group.

Second, we wanted to investigate effects of duration across two different groups of children (drawn from the same participant pool) to analyze the potential chronological and reading age effects. Third, we wanted to isolate the effects of individual prime durations as much as possible;

running two experiments allowed us to observe whether a different pattern occurred depending on whether a 16-second prime was presented in the second part or the first part of an experimental session. In addition to the manipulation of duration and the investigation of CA and RA, the current study is the first to analyze correct response times as well as d prime and accuracy in grammaticality judgments following the primes. In the following, we first present the method common for the two experiments followed by the presentation of Experiment 1 and Experiment 2.

Common Method

Design

Experiments 1 and 2 were based on a 2 (prime duration: short, long) by 2 (prime regularity: regular, irregular) by 2 (sentences: grammatical, ungrammatical) within-subject design. As in gating paradigms, which introduce increasingly large segments of information (e.g., [START_REF] Walley | The gating paradigm: Effects of presentation format on spoken word recognition by children and adults[END_REF], short primes were presented in the first part of each experiment, and long primes in the second part of each experiment. Each experiment contained 16 blocks (eight short and eight long blocks), with a block consisting of one prime rhythm followed by six sentences (three grammatical, three ungrammatical, randomly ordered).

Rhythmic primes were pseudo-randomized so that two primes of the same type (regular or irregular) were presented in succession (e.g., AA BB AA BB etc.), and the same individual prime was not played twice in a row. Individual (regular and irregular) rhythms were played once in the short condition and once in the long condition, so that participants heard the same rhythms twice throughout the experiment. The starting rhythm (regular, irregular) and sentence list (list A, list B, see below) were counterbalanced across participants. See Figure 1 for a schematic representation of the paradigm. (ungrammatical)-an example of a number error. Note that three of the six sentences in each block were grammatical and three ungrammatical. After each sentence, children indicated whether they thought the sentence was grammatical or ungrammatical.

Stimuli

Rhythms. Four regular rhythms were created by a musicologist (R1, R2, R3, R4).

Regular rhythms had a 4/4 meter with a tempo of 120 beats per minutes (bpm), corresponding to an inter-beat-interval (IBI) of 500 milliseconds (ms) or 2 Hz, and were created with several percussion instruments and electronic sounds based on MIDI VST instrument timbres (i.e., bass drum, snare drum, tom-tom, cymbal) to increase acoustic complexity and musicality. The shortest, 8 s rhythm contained one cycle of 16 beats. The 16 s and 32 s rhythms contained two and four cycles of the short rhythm, respectively. At the end of each rhythm, the first beat of the cycle was played again to create a feeling of completion, including a small reverberation effect which added about 1 s to the rhythm, resulting in total durations of 9 s, 17 s and 33 s, respectively. Nevertheless, for clarity, we will refer to the rhythms as 8 s, 16 s, and 32 s rhythms.

The irregular rhythms contained the same acoustic information as the regular rhythms (event duration, total duration, and instruments were identical), but the acoustic events were redistributed in time to create highly irregular sequences with no underlying meter or pulse (thus leading to four items, I1, I2, I3, I4). Sequences were exported in 16 bit, 48 000 Hz mono wav files, and normalized in loudness (-3 dB). Eight types of grammatical errors were created by a French linguist: errors of (1) number, (2) person, (3) gender, (4) tense, (5) auxiliary, (6) morphology, (7) position, and (8) past participle.

Error words were distributed in different positions throughout the sentences so that they could not be predicted. All sentences and error types can be seen in Supplementary Material. The three ungrammatical sentences of a block always included three different error types, and the lexical properties of grammatical and ungrammatical sentences were matched within each block to control for differences between sentence structure within blocks. The sentences were matched for peak intensity by rescaling them by their maximum absolute amplitude value.

Procedure

Children were tested two at a time in a quiet classroom. Common instructions were provided, whereby children were told that they would listen to music, and then hear some sentences. They were shown pictures of two dragons: one that always said correct sentences (clever dragon), and the other who was confused and always made mistakes (confused dragon).

It was reinforced that the confused dragon would make French errors rather than errors of meaning. After a (grammatical) example sentence, children were taken to separate computers to begin the experiment. Each child performed the experiment separately on different MacBook Pro laptops facing opposite directions and on opposite sides of the room. One experimenter stayed with one child, and a second experimenter stayed with the other child throughout the experiment to ensure adherence to the task, quiet behavior, and to initiate each trial.

During the experiment, a fixation cross was presented on the screen during the rhythmic primes, and children were encouraged to listen carefully. While the sentences were playing, the two dragons appeared on the screen. Children responded using the keyboard to indicate whether the clever dragon or the confused dragon spoke the sentence. If the child responded before the sentence finished, the dragons disappeared, but the sentence continued. Once the child had responded, a question mark appeared on the screen, and the experimenter started the next trial by pressing a button when the child was concentrated and ready to continue. It was ensured that the children rested their hands on the keys to record response times, and all unused keys were covered with cardboard. After the first part of the experiment with the shorter primes, children were told that for the next part of the experiment, the music would be a bit longer, but that they would continue with the same task. Stimuli were presented through headphones at a comfortable listening level. The experiments were run with Matlab (version 2018a) and Psychtoolbox (version 3.0.14). To avoid sampling bias between schools or participants, Experiments 1 and 2 were alternately tested during each testing day.

At the end of the experiment, the children were tested separately on a classical, French age-normed measure of reading (i.e., L'alouette test, [START_REF] Lefavrais | Test de l'Alouette[END_REF]. The child had to read out loud (within three minutes) a text for which no efficient semantic prediction was possible to avoid guessing. The score was calculated by taking into account reading speed and mistakes made, which were referenced to normed values providing a measure of reading age in French.

Children were encouraged and told they did a good job at the end of the reading test, regardless of their performance.

Analysis

Sensitivity analysis. In accordance with signal detection theory [START_REF] Stanislaw | Calculation of signal detection theory measures[END_REF], d prime (d') values were calculated by subtracting the z-score of the false alarm rate (there was no grammatical error, but the participant responded ungrammatical) from the z-score of the hit rate (there was an error and the participant responded ungrammatical) as a measure of sensitivity to the signal. A d' of zero suggests that the participant could not distinguish the signal (a grammatical error) from noise (no grammatical error). Extreme hit and false alarm rates of 1 and 0 were corrected to .99 and .01 respectively for the calculations. A measure of response bias c was also calculated by taking the sum of the z-scores of hits and false alarms multiplied by -0.5. Positive values suggest a bias to respond grammatical, and negative values suggest a bias to respond ungrammatical.

For each experiment, d' and response bias c were calculated for all sentences following the four priming conditions: regular short, irregular short, regular long, irregular long. A 2 × 2 ANOVA with prime regularity (regular, irregular) and duration (short, long) as within-subject factors was performed on d' and c values, respectively. Correlations between d' and response bias c with reading age and chronological age are also reported. Interaction effects were investigated with paired-samples t-tests (two-sided), using Cohen's d effect sizes that take into account paired-samples correlations. Effect sizes from ANOVAs are reported with partial eta squared (ηp 2 ).

