Objective music measures in IAMT sessions are vital for evaluating therapeutic efficacy, identifying musical elements linked to positive outcomes, assessing motor and temporal symptoms, and tailoring interventions. While Musical Instrument Digital Interface (MIDI) data analysis is growing, no prior studies have specifically explored asynchrony dispersity within IAMT sessions. Dispersity of asynchrony, encompassing both the mean temporal misalignment and its variability (measured as standard deviation), reveals patterns of rhythmic interaction stability. This study analyzes existing data to quantify asynchrony dispersity, which here represents the mean asynchrony (averaged across sessions within each segment) in IAMT sessions for PD, elucidating the dynamic interplay between participants and therapists to advance therapeutic knowledge.

Baseline and treatment sessions were aggregated (61 sessions: P1 = 20, P2 = 17, P3 = 24) and segmented into 25 equal intervals (1 - 25), averaged at 53.28 seconds per segment. Varying session duration, averaged at 22.2 minutes per session, was measured from first to last note, excluding before and after silent periods. Python (version 3.9) processed MIDI data recorded via Logic Pro.

Asynchrony was computed from MIDI data using the following step-by-step procedure:

1) MIDI note-onset events were extracted for participant drum-set strikes (categorized by trigger codes into upper extremities—UE: combined drum pads/cymbals; left foot—LF; right foot—RF) and music therapist guitar notes.

2) The reference stream was the ideal metronome grid at constant tempo, with inter-beat interval in seconds derived from the BPM value provided by Logic Pro software (denoted here as bpms for the interval in seconds; i.e., bpms = 60/BPM).

3) For each note timestamp t1 (in seconds), the nearest beat time on the grid was calculated as intquantize = bpms × round(t1/bpms).

4) Asynchrony for each event was the signed difference t1—intquantize (in seconds), with negative values indicating anticipation (note played before the beat) and positive values indicating delay (note played after the beat).

5) Only events with absolute asynchrony ≤ threshold were retained, where threshold = bpms/8 (equivalent to half the minimum inter-onset interval of bpms/4, providing a symmetric acceptance window around each beat to exclude off-beat or non-metrical events).

6) Retained asynchrony values were averaged within each of the 25 segments, separately by participant, music therapist, limb category (UE, LF, RF), and across all events (total average); segment means were then averaged across sessions to obtain the reported dispersity measures (here representing the mean asynchrony across sessions within a segment). Final asynchrony values were converted to milliseconds by multiplying by 1000 for reporting and interpretation.

The music therapist used in-ear headphones with a metronome to maintain rhythmic consistency, meaning participants responded to the music therapist’s guitar accompaniment, which was influenced by the music therapist’s asynchrony relative to the metronome [13]. Participants played a simplified electronic drum-set, encouraged to use all limbs freely, while the music therapist accompanied on acoustic guitar [11][15].

Visual inspection, standard for single-subject designs, analyzed asynchrony dispersity using Microsoft Excel. Pearson correlations (r) explored synchrony relationships using IBM SPSS Statistics (Version 28.0.1.1), with significance at 0.05 and 0.01 (2-tailed). Effect sizes were interpreted as large (r > 0.5), moderate (r = 0.3 - 0.5), or small (r < 0.3) [16].

Because the 25 segments are sequential within each session, potential temporal autocorrelation could violate the independence assumption of Pearson correlations. The present analysis is therefore treated as exploratory, describing within-session trends rather than providing formal inferential tests. Sessions were aggregated across baseline (low-to-moderate syncopation) and treatment (moderate-to-high syncopation) phases due to the staggered, multiple-baseline design. The introduction of moderate-to-high syncopation occurred at different points for each participant (between sessions 4 and 8 across the sample), reflecting the study's aim to observe changes in rhythmic interaction whenever the music therapist increased rhythmic complexity, rather than at a fixed session number or after a predetermined number of baseline sessions. Because the transitions from low-to-moderate complexity to moderate-to-high complexity were not temporally aligned across participants, condition-specific aggregation by segment was not methodologically feasible. Therefore, all available sessions were pooled and segmented uniformly into 25 intervals (average 53.28 seconds each) to enable consistent within-session trend examination across the full sample.

