Revisiting Expressive Timing in Piano Performance at Scale: A Distant Listening, Multi‑Corpus Study

2.1 Relational invariance

In the first experiment, we ask the question of whether note inter‑onset intervals (IOIs) (termed ‘timing patterns’ or ‘timing profiles’ by Repp (1990, 1992a, 1994) and Desain and Honing (1994)) scale proportionally with global tempo or, alternatively, if a change in global tempo necessitates a change in timing patterns. This question can be formalized as a hypothesis test. The null hypothesis (H0) corresponds to the relational invariance hypothesis, which assumes that variations in timing patterns remain relationally invariant under moderate changes in global tempo (Repp, 1994). In contrast, the alternative hypothesis (HA) is the tempo‑specific timing hypothesis, which states that timing patterns are intrinsically linked to tempo such that different (phrase‑)structural levels become salient at different global tempi (Honing, 2007).

Evidence has been found both in favor of the relational invariance hypothesis (H0, in the following) and its alternative tempo‑specific timing hypothesis (HA). Repp (1994) compared recordings by two pianists playing Schumann’s ‘Träumerei’ three times at three different tempi on a computer‑controlled piano and found IOIs to scale roughly in proportion with global tempo, concluding relational invariance to hold up. Following the same procedure, Desain and Honing (1994) studied recordings of the theme and first variation of the Beethoven variations WoO 70, played by two pianists again at three different tempi, and found significant interactions between global tempo and IOIs, concluding that timing patterns do not scale proportionally with global tempo. Contrasting their results with the then‑recent results by Repp (1994), the underlying musical structure, the range of tempi considered, and finally methodological issues related to IOI measurement were listed as potential factors having influenced the analysis.

2.2 Articulation: Score markings, interval consonance, and register

Prior empirical performance studies have proposed several musical factors that systematically influence performed articulation. Bresin and Battel (2000) investigated articulation strategies in the second movement of Mozart’s Piano Sonata KV.545, comparing passages marked legato and staccato. They showed that articulation markings are reflected in measurable differences in the ratio between performed note duration and IOI, providing evidence for a score‑marking hypothesis.

Register has also been proposed as an influencing factor. Due to the acoustic properties of the piano, higher‑pitched tones decay faster than lower ones (Benade, 1977). Based on this, Repp (1995) observed that pianists tend to adapt their articulation across registers to achieve perceptually consistent continuity, motivating a register hypothesis.

A further proposal concerns interval consonance. Repp (1996b) suggested that dissonant intervals may be articulated with less overlap than consonant ones, forming an interval consonance hypothesis. However, this hypothesis has so far only been supported by controlled listening experiments and not yet confirmed on performance data.

2.3 Chord asynchrony

In expressive piano performance, temporal asynchronies between voices, i.e., where notes notated at the same score onset are played non‑simultaneously, either within one or across both hands, are a well‑documented phenomenon. These asynchronies can occur in various forms, most prominently as melody lead (also known as bass lag), where the melody voice precedes accompanying voices by 20–30 ms, or bass anticipation (also known as bass lead), where the bass note occurs approximately 50 ms earlier than other chord notes (Goebl, 2001; Goebl et al., 2010; Palmer, 1996b).

A central question concerns the underlying mechanism of these asynchronies: do they arise from intentional temporal accentuation or from dynamic emphasis? This alternative velocity hypothesis proposes that observed onset differences may be mechanical consequences of playing melody notes louder, rather than deliberate timing choices. While early studies found weak or inconsistent correlations between MIDI velocity and onset timing (Palmer, 1989), later work demonstrated a strong relationship between voice‑leading asynchronies, and dynamic differentiation (Repp, 1996a). Goebl (2001) further showed that melody lead disappears almost entirely when measuring finger‑key contact times, implying that dynamic accentuation, rather than timing intention, may drive observed onset differences.

Beyond melody lead, research has documented systematic variations in asynchrony patterns according to musical structure. Between‑hand asynchronies vary with texture, tempo, and metrical position: Performances of pieces of predominantly chordal textures show less asynchrony than those with sustained melodic lines, and faster tempi tend to reduce both the magnitude and variability of asynchrony (Goebl et al., 2010). Likewise, both melody lead and bass anticipation have been observed to be particularly pronounced on metrically strong positions (Palmer, 1996b), followed by other on‑beat and least frequently off‑beat metrical positions (Goebl et al., 2010).