Response time calculation.

Response times (RTs) for correct responses were calculated from the end of the sentence for grammatical sentences, and from the end of the syllable that introduced the grammatical error for ungrammatical sentences. Negative RTs were excluded for the ungrammatical sentences, as the participant would not yet have heard the error. Negative RTs were not removed for grammatical sentences, as it was possible to predict that there was no error by the end of the sound file. Individual RTs deviating more than three standard deviations (SD) from the participant's average RT (calculated separately for grammatical and ungrammatical sentences) were removed to exclude any particularly early or late responses.

Linear mixed models: Accuracy and RT. Accuracy and RT were analyzed using the lme4 package for linear mixed models [START_REF] Bates | Fitting linear mixed-effects models using lme4[END_REF] in R (R Core Team, 2018). Linear mixed models were used to allow us to investigate the effects of interest on a trial-by-trial basis, while controlling for random effects of participant and sentence. They also allowed us to investigate more closely the effect of RA and CA on performance across trials. Trial-by-trial accuracy data were therefore included to complement the d' analysis.

Accuracy. As the accuracy data were binomial (correct or incorrect), a mixed effects logistic regression was run using the glmer command in R (generalized linear mixed model, GLMM, family = binomial, link = logit). The model was fitted with the maximum likelihood method, using a Laplace approximation. For significance testing of fixed effects, the Anova function (using type III Wald chi square tests) from the car package [START_REF] Fox | An {R} Companion to Applied Regression (Second)[END_REF] was used. The base model included the fixed effects of prime regularity and duration (and their interaction) to investigate effects of the independent variables. Different combinations of random effects were modelled to find the best compromise between having a maximal effects random structure and a converging model (see [START_REF] Baayen | Mixed-effects modeling with crossed random effects for subjects and items[END_REF][START_REF] Barr | Random effects structure for confirmatory hypothesis testing: Keep it maximal[END_REF]. The best performing model (based on a likelihood ratio test using the anova function in R and the Akaike information criterion) included random intercepts for participant and sentences, as well as bysentence slopes depending on sentence list presented to participants (list A or B), as suggested in Baayen et al., 2008. See (1). To investigate whether prime regularity and duration affected grammatical and ungrammatical sentence judgments differently, grammaticality and its interactions were included into Model 2 (2). For each of the two experiments, there were no interactions between grammaticality and prime regularity and/or duration, so grammaticality was removed from subsequent models.

( To investigate the effects of chronological and reading age, these variables (z-score scaled and centered using the scale function in R) were added to the base model (see 3 and 4) in two separate models as we were interested in the direct effect of each continuous variable, rather than their interaction.

( Response time data. As RTs for ungrammatical sentences were measured from the end of the error syllable, and RTs for grammatical sentences were measured from the end of the sentence, this introduced an artificial bimodal distribution (with faster RTs for grammatical than for ungrammatical items), and allowed for negative RT values for grammatical sentences (as participants were able to predict that there was no error before the end of the sound file). This data therefore did not fit a gamma or inverse gaussian distribution to use with GLMER (as suggested in [START_REF] Lo | To transform or not to transform: Using generalized linear mixed models to analyse reaction time data[END_REF] for adult RT data), and so we ran a linear mixed effects model, maintaining grammaticality as a fixed effect.

Our base model for RT (5) included the fixed effects of prime regularity, duration, grammaticality, and all interactions. We again compared all different random effect structures to find the balance between maximal random effects and convergence of the model [START_REF] Baayen | Mixed-effects modeling with crossed random effects for subjects and items[END_REF]. The full random effect structure (when random slopes for both independent variables were included) did not converge for the data of Experiment 2, so for comparison between the two experiments and the accuracy models, we included the same random effects structure as in the accuracy model (random intercepts for participant and sentences, as well as by-sentence slopes depending on sentence list presented to participants: list A or B).

(5) Model5 <-lmer(RT ~ PrimeRegularity * Duration * Grammaticality + (1 |Participant) + (1 + Sent_List | Sent_Num), data = data).

We then added RA (6) and CA (7) separately, as in the accuracy analyses. For all models, significant effects were compared using the emmeans package (Length et al., 2019, version 1.4.3.01). This package determines whether there are significant differences between conditions based on the estimates and standard errors within the model. Reported pvalues were adjusted using the Tukey method for a family of estimates (implemented via emmeans, Length et al., 2019). For interactions including continuous variables (RA and CA), emtrends (part of the emmeans package) was used to determine whether there were significant trends in performance depending on the continuous variable as a function of the categorical variables.

Experiment 1 Participants

Thirty-six children (16 girls, 20 boys) between the ages of seven and nine from two different private schools participated in Experiment 1. Four children had a RA that was 18 months or more inferior to their CA, which is considered at-risk for dyslexia [START_REF] Lefavrais | Test de l'Alouette[END_REF].

These children were therefore removed from the analysis. For the remaining 32 participants, the mean CA was 104 months (SD = 6.19; range = 90 to 111 months), the mean RA was 116 months (SD = 17.87; range = 88 to 171 months), and the difference between RA and CA averaged +12 months (SD = 14.55; range = -6 to +61 months). Note that one participant did not have any RA information because s/he did not bring glasses and therefore could not read the text. The experiment was run in accordance with the Declaration of Helsinki, all data were anonymized, and parents of all children provided written informed consent prior to the experiment.

Data Analyses

Response time removal. Incorrect responses averaged 15.8% (SD = 10.47%) across all conditions and participants. Removed RTs +/-3SD from each individual's mean RT averaged 1.76% (SD = 0.97%).

Results

D prime and response bias c.

There was a non-significant trend for d' values to be higher after 16 s primes than 8 s primes, F(1, 31) = 3.82, p = .06, ηp 2 = .11 (see Figure 2), but there was no main effect of prime regularity (p = .88), nor an interaction between prime regularity and duration (p = .66). There were no significant effects for response bias c (see Supplementary

Accuracy. Model 1 (main effects only).

The main effect of duration was marginal, X 2 (1, N = 32) = 3.73, p = .053, with participants performing better overall for 16 s primes than for 8s

primes. There was no main effect of prime regularity, X 2 (1, N = 32) = 0.14, p = .71, nor an interaction between prime regularity and duration, X 2 (1, N = 32) = 0.01, p = .91.

Model 2 (including grammaticality).

With grammaticality included in the model, the main effect of duration was significant, X 2 (1, N = 32) = 4.79, p = .03, and there was a main effect of grammaticality, X 2 (1, N = 32) = 24.31, p < .001, as participants were more accurate for grammatical than ungrammatical sentences. There were no other significant effects (all p-values > .24).

Model 3 (RA added).

The main effects of duration, X 2 (1, N = 32) = 3.50, p = .06 and RA, X 2 (1, N = 32) = 3.21, p = .07 were marginal, with a trend for children with a higher RA to perform better overall. No other effects were significant (all p-values > .14).

Model 4 (CA added).

There was a main effect of CA, X 2 (1, N = 32) = 4.87, p = .03:

participants performed more accurately with age. There was no main effect of duration, X 2 (1, N = 32) = 2.94, p = .09, and no other significant effects (all p-values > .21).