P1’s average asynchrony (Figure 1(a)) showed variability (−9.32 to −16.20 ms), with a slight upward trend across 20 sessions, suggesting modest synchronization improvement. P2’s asynchrony (Figure 1(b)) exhibited variability (−1.83 to −10.17

Figure 1. Average asynchrony over time for (a) Participant 1 (P1) and Music Therapist 1 (MT1), (b) Participant 2 (P2) and Music Therapist 2 (MT2), and (c) Participant 3 (P3) and Music Therapist 3 (MT3).

ms), with no clear improvement across 17 sessions, indicating inconsistent performance. P3’s asynchrony (Figure 1(c)) trended toward 0 ms across 24 sessions (−5.29 to −0.61 ms), suggesting potential synchronization gains. The average asynchrony across all participants and music therapists (Figure 2(a)) showed a downward trend in segments 1 - 7 (participants: −5.48 to −7.23 ms; music therapists: 14.87 to 12.62 ms), followed by fluctuations in segments 8 - 25 (participants:

Figure 2. Multi-panel plot showing (a) the average of average asynchrony across all participants and music therapists (total average), with a downward trend in segments 1 - 7 followed by fluctuations in segments 8 - 25, and (b) the average of average asynchrony across all participants’ lower extremities (LF and RF), showing variability with no clear trend.

to −5.80 ms; music therapists: to 13.87 ms). The average asynchrony across participants’ lower extremities (LF and RF, Figure 2(a)) showed variability (LF: −2.82 to −7.04 ms; RF: −4.01 to −6.89 ms) with no clear trend, reflecting inconsistent LE coordination. These trends reflect averages across multiple sessions (P1: 20, P2: 17, P3: 24), which may obscure session-specific patterns. Additionally, because rhythmic complexity phases were introduced at different session points across participants, these averaged segments include a mixture of low-to-moderate and moderate-to-high syncopation conditions.

The asynchrony of music therapists (MT1, MT2, MT3) was analyzed across 25 segments (Figures 1(a)-(c)). MT1 (with P1) showed positive asynchrony (7.16 to 11.65 ms), with a slight upward trend, possibly adapting to P1’s anticipatory timing. MT2 (with P2) maintained stable positive asynchrony (16.13 to 20.84 ms), suggesting consistent rhythmic guidance. MT3 (with P3) exhibited fluctuating positive asynchrony (8.67 to 17.49 ms), reflecting P3’s variable synchronization. Music therapists’ positive asynchrony contrasts with participants’ negative values, highlighting their possible guiding role. As music therapists used a metronome via in-ear headphones, their asynchrony influenced the guitar accompaniment heard by participants, likely contributing to the observed participant asynchrony patterns and correlations.

Correlations used a sample size of 25, corresponding to the 25 almost-one-minute segments per session (53.28 seconds). P1 showed strong correlations: P1-MT1 (r = 0.900, p < 0.001, large effect), UE-MT1 (r = 0.870, p < 0.001, large effect), Avg-UE (r = 0.931, p < 0.001, large effect, expected due to UE dominance), RF-LF (r = 0.640, p < 0.001, large effect), and moderate LF-MT1 (r = 0.451, p = 0.024, moderate effect). P2 showed strong Avg-UE (r = 0.981, p < 0.001, large effect), moderate LF-RF (r = 0.492, p = 0.012, moderate effect), and negative UE-MT2 (r = -0.410, p = 0.042, moderate effect). P3 showed strong Avg-UE (r = 0.981, p < 0.001, large effect), but no significant MT3 correlations (e.g., Avg-MT3: r = 0.015, p = 0.943, small effect). Combined correlations included Total Avg-MT Total (r = 0.674, p < 0.001, large effect), UE-MT Total (r = 0.677, p < 0.001, large effect), LF-RF (r = 0.692, p < 0.001, large effect), LF-Total Avg (r = 0.594, p = 0.002, large effect), RF-Total Avg (r = 0.577, p = 0.003, large effect), and RF-UE (r = 0.493, p = 0.012, moderate effect). Non-significant correlations included MTs’ Total Avg-LF (r = 0.354, p = 0.082, moderate effect) and MTs’ Total Avg-RF (r = 0.169, p = 0.419, small effect). These correlations reflect the influence of the music therapists’ metronome-guided accompaniment on participants’ timing, as participants responded to the music therapists’ music rather than the metronome directly.