4.1 Data format

To facilitate the analysis of multiple datasets, we used a standardized pipeline based on scores in MusicXML format and piano performances as MIDI files. Note‑level alignments between score and performance stem either from manual curation or from state‑of‑the‑art symbolic alignment algorithms (Peter, 2023; Peter et al., 2023) and are encoded in the match file format (Foscarin et al., 2022).

4.2 Corpora

The corpora vary in size, performance skill level, repertoire, and measurement precision. Three stem from recordings by professional pianists, each focusing on the oeuvre of a specific composer. The remaining three datasets encompass a broader range of Western Common Practice solo piano music, including compositions from the Baroque to the late Romantic era. See Table 1 for an overview.

The Magaloff/Chopin corpus (Flossmann et al., 2010) is a collection of on‑stage recordings of the complete works of F. Chopin for solo piano by world‑class pianist Nikita Magaloff on a Bösendorfer SE computer‑monitored grand piano. The recordings were converted from proprietary Bösendorfer SE to standard MIDI format and subsequently note‑level–aligned with their corresponding scores. The complete corpus consists of 155 performances and 336,581 played notes and represents approximately 10 hours of music.

The Zeilinger/Beethoven corpus (Cancino‑Chacón et al., 2017) consists of performances of 31 movements from nine Piano Sonatas by L. v. Beethoven performed by the Austrian concert pianist Clemens Zeilinger and subsequently aligned using the same curation protocol as Magaloff/Chopin. This dataset comprises over 70,000 performed notes, amounting to just over 3 hours of music.

The Batik‑plays‑Mozart corpus (Hu and Widmer, 2023) contains 36 movements from 12 Piano Sonatas by W. A. Mozart performed by Viennese concert pianist Roland Batik and subsequently note‑level–aligned to a standard edition (the New Mozart Edition) of the score, which is further linked to musicological annotations (Hentschel et al., 2021). The corpus contains approximately 102,400 performed notes, totaling nearly 4 hours of music.

The Vienna 4×22 dataset (Goebl, 1999) contains 22 different performances by piano students and professors from the University of Music and Performing Arts Vienna, each of excerpts of four different pieces from the Classical–Romantic repertoire: the Etude Op. 10, No. 3 and the Ballade Op. 38 by F. Chopin, the first movement of the Sonata KV331 by W. A. Mozart, and the Deutscher Tanz D. 783 No. 15 by F. Schubert. The dataset contains close to 44,000 performed notes.

The (n)ASAP dataset (Peter et al., 2023) is the largest fully note‑aligned collection of solo piano performances, originating from the Yamaha Piano‑e‑competition and comprising over 7M annotated notes and nearly 100 hours of music by 15 composers from the Common Practice Period.

ATEPP (Zhang et al., 2022) is a large‑scale dataset of transcribed expressive piano performances by virtuoso pianists. The dataset contains 5094 aligned performances (approx. 525 hours) by 49 pianists and 25 composers ranging from the Baroque to the Modern period. The alignments were obtained using the current state‑of‑the‑art offline symbolic alignment method (99% average test F‑score) from Peter (2023).

5.1 Hypothesis

We tested H0 (relational invariance) against HA (tempo‑specific timing) by examining whether timing patterns scale proportionally with tempo changes (supporting H0) or instead change systematically in a non‑proportional manner (supporting HA). For a detailed discussion on the related debate, see Section 2.1.

5.2 Method

As pointed out by Desain and Honing (1994), the measurement and calculation of note IOIs is not trivial, as parallel (joint note onset and chord) and ornamental (grace note) structures in particular can substantially bias the results toward or against the relational invariance hypothesis.