Correct Response Times. Model 5 (main effects only).

There were main effects of grammaticality, X 2 (1, N = 32) = 487.40, p < .001 and duration, X 2 (1, N = 32) = 18.76, p < .001, which showed that participants were faster to detect grammatical sentences compared to ungrammatical sentences, and faster in the 16 s condition compared to the 8 s condition, in line with the accuracy data. All other effects were non-significant (all p-values > .39).

Model 6 (RA added). The significant main effects of grammaticality X 2 (1, N = 32) = 458.93, p < .001 and duration, X 2 (1, N = 32) = 20.09, p < .001 were confirmed. There were no other significant effects (all p-values > .20).

Model 7 (CA added). The significant main effects of grammaticality, X 2 (1, N = 32) = 500.31, p < .001 and duration, X 2 (1, N = 32) = 17.66, p < .001 were confirmed. There were additionally Duration × CA, X 2 (1, N = 32) = 7.63, p = .006 and Grammaticality × CA interactions, X 2 (1, N = 32) = 8.00, p = .005. The Duration × CA interaction suggested, though not significantly, that participants were generally slower with increased CA for the 8 s primes (trend = 74.64, SE = 84.6, t-ratio = 0.88, p = .38), but not for 16 s primes (trend = -5.46, SE = 84.6, t-ratio = -0.07, p = .95). The Grammaticality × CA interaction suggested, again not significantly, that RTs were slower with increasing age for grammatical sentences (trend = 75.36, SE = 84.2, t-ratio = 0.90, p = .38) but not for ungrammatical sentences (trend = -6.18, SE = 85.0, t-ratio = -0.07, p = .94).

Discussion

Across all children, there was no benefit of regular rhythmic primes compared to irregular rhythmic primes at either 8 s or 16 s durations for d', accuracy, or RT. There was also no influence of prime regularity or duration on bias to respond grammatical or ungrammatical, as measured by response bias c. However, significant positive correlations between RA and d' after regular (but not irregular) primes with both durations suggest that the regular primes had a greater influence on children with higher compared to lower RAs. Thus, it appears that regularity in rhythms boosted performance level with increased RA, while performance level after irregular primes was not modulated by RA. This finding suggests that children who have a higher reading ability might benefit more strongly from regular primes compared to children who have a lower reading ability at these shorter durations. Based on previous findings showing potential links between children's rhythmic processing capacities and reading capacities (e.g., [START_REF] Bekius | The beat to read: A cross-lingual link between rhythmic regularity perception and reading skill[END_REF][START_REF] Dellatolas | Rhythm reproduction in kindergarten, reading performance at second grade, and developmental dyslexia theories[END_REF][START_REF] Flaugnacco | Rhythm perception and production predict reading abilities in developmental dyslexia[END_REF], one could argue that children with lower reading ages were less able to synchronize with the rhythms than the high RA children, especially presented over short durations, such as the primes used in the current experiment. This possibility will be discussed together with the findings of Experiment 2 in the General Discussion.

Experiment 2

Participants

Thirty-six different children (18 girls, 18 boys) between the ages of seven and nine years from two different private schools participated in Experiment 2. One participant had a RA more than 18 months inferior to her/his CA, so was removed from the analysis. For the remaining 35 participants, the mean CA was 103 months (SD = 5.59; range = 91 to 112 months), the mean RA was 109 months (SD = 16.30; range = 85 to 166 months), and the difference between RA and CA averaged +6 months (SD = 16.71, range = -15 to +59 months). The experiment was run in accordance with the Declaration of Helsinki, data were anonymized, and parents of all children provided written informed consent prior to the experiment.

Data Analyses

All data analyses were performed as in Experiment 1.

Response time removal. Incorrect responses averaged 12.9% of trials across participants (SD = 8.06%). Removed RTs +/-3SD from each individual's mean RT averaged 1.40% (SD = 0.83%).

Results

D prime and response bias c. For d', the main effect of prime fell short of significance, F(1, 34) = 3.53, p = .07, ηp 2 = .09, but indicated a non-significant trend for higher d' after regular primes than after irregular primes. The main effect of duration was significant, F(1, 34) = 4.19, p = .048, ηp 2 = .11, with better performance after 32 s compared to 16 s primes, but there was no Prime Regularity × Duration interaction, F(1, 34) = 1.72, p = .20, even though Figure 4 shows an interactive pattern. Based on this observation and our strong hypothesis of a priming effect with 32 s primes based on previous work, we tested for prime effects at each duration. For 32 s primes, d' values were significantly higher after regular primes than after irregular primes t(34) = 2.19, p = .036, d = 0.33, whereas for 16 s durations, performance did not differ depending on prime regularity, p = .94. There were no significant effects for response bias c (see Supplementary

Accuracy. Model 1 (main effects only).

The main effect of duration was significant, X 2

(1, N = 35) = 7.36, p = .007, with better performance after the 32 s primes compared to the 16 s primes. The interaction between prime regularity and duration just fell short of significance, X 2

(1, N = 35) = 3.79, p = .051, and there was no main effect of prime regularity, X 2 (1, N = 35) = 1.30, p = .25. Based on the marginal interaction and theoretical hypotheses, we ran pairedcontrasts between regular and irregular primes for each duration, which showed that accuracy after regular primes was higher than after irregular primes in the 32 s condition (estimate = 0.37, SE = 0.18, z-ratio = 2.09, p = .037), but there was no difference in the 16 s condition (estimate = -0.10, SE = 0.16, z-ratio = -0.60, p = .55), supporting the d' analysis.

Model 2 (grammaticality added).

Including grammaticality in the model gave a main effect of grammaticality, X 2 (1, N = 35) = 25.16, p < .001 (with better performance for grammatical sentences), and confirmed the significant main effect of duration, X 2 (1, N = 35) = 5.46, p = .02, and the marginally significant interaction between prime regularity and duration, X 2 (1, N = 35) = 3.20, p = .07. No other effects were significant (all p-values > .29).

Model 3 (RA added).

With RA included in the model, the Prime Regularity × Duration interaction reached significance, X 2 (1, N = 35) = 3.95, p = .047. In addition, there was a significant main effect of RA, X 2 (1, N = 35) = 3.96, p = .046, indicating increased performance with increased RA. Finally, the significant main effect of duration, X 2 (1, N = 35) = 7.47, p = .006 was confirmed. No other effects were significant (all p-values > .20).

Model 4 (CA added).

With CA included in the model, the Prime Regularity × Duration interaction, X 2 (1, N = 35) = 4.35, p = .04, was significant, and the main effect of duration was confirmed, X 2 (1, N = 35) = 7.94, p = .005. There was also a Prime Regularity × Duration × CA interaction, X 2 (1, N = 35) = 4.85, p = .03. The trend analysis showed that there was a significant trend for performance to increase with increasing CA in the 32 s regular condition (trend = 0.38, SE = 0.19, z-ratio = 2.02, p = .04). The other trends were not significant: 32 s irregular (trend = -0.01, p = .94), 16 s regular (trend = 0.02, p = .93), 16 s irregular (trend = 0.14, p = .42). See for regular rhythmic primes, the trend over chronological age was significant (p = .04).