These correlations reflect the shared coupling pathway in the setup: the music therapist maintained timing via an in-ear metronome, while participants synchronized to the therapist’s guitar accompaniment (itself shaped by the therapist’s metronome asynchrony). To distinguish whether the therapist primarily adapts to the participant versus the participant following the therapist would require additional evidence such as cross-lagged correlations, directional phase-locking analyses, or experimental designs that manipulate leadership roles.

Non-significant correlations included: MT2-P2 Avg (r = −0.394, p = 0.051, moderate effect); MT3-P3 Avg (r = 0.015, p = 0.943, small effect); MT1-P1 RF (r = 0.386, p = 0.056, moderate effect); MT2-P2 LF (r = 0.132, p = 0.529, small effect); MT2-P2 RF (r = −0.068, p = 0.747, small effect); MT3-P3 LF (r = 0.056, p = 0.792, small effect); MT3-P3 RF (r = −0.133, p = 0.525, small effect); P3 RF-LF (r = 0.073, p = 0.727, small effect); P3 UE-MT3 (r = 0.071, p = 0.735, small effect); MTs Total Avg-LF (r = 0.354, p = 0.082, moderate effect); and MTs Total Avg-RF (r = 0.169, p = 0.419, small effect). These findings delineate non-robust interrelations.

IAMT can enhance motor synchronization in PD, particularly for upper extremity tasks [18]. The trend in Figure 2(a) suggests structuring sessions to capitalize on early engagement (first 7 minutes), using rhythmic cues like clapping or drumming to stabilize timing, while simplifying patterns later to manage fluctuations due to fatigue or motor challenges. The LE dispersity trend (Figures 3(a)-(c)) supports incorporating lower extremity exercises, such as foot-tapping to rhythmic cues, to improve gait and balance, complementing rhythmic auditory stimulation (RAS) to reduce fall risk [19][20]. Music therapists can monitor asynchrony in real-time by listening for timing inconsistencies in client responses relative to their accompaniment, adjusting tempo or complexity based on observed motor variability or client feedback (e.g., P2’s enjoyment, P1’s dexterity improvements). For clients with musical experience (e.g., P1), complex rhythms can leverage skills to enhance engagement [13], while simpler, repetitive cues may benefit clients with inconsistent timing (e.g., P2, P3) [21]. Music therapists should collect qualitative feedback through post-session discussions to assess engagement, emotional outcomes (e.g., P3’s independence concerns), and motor gains (e.g., P2’s step count), tailoring interventions to individual needs. In low-resource settings, music therapists can use basic instruments (e.g., hand drums) or vocal cues to replicate rhythmic guidance without technology, ensuring applicability across diverse clinical contexts. Music therapists can collaborate with physical therapists or neurologists to share asynchrony insights, integrating findings into broader care plans to address motor and emotional needs. Integrating IAMT with physical therapy may enhance neuroplasticity, improving daily function [22]. Clinicians should assess clients’ musical background and motor abilities to tailor interventions and monitor dispersity to adjust session pacing.

Larger studies should explore variability factors (e.g., motor skills, therapist training) and longitudinal designs to assess synchrony development. Qualitative data on participant and therapist experiences could enrich findings with emphasis on reflective practice. Investigating IAMT in diverse PD populations globally could enhance applicability, given the international scope of music therapy. Investigating tempo and rhythm complexity may inform targeted PD interventions.

The small sample (n = 3) limits generalizability. Averaging across sessions may obscure individual trends. Unmeasured factors (e.g., musical experience, fatigue) influence outcomes. Asynchrony focus may overlook emotional benefits. Further research is needed to validate findings. Additionally, the study did not collect data on participants’ length of time since diagnosis, which may have influenced motor variability and synchronization patterns. Another limitation is the lack of specificity in distinguishing upper extremity contributions, as the analysis did not differentiate between individual upper limb movements, reducing the precision of interpretation.

A further limitation is the pooling of baseline (low-to-moderate syncopation) and treatment (moderate-to-high syncopation) sessions due to the staggered multiple-baseline design, which prevented clean separation of conditions for within-session analysis. This pooling may confound the observed within-session trends in asynchrony and timing variability, as rhythmic complexity is a direct driver of timing variability [11][23]. Future studies should introduce rhythmic complexity at the same time point across participants or systematically vary its order to better separate the effects of complexity from general within-session changes.