Correct Response Times. Model 5 (main effects only).

A significant main effect of duration, X 2 (1, N = 35) = 9.89, p = .002 showed that RTs were faster in the 32 s conditions compared to the 16 s conditions, and a significant main effect of grammaticality, X 2 (1, N = 35) = 339.52, p < .001 showed that RTs were faster for grammatical sentences compared to ungrammatical sentences. No other effects were significant (all p-values > .23).

Model 6 (RA added).

The main effects of duration, X 2 (1, N = 35) = 9.95, p = .002 and grammaticality, X 2 (1, N = 35) = 346.38, p < .001 were significant again. There was a significant Prime Regularity × RA interaction, X 2 (1, N = 35) = 4.81, p = .03, which was further modulated by grammaticality, as reflected in a significant Prime Regularity × RA × Grammaticality

• • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • •

16-Seconds 32-Seconds

-1.8 -0.8 -0.4 0 0.3 0.7 1.1 1.6 -1.8 -0.8 -0.4 0 0.3 0.7 1.1 1.6

2.5 3.0 3.5

Chronological Age (scaled) Linear Prediction (accuracy)

• Regular Irregular interaction, X 2 (1, N = 35) = 5.11, p = .02 (Figure 7). For grammatical items, the trends of regular and irregular conditions did not differ, and while both were decreasing with RA, the trends were not significant (trend = -81.2, p = .28 for regular, trend = -79.6, p = .29, for irregular). For ungrammatical items, the trend analysis showed a significant trend for ungrammatical responses to be faster with increasing RA in the irregular prime condition (trend = -160.6, SE = 74.9, t-ratio = -2.14, p = .04), but not in the regular condition, even though in the same direction (trend = -54.7, p = .47). It therefore appears that the interactions between RA and prime regularity were related to faster RTs for ungrammatical sentences after regular compared to irregular primes for children with low RAs. As shown in Figure 7, children with lower RAs were faster to respond after regular primes compared to irregular primes (for ungrammatical items). With increasing RA, the difference between regular and irregular equalized, and then a slight reversal of the effect can be seen.

• • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • Grammatical Ungrammatical -1
.5 -1 -0.7-0.4 0 0.6 1 1.4 3.5-1.5 -1 -0.7-0.4 0 0.6 1 1.4 3.5 500 1000 1500

Reading Age (scaled) Linear Prediction (response time)

• Regular Irregular

Age Comparison Across Experiments

We ran further analyses to investigate whether there were age-related differences in our two experiment samples. Independent samples t-tests showed that there were no significant differences in CA, t(65) = 0.64, p = .52, or in RA, t(64) = 1.62, p = .11, between Experiments 1 and 2.

Discussion

Experiment 2 replicated the rhythmic priming effect in typically developing French children aged seven to nine years. For d' and accuracy analyses, the rhythmic priming effect was observed only for the 32-second primes, but not for the 16-second primes. After 32-second regular primes, RA correlated with sensitivity to grammaticality judgments (d') and CA correlated with accuracy. Note that the d' effect was not accompanied by an observed response bias, suggesting that the primes did not bias the children to respond in a particular way, but rather, the regular primes boosted sensitivity to grammatical errors. Both RA and CA therefore appear to modulate the rhythmic priming effect, particularly with 32-second primes.

Response time analyses also revealed some interesting trends with RA, which were not modulated by prime duration: children with lower RAs were particularly slow to respond to ungrammatical sentences after irregular primes, and as RA increased, RT improved and joined the RT level after the regular primes, which were faster even at younger RAs. Put differently, the RT analyses suggest for children with younger RAs that the RT to ungrammatical items benefit from the regular primes, leading to faster RT in comparison to the irregular primes. These findings will be discussed further in the General Discussion.

General Discussion

The current study was designed to (1) investigate the prime duration necessary to facilitate subsequent grammaticality judgments in children, and ( 2) make a first attempt to investigate differences depending on chronological and reading age on the rhythmic priming effect. To this end, two different groups of children aged between seven and nine were presented with 8 s and 16 s primes (Experiment 1), or 16 s and 32 s primes (Experiment 2) followed by six sentences (as in [START_REF] Bedoin | Temporally regular musical primes facilitate subsequent syntax processing in children with specific language impairment[END_REF][START_REF] Chern | New evidence of a rhythmic priming effect that enhances grammaticality judgments in children[END_REF]Ladányi et al., submitted;[START_REF] Przybylski | Rhythmic auditory stimulation influences syntactic processing in children with developmental language disorders[END_REF]. Replicating this previous research, 32 s regular primes facilitated grammaticality judgments (both sensitivity and accuracy) compared to irregular primes. Across all children, the shorter primes in Experiment 1 (8 s, 16 s) and Experiment 2 (16 s) did not show a rhythmic priming effect for sensitivity or accuracy to grammaticality judgments. However, RA and CA appeared to modulate the rhythmic priming effect, with increased benefits of the regular rhythmic primes for older children and children with higher RAs. Performance after regular rhythmic primes was correlated with RA for both 8-second and 16-second primes in Experiment 1, and with 32-second primes in Experiment 2, suggesting that regular primes were more effective with increased RA. In the 32-second condition of Experiment 2, accuracy after regular primes increased with CA, and children with a low RA appeared to be specifically faster after regular primes (in comparison to irregular ones) across both durations. These results will be discussed below in relation to applications of rhythmic priming and developmental rhythm and language processing, within a DAT framework.

The main finding from the current study is that longer primes (here, 32 s) were more effective than shorter primes (i.e., 16 s, 8 s) at enhancing grammaticality judgments in children.

The hypothesis behind global rhythmic priming paradigms is that the neural oscillations entrained by the regular rhythmic primes sustain over time, resulting in a state of enhanced activation that persists across the subsequent sentences, boosting perception and processing of the natural prosodic contours within subsequent sentences. According to Jones (2019, p. 71), strong driven oscillations can continue in their intrinsic period even when the original stimulus has stopped and new rhythms are encountered, making them more stable and resistant to change (e.g., from a probe tone or a new sentence). In the current paradigm, this continuation could result in persistent global oscillatory energy that maintains across the phase-reset incurred by each incoming sentence. Weak driven oscillations on the other hand are more likely to be entirely "captured" by a new rhythm or event. Oscillations are suggested to become stronger depending on the regularity and strength of the external (driving) rhythm [START_REF] Jones | Time will tell[END_REF]. It is therefore likely that the longer regular recurring input of the 32-second rhythms was required to sufficiently entrain endogenous oscillations that were strong enough to persist across the six subsequent sentences. The current results therefore suggest that at the group level, for children in this age range, 8-second and 16-second primes are not long enough to entrain neural oscillations that are strong enough to concretely affect subsequent grammaticality judgments across a number of subsequent naturally spoken sentences. However, it appears that other factors, including RA and CA can enhance the strength of the prime effect by potentially enhancing the strength of the entrained oscillations.

Influence of Reading Age

Across both experiments, correlations were observed between RA and sensitivity to grammatical errors after regular (but not irregular) primes. These correlations were particularly evident for 8-second and 16-second primes in Experiment 1, as well as for 32-second primes in Experiment 2. Such correlations are particularly interesting for the shorter primes, as they suggest that shorter rhythmic primes may benefit children with higher RAs. Children with higher

RAs might be better and more quickly able to attend and entrain to the rhythms with shorter durations, resulting in stronger oscillations that were able to persist across the subsequent sentences. This suggestion is supported by previously reported correlational research that shows connections between rhythmic abilities and reading skills in typically developing children and adolescents [START_REF] Bonacina | Clapping in time parallels literacy and calls upon overlapping neural mechanisms in early readers[END_REF][START_REF] Douglas | The relationship between musical ability and literacy skills[END_REF][START_REF] González-Trujillo | The role of nonspeech rhythm in Spanish word reading[END_REF][START_REF] Gordon | Musical rhythm discrimination explains individual differences in grammar skills in children[END_REF][START_REF] Rautenberg | The effects of musical training on the decoding skills of German-speaking primary school children[END_REF][START_REF] Tierney | The ability to tap to a beat relates to cognitive, linguistic, and perceptual skills[END_REF][START_REF] Wigley | Motor timing and precursor literacy skills in very young children[END_REF], correlations between length of music training and reading comprehension in 6 -9 year old children [START_REF] Corrigall | Associations between length of music training and reading skills in children[END_REF], and benefits of rhythmic music training on reading skills in 7-to 8-year-old children compared to control groups [START_REF] Moreno | Musical training influences linguistic abilities in 8-year-old children: More evidence for brain plasticity[END_REF][START_REF] Rautenberg | The effects of musical training on the decoding skills of German-speaking primary school children[END_REF]; see also [START_REF] Flaugnacco | Music training increases phonological awareness and reading skills in developmental dyslexia: A randomized control trial[END_REF] for enhanced reading skills in 8-to 11-year-old dyslexic children after music training compared to painting training). Note also that children with a younger RA appeared to respond faster after the regular primes than after the irregular primes (for which RT decreased with RA to reach the speed observed after regular primes), as measured by the more sensitive measure of response time.

Connections between language skills and rhythmic processing are also predicted by the temporal sampling framework (TSF) of developmental dyslexia [START_REF] Goswami | A temporal sampling framework for developmental dyslexia[END_REF], which suggests that impairments in phonological processing (and subsequently reading skills) are based on impaired tracking of the speech envelope. The TSF predicts that children who are poor readers may also have difficulties processing musical rhythm. Supporting this hypothesis, correlations have been observed between rhythmic processing tasks and various measures of reading across both typically developing children and children with dyslexia (paced tapping:

Thomson [START_REF] Thomson | Rhythmic processing in children with developmental dyslexia: Auditory and motor rhythms link to reading and spelling[END_REF]; metrical same-different task: Huss, Verney, Fosker, Mead, & Goswami, 2011; rhythm reproduction: [START_REF] Flaugnacco | Rhythm perception and production predict reading abilities in developmental dyslexia[END_REF] and children with DLD (paced tapping; [START_REF] Corriveau | Rhythmic motor entrainment in children with speech and language impairments: Tapping to the beat[END_REF]. Children with a higher RA in our study may also have had better rhythm processing skills, allowing for better synchronization with the rhythms, and a benefit of the rhythmic primes despite their short duration. This possibility now needs to be investigated experimentally by measuring rhythm perception and production skills in subsequent experiments to observe whether greater rhythmic ability is associated with a stronger effect of the regular rhythmic prime on subsequent grammaticality judgments, and whether this benefit can be seen with shorter primes for children with better rhythm skills. Relatedly, it would be interesting to investigate whether children in a rhythmic training group show an increased rhythmic priming effect from pre-to post-training compared to a control group. Such work would suggest that long-term rhythmic training can also influence short-term effects of musical rhythm, and could be useful for rehabilitation and training.

Influence of Chronological Age

Experiment 2 revealed that the effect of the 32 s rhythmic primes was stronger with increasing age. Previous developmental research has shown that beat synchronization ability increases with age [START_REF] Drake | The development of rhythmic attending in auditory sequences: Attunement, referent period, focal attending[END_REF][START_REF] Drewing | Sensorimotor synchronization across the life span[END_REF][START_REF] Ireland | Rhythm and melody tasks for schoolaged children with and without musical training: Age-equivalent scores and reliability[END_REF][START_REF] Mcauley | The time of our lives: Life span development of timing and event tracking[END_REF][START_REF] Savion-Lemieux | Developmental contributions to motor sequence learning[END_REF][START_REF] Tryfon | Auditory-motor rhythm synchronization in children with autism spectrum disorder[END_REF], as does the ability to synchronize to multiple hierarchical levels [START_REF] Drake | The development of rhythmic attending in auditory sequences: Attunement, referent period, focal attending[END_REF]. It is therefore possible that the older children in Experiment 2 were able to better synchronize with the rhythms and to extract the beat than the younger children, enhancing the effect of the rhythmic prime on subsequent sentence processing.

Effects of sentence envelope priming have also been shown for older children (M = 11;0, years;months), but not younger children (M = 7;7) (Ríos-López, Molnar, Lizarazu, & Lallier, 2017). It should be noted that the effect of the 32-second primes emerged across all children in Experiment 2, confirming rhythmic priming effects of 32-second primes for young children in French (6;6 -12;11;Przybylski et al., 2013), English (5;6 -8;7;[START_REF] Chern | New evidence of a rhythmic priming effect that enhances grammaticality judgments in children[END_REF] and Hungarian (5;[0][1][2][3][4][5][6][7]0;Ládanyi et al.,submitted). The trend for increased accuracy with increased CA after 32-second primes may have emerged in Experiment 2 because the rhythmic primes were more difficult to synchronize with for younger children than for older children. Indeed, the aging hypothesis as stated by [START_REF] Jones | Time will tell[END_REF] [START_REF] Cason | Bridging music and speech rhythm: Rhythmic priming and audio-motor training affect speech perception[END_REF]; tapping along to the regular rhythm, [START_REF] Morillon | Motor origin of temporal predictions in auditory attention[END_REF][START_REF] Tierney | Auditory-motor entrainment and phonological skills: Precise auditory timing hypothesis (PATH)[END_REF], which could result in stronger entrainment to the rhythms and a potentially stronger effect of the rhythmic prime, even with shorter prime durations.

One might also argue that the metrical complexity and tempo of the rhythmic primes were not optimal for the younger participants. [START_REF] Drake | The development of rhythmic attending in auditory sequences: Attunement, referent period, focal attending[END_REF] tested 4-, 6-, 8-, and 10-yearold French-speaking children (and adults), and reported that the younger children were less flexible in the tempi they could tap to, synchronize with, and discriminate (a similar pattern can be observed for English-speaking children in [START_REF] Mcauley | The time of our lives: Life span development of timing and event tracking[END_REF]. The 4-year-olds showed a limit between 300-400 ms inter-beat-interval (IBI), which widened with age, and the spontaneous tapping rate (suggesting an internal referent period) increased from approximately 385 ms inter-tap-interval (ITI) for 4-and 6-year-olds, to 456 ITI for 8-year-olds, 478 ITI for 10year-olds, and 628 ITI for adults. Our rhythms had a 500 ms IBI. It is therefore possible that the older children in Experiment 2 had a preferred tempo that was closer to the beat level of the presented rhythms than the younger children. However, it is important to note that even the younger children can benefit from this slightly slower IBI when the prime duration is longer, as shown here with the 32-second primes, and seen in previous studies (e.g., [START_REF] Bedoin | Temporally regular musical primes facilitate subsequent syntax processing in children with specific language impairment[END_REF][START_REF] Chern | New evidence of a rhythmic priming effect that enhances grammaticality judgments in children[END_REF][START_REF] Przybylski | Rhythmic auditory stimulation influences syntactic processing in children with developmental language disorders[END_REF]. Based on our present findings, it would be interesting to systematically manipulate CA and the relation of the prime's IBI with preferred tempo to investigate whether these factors have an effect on the strength of the rhythmic priming effect, as well as the necessary prime duration.

Differences Between CA and RA and Implications

Data of Experiment 1 suggest an enhanced rhythmic priming effect for children with a higher RA, whereas data of Experiment 2 suggest an enhanced rhythmic priming effect for older children (increased CA). No significant differences in CA or RA were observed between experiments, suggesting that the children were comparable in CA and RA across experiments.

The different effects may have emerged because of the duration of the primes being tested. To benefit from the rhythmicity of the short primes in Experiment 1, it was necessary to quickly and accurately entrain to the rhythm to create strong expectations that continued across the subsequent sentences. Children with higher RAs (perhaps linked also to greater beat processing abilities) may have been better able to quickly and successfully entrain to the rhythms compared to those with lower RAs. To benefit from the longer primes in Experiment 2, children had to listen attentively for up to 32 seconds. Research has shown that the ability to sustain attention over time increases with chronological age [START_REF] Greenberg | Developmental normative data on the Test of Variables of Attention (T.O.V.A.)[END_REF][START_REF] Lin | Development of sustained attention assessed using the continuous performance test among children 6-15 years of age[END_REF], and [START_REF] Lin | Development of sustained attention assessed using the continuous performance test among children 6-15 years of age[END_REF] show a particular increase in sustained attention from the ages of seven to eight.

The current results may therefore reflect different skills necessary to benefit from rhythmic primes depending on their duration.

These findings have implications for future rhythmic priming and rhythmic training studies. Our results obtained with children in the age range from seven to nine years suggest that rhythmic priming (1) is more successful with longer prime durations, and for older children, and

(2) may also be successful at shorter prime durations for children with a higher reading age. For the longest prime length (32 s), a benefit for the regular compared to irregular primes was found across all children, suggesting that this length of prime is appropriate for use with the current age group (as seen in previous research, e.g., [START_REF] Bedoin | Temporally regular musical primes facilitate subsequent syntax processing in children with specific language impairment[END_REF][START_REF] Przybylski | Rhythmic auditory stimulation influences syntactic processing in children with developmental language disorders[END_REF]. A recent study by [START_REF] Canette | Rhythmic and textural musical sequences differently influence syntax and semantic processing in children[END_REF] used 16-second regular rhythmic primes as in the current experiments and found a significant benefit for regular rhythmic primes compared to textural sound primes and a baseline silence condition (tested in a different sample of participants) on a grammaticality judgment task in children aged 7;2 -8;11. It is possible that the children in this study might have had high reading ages, or that the comparison with textured primes changed the experimental context, resulting in a benefit from short rhythmic primes. Another difference to the current experiment is that [START_REF] Canette | Rhythmic and textural musical sequences differently influence syntax and semantic processing in children[END_REF] presented only four sentences after each prime instead of six sentences. It would therefore be interesting to further investigate the potential interaction between prime duration and the persistence of the priming effect over time. Our current findings suggest that RA should be more systematically assessed and reported in studies of rhythmic processing abilities, as well as studies investigating rhythmic stimulation on language processing.

One outstanding question relates to the observation that correlations with RA and performance after a regular prime were observed in all regular conditions except for the 16 s condition in Experiment 2. It is possible that the priming effect is related to RA most strongly at short prime durations, and that the experimental context played a role in the current result pattern. As discussed above, children with higher RAs may have been better able to immediately entrain to the beat of the 8 s primes, which then persisted over time to the second part of the experiment with 16 s primes. However, the difference between children with low and high RAs when starting with 16 s primes might not have been so large, as both may have been able to successfully entrain, but not benefit from sustained oscillations. Again, in the second part of Experiment 2, and for the longer primes, the correlation with RA emerged again, suggesting a benefit of the longer prime over time for children with higher RAs. To further investigate these questions, it would be valuable to measure rhythmic entrainment in children, and investigate whether there are connections between entrainment to the beat, reading age, and prime duration.

The current experiments provided an initial attempt to investigate CA and RA effects within the rhythmic priming paradigm. Future research should manipulate CA and RA more directly by creating distinct groups to compare, and with a larger age range. The benefit of the rhythmic prime may also be optimal at different ages depending on the language tested; for example, English-speaking children [START_REF] Chern | New evidence of a rhythmic priming effect that enhances grammaticality judgments in children[END_REF]) might be able to benefit from rhythmic primes at a younger age than French-speaking children [START_REF] Bedoin | Temporally regular musical primes facilitate subsequent syntax processing in children with specific language impairment[END_REF][START_REF] Przybylski | Rhythmic auditory stimulation influences syntactic processing in children with developmental language disorders[END_REF] due to a clearer rhythmic structure in English [START_REF] Lidji | Listeners feel the beat: Entrainment to English and French speech rhythms[END_REF].

Conclusion

The current experiments replicated previous findings showing that 32-second regular rhythmic primes enhance grammaticality judgments compared to irregular rhythmic primes in seven-to nine-year-old children. Our study revealed this duration as optimal compared to shorter prime lengths (16 s, 8 s), likely because of stronger expectations and neural entrainment to the regular rhythms that persisted across the subsequent block of sentences. Our study provided new contributions to show that reading age was correlated with sensitivity to grammaticality judgements after short (8 s, 16 s) regular primes in Experiment 1, and after long (32 s) rhythmic primes in Experiment 2, and that accuracy after 32-second regular rhythmic primes was linked with age in Experiment 2. Based on our findings, future research should continue to investigate effects of CA and RA on the rhythmic priming effect, in line with the development of neural entrainment and synchronization to the beat in young children within the dynamic attending framework [START_REF] Drake | The development of rhythmic attending in auditory sequences: Attunement, referent period, focal attending[END_REF][START_REF] Jones | Time will tell[END_REF][START_REF] Mcauley | The time of our lives: Life span development of timing and event tracking[END_REF].

Figure 1 .

 1 Figure 1. Method for Experiments 1 and 2. Short primes were presented in the first part of the

Sentences.

  Two lists (A, B) of 96 French sentences spoken naturally by a native French female speaker were used. Each list contained 48 grammatical and 48 ungrammatical sentences. Sentences that were grammatical in List A were ungrammatical in List B. Sentences of List A and List B were matched on a number of lexical properties, such as the number of words and the number of syllables, the lexical frequency, and the grammatical type of the open-class words.

( 1 )

 1 Model1 <-glmer(Correct ~ PrimeRegularity * Duration + (1 |Participant) + (1 + Sent_List | Sent_Num), data = data, family = binomial(link="logit"))

  ) Model2 <-glmer(Correct ~ PrimeRegularity * Duration * Grammaticality + (1 |Participant) + (1 + Sent_List | Sent_Num), data = data, family = binomial(link="logit"))

  ) Model3 <-glmer(Correct ~ PrimeRegularity * Duration * RAScaled + (1 |Participant) + (1 + Sent_List | Sent_Num), data = data, family = binomial(link="logit")) (4) Model4 <-glmer(Correct ~ PrimeRegularity * Duration * CAScaled + (1 |Participant) +(1 + Sent_List | Sent_Num), data = data, family = binomial(link="logit"))

( 6 )

 6 Model6 <-lmer(RT ~ PrimeRegularity * Duration * Grammaticality * RAScaled+ (1 |Participant) + (1 + Sent_List | Sent_Num), data = data). (7) Model 7 <-lmer(RT ~ PrimeRegularity * Duration * Grammaticality * CAScaled+ (1 |Participant) + (1 + Sent_List | Sent_Num), data = data).

Figure 2 .Figure 3 .

 23 Figure 2. Sensitivity to grammaticality judgments after regular and irregular rhythms in the 8 s

Figure 4 .

 4 Figure 4. Sensitivity to grammaticality judgments after regular and irregular primes in the 16 s

Figure 5 .

 5 Figure 5. Correlations between reading age (in months) and d prime depending on prime

Figure 6 .

 6 Figure 6. No other effects were significant (all p-values > .20).

Figure 6 .

 6 Figure 6. Visual representation of the Prime Regularity × Duration × Chronological Age

Figure 7 .

 7 Figure 7. Visual representation of Model 6 (response times), to show the interaction between

Table 1

 1

, all p-values > .64). Reading age correlated positively with d' judgments after regular rhythmic primes for both 8 s, r(30) = .37, p = .039 and 16 s, r(30) = .36, p = .046 durations, but not after irregular rhythmic primes for 8 s, r(30) = .24, p = .19, or 16 s, r(30) = .11, p = .55, durations. See Figure

3

. Chronological age did not correlate with any of the conditions (all p-values > .13), nor did response bias c (all p-values > .13).

Table 1

 1

, all p-values > .40).

Reading age positively correlated with d' after 32-second regular primes, r(34) = .33, p = .050, but not 16 s regular primes, r(34) = .28, p = .11, or irregular primes at either 16 s, r(34) = .27, p = .11 or 32 s, r(34) = .08, p = .67. See Figure

5

. Chronological age did not correlate with any of the conditions (all p-values > .28), nor did response bias c (all p-values > .24).

  suggests that the strength of endogenous oscillations to external rhythmic stimuli increases with age, with weaker driven oscillations in younger children. Future research could aim to boost synchronization capacity in younger children by adding a motor component to the experiment (e.g., short-term rhythmic or audio-motor training,

  Les chaussures du bébé ne sont pas propres Les parents des élèves ne suis pas contents 17 Gender Le lapin saute dans le trou au fond du jardin Le cheval dort dans la pré à côté du lac 17 Gender Le cheval dort dans le pré à côté du lac Le lapin saute dans la trou au fond du jardin 18 Gender Les oiseaux volents dans le ciel tout l'été Les vaches mangent dans la champ toute la journée 18 Gender Les vaches mangent dans le champ toute la journée Les oiseaux volents dans la ciel tout l'été 19 Gender La salade pousse dans le jardin chez mon grand-père Le mari de le voisine chante dans son salon 19 Gender Le mari de la voisine chante dans son salon La salade pousse dans la jardin chez mon grand-père 20 Gender La caméra filme la danseuse pendant le spectacle Le policier cache la révolver derrière la voiture 20 Gender Le policier cache le révolver derrière la voiture La caméra filme le danseuse pendant le spectacle 21 Gender Le vent souffle sur la colline ce soir La neige tombe sur le piste en hiver 21 Gender La neige tombe sur la piste en hiver Le vent souffle sur le colline ce soir 22 Gender Le voisin ramasse le courrier et nous l'apporte Le gardien arrête la ballon et nous le renvoie 22 Gender Le gardien arrête le ballon et nous le renvoie Le voisin ramasse la courrier et nous l'apporte 23 Gender Le patron a terminé le travail que nous avions commencé Le directeur a appelé la taxi qu'il avait réservé 23 Gender Le directeur a appelé le taxi qu'il avait réservé Le patron a terminé la travail que nous avions commencé 24 Gender La maîtresse parle à la classe et écrit au tableau Le chasseur part à le chasse dès le petit matin 24 Gender Le chasseur part à la chasse dès le petit matin La maîtresse parle à le classe et écrit au tableau 25 Tense Nous attendons qu'il ait fini son repas Nous attendons qu'il a changé ses lunettes 25 Tense Nous attendons qu'il ait changé ses lunettes Nous attendons qu'il a fini son repas 26 Tense Il est possible qu'Antoine soit en vacances cette semaine Il est possible que Paul est au marché ce matin 26 Tense Il est possible que Paul soit au marché ce matin Il est possible qu'Antoine est en vacances cette semaine 27 Tense J'aimerais qu'ils aillent au cinéma J'aimerais qu'il vient pour dîner 27 Tense J'aimerais qu'il vienne pour dîner J'aimerais qu'ils vont au cinéma 28 Tense Il faut que tes affaires soient propres pour demain Il faut que nous partons dans peu de temps 28 Tense Il faut que nous partions dans peu de temps Il faut que tes affaires sont propres pour demain 29 Tense Il serait intéressant que vous écoutiez cette émission Il serait intéressant que vous regardez quelques dossiers 29 Tense Il serait intéressant que vous regardiez quelques dossiers Il serait intéressant que vous écoutez cette émission 30 Tense Elle refuse que tu prennes un deuxième bonbon Il refuse que tu mets son manteau noir 30 Tense Il refuse que tu mettes son manteau noir Elle refuse que tu prends un deuxième bonbon 31 Tense Tu préfèrerais qu'il vienne ce matin Tu préfèrerais qu'elle prend le train 31 Tense Tu préfèrerais qu'elle prenne le train Tu préfèrerais qu'il vient ce matin 32 Tense Il faudrait qu'Olivier dorme chez vous Il faudrait que papa fait les courses 32 Tense Il faudrait que papa fasse les courses Il faudrait qu'Olivier dort chez vous 33 Auxiliary Aujourd'hui, Marie est rentrée tôt chez elle Samedi, mes frères ont arrivés en retard 33 Auxiliary Samedi, mes frères sont arrivés en retard Aujourd'hui, Marie a rentrée tôt chez elle 34 Auxiliary Je me suis trompée dans mes dossiers Je m'ai fait mal au genou 34 Auxiliary Je me suis fait mal au genou Je m'ai trompée dans mes dossiers 35 Auxiliary Dimanche, mes parents sont partis en vacances Hier, elle a restée manger chez moi 35 Auxiliary Hier, elle est restée manger chez moi Dimanche, mes parents ont partis en vacances 36 Auxiliary Hier, je me suis cassé le bras Je m'ai baigné dans la mer 36 Auxiliary Je me suis baigné dans la mer Hier, je m'ai cassé le bras 37 Morphology Thomas dessine de mieux en mieux depuis quelques tempsHélène écrit de mieux en bien depuis cette année 37 Morphology Hélène écrit de mieux en mieux depuis cette année Thomas dessine de mieux en bien depuis quelques temps 38 Morphology Le pantalon ne semble ni vert ni bleu clair La jeune fille ne veut ni parler pas chanter 38 Morphology La jeune fille ne veut ni parler ni chanter Le pantalon ne semble ni vert pas bleu clair 39 Morphology Je rentre chez moi en voiture tous les soirs Il va au théâtre par vélo tous les jours 39 Morphology Il va au théâtre à vélo tous les jours Je rentre chez moi par voiture tous les soirs 40 Morphology Ce parc paraît grand comparé à l'autre L'été semble court comparé que l'hiver 40 Morphology L'été semble court comparé à l'hiver Ce parc paraît grand comparé que l'autre 41 Position Elle veut un gâteau et je le lui donne dans une assiette C'est mon journal, il faudra le me rendre au plus vite 41 Position C'est mon journal, il faudra me le rendre au plus vite Elle veut un gâteau et je le donne lui dans une assiette 42 Position Il travaille avec moi, je le connais bien depuis longtemps Si tu es trop fatigué, dis moi le sans plus attendre 42 Position Si tu es trop fatigué, dis le moi sans plus attendre Il travaille avec moi, je connais le bien depuis longtemps 43 Position Il ignore ce mot, explique le lui pour qu'il puisse le comprendre Si le médecin appelle, passe nous le pour que nous puissions prendre rendez-vous 43 Position Si le médecin appelle, passe le nous pour que nous puissions prendre rendez-vous Il ignore ce mot, explique lui le pour qu'il puisse le comprendre 44 Position Tu as un nouveau chat, montre le moi tout de suite Il vient d'arriver, je trouve le aimable et très beau 44 Position Il vient d'arriver, je le trouve aimable et très beau Tu as un nouveau chat, montre moi le tout de suite 45 Past Participle Hier soir, il a ouvert ses cadeaux Le monsieur a vendre tous ses fruits 45 Past Participle Le monsieur a vendu tous ses fruits Hier soir, il a ouvrir ses cadeaux 46 Past Participle Elle a lu une histoire aux élèves Ils ont vouloir jouer avec ta balle 46 Past Participle Ils ont voulu jouer avec ta balle Elle a lire une histoire aux élèves 47 Past Participle Le gardien a éteint toutes les lumières Hier matin, nous avons prendre l'avion 47 Past Participle Hier matin, nous avons pris l'avion Le gardien a éteindre toutes les lumières 48 Past Participle Les enfants ont vu un grand chien Il a mettre son plus beau costume 48 Past Participle Il a mis son plus beau costume Les enfants ont voir un grand chien

	List A			List B
	Sentence Number Error Type Grammatical	Ungrammatical *	Sentence Number Error Type Grammatical	Ungrammatical *
	1 Number	L'air est pur dans la montagne	L'herbe sont haute dans le jardin	1 Number	L'herbe est haute dans le jardin	L'air sont pur dans la montagne
	2 Number	La campagne est pleine de fleurs	La montagne sont blanche de neige	2 Number	La montagne est blanche de neige	La campagne sont pleine de fleurs
	3 Number	Les garçons partiront couper le bois	Les policiers veut arrêter le voleur	3 Number	Les policiers veulent arrêter le voleur	Les garçons partira couper le bois
	4 Number	L'enfant a entendu une belle histoire	L'ingénieur ont entendu un grand bruit	4 Number	L'ingénieur a entendu un grand bruit	L'enfant ont entendu une belle histoire
	5 Number	Les maisons sont construites	Les routes est dangereuses	5 Number	Les routes sont dangereuses	Les maisons est construites
	6 Number	Ma fille a oublié sa valise	Mon fils ont réussi son contrôle	6 Number	Mon fils a réussi son contrôle	Ma fille ont oublié sa valise
	7 Number	La maîtresse est très gentille	Le directeur sont très jeune	7 Number	Le directeur est très jeune	La maîtresse sont très gentille
	8 Number	Mon bébé a caché beaucoup de gâteaux	Le camion ont roulé pendant la nuit	8 Number	Le camion a roulé pendant la nuit	Mon bébé ont caché beaucoup de gâteaux
	9 Person	Mon papa a coupé du bois pour me chauffer	Mon ami avons donné son vélo à son frère	9 Person	Mon ami a donné son vélo à son frère	Mon papa avons coupé du bois pour me chauffer
	10 Person	Ces instruments sont en bois	Ces maisons sommes très belles	10 Person	Ces maisons sont très belles	Ces instruments sommes en bois
	11 Person	Les enfants jouent dans le jardin	Les amis parlons devant la porte	11 Person	Les amis parlent devant la porte	Les enfants jouons dans le jardin
	12 Person	Adèle cherche le jouet qu'elle a perdu	Anne ouvre le cadeau qu'elle avons reçu	12 Person	Anne ouvre le cadeau qu'elle a reçu	Adèle cherche le jouet qu'elle avons perdu
	13 Person	L'avocat aura une autre chance	L'équipe aurez un nouveau joueur	13 Person	L'équipe aura un nouveau joueur	L'avocat aurez une autre chance
	14 Person	Tes clients mettent un sucre dans leur café	Ta maman prenez son sac dans le salon	14 Person	Ta maman prend son sac dans le salon	Tes clients mettez un sucre dans leur café
	15 Person	L'enfant va aller se changer	La fille vais prendre ses lunettes	15 Person	La fille va prendre ses lunettes	L'enfant vais aller se changer
	16 Person	Les parents des élèves ne sont pas contents	Les chaussures du bébé ne sommes pas propres	16 Person

Acknowledgements

We would like to thank the children, teachers, schools, and parents who were involved in this project. We would also like to thank Florian Lecuelle, Claire Pleche, Paul Lalande-Robert, Juliette Gaillard, and Inès Leproult for help with testing, and Caroline Imbert for advice on sentence stimuli construction. This research was supported by a grant from Agence Nationale de la Recherche (ANR-16-CE28-0012-02) to BT and NB. The team Auditory Cognition and Psychoacoustics is part of the LabEx CeLyA (Centre Lyonnais d'Acoustique, ANR-10-LABX-60), and the Laboratory Dynamique Du Langage is part of the LabEx ASLAN (ANR-10-LABEX-81).

Competing Interests Statement

Declarations of interest: none.