We combined the measurement procedures proposed by Repp (1994) and Desain and Honing (1994) and computed IOIs as follows: we excluded grace notes and selected, for parallel structures, either the onset of the melody note where voicing information is available or the earliest onset where it is not. We then defined the IOI as the physical time difference between two successive onsets, which we normalized by the nominal score position distance between the corresponding note pair (e.g., a quarter note if the onsets are a quarter note value–equivalent apart, an eighth note if they are an eighth note apart, etc.). To standardize proportional tempo changes across varying average tempi and to better reflect perceptual sensitivity to tempo and timing variations, we lastly applied logarithmic transformation. We chose this hybrid approach because the two earlier studies reached conflicting conclusions, and we argue that the combination of score normalization and logarithmic scaling, without excluding notes immediately surrounding grace notes, allows us to analyze the timing–tempo relationship without bias toward invariance.

To answer the question of whether timing patterns scale proportionally with tempo, we performed two analyses. First, we compare within‑tempo group correlations to slow–fast between‑group correlations. Following Desain and Honing (1994), we avoided averaging IOIs across performances before correlation computation. Instead, for each piece, we computed all pairwise correlations between individual performances, separately for within‑tempo group pairs (e.g., slow vs. slow) and between‑tempo group pairs (e.g., slow vs. fast). We then averaged these pairwise correlations within each comparison type and report the mean and standard deviation across pieces. If relational invariance (H0) holds, between‑group correlation should be at similar levels as within‑group correlation. In line with the reference study, we tested for significance using the Fisher Z‑transform with $\alpha =0.05$.

Second, to test whether timing scales multiplicatively with tempo (H0) or exhibits tempo‑specific patterns (HA), we analyzed log‑transformed IOI sequences using separate analyses of variance (ANOVA) per piece, with tempo group (slow, medium, fast) and metrical strength (offbeat, beat, downbeat) as fixed factors. The log‑transformation converts multiplicative relationships to additive ones, allowing us to distinguish the hypotheses: H0 would predict only main effects (parallel patterns across tempos), while HA would predict a significant tempo $\times$ metrical strength interaction (non‑parallel patterns).²

Note that our analysis compares timing pattern variations across performances by different performers, unlike the within‑performer timing variation approaches of Desain and Honing (1994) and Repp (1990). We chose to apply the same method nonetheless, as empirical evidence suggests that systematic effects of musical structure (e.g., phrase boundaries, harmonic tension) tend to emerge consistently across performers—that is, there seems to be a shared cognitive strategy for timing variations related to the underlying musical structure (Desain and Honing, 1989; Langner and Goebl, 2003; Repp, 1992b).

5.3 Results

For our analysis, we considered all pieces for which there are at least three performances at three distinct estimated global tempi. We used a crude estimate of the global tempo of a performance in beats per minute (BPM) following Desain and Honing (1994), using the duration of a piece divided by the number of beats it contains. We then sorted the performances and split them into three groups (slow/medium/fast) based on their tertiles.³ Figure 1 illustrates the distribution of tempi across 1326 performances of 80 Chopin pieces in the ATEPP dataset (where each performance’s tempo is normalized by the median tempo of all performances of the same piece), along with the resulting tertile‑based grouping.

Figure 1

6.1 Hypothesis

Based on prior literature, we tested the following hypotheses in Experiment 2: H1 (Score‑marking hypothesis): Notes marked as legato exhibit greater overlap (higher key overlap ratio [KOR]) than those marked as staccato. H2 (Register hypothesis): Articulation varies systematically with pitch register, with higher registers encouraging increased overlap. H3 (Interval consonance hypothesis): Consonant intervals exhibit greater overlap than dissonant intervals. The second and third hypotheses remain empirically underexplored in real‑world performance data and are evaluated at scale in this section.

6.2 Method

The three factors investigated in this experiment—score markings, octave register, and interval consonance—were selected on the basis of established empirical findings and theoretical proposals in the performance literature. Score‑articulation markings (legato/staccato) are the most direct link between compositional intent and performed overlap (Bresin and Battel, 2000). Octave register is included because piano tone decay accelerates in higher registers, and prior work shows that pianists compensate by increasing key overlap to maintain perceptual continuity (Repp, 1995). Interval consonance is included following Repp (1996b), who proposed that consonant intervals may be held with greater overlap than dissonant ones; this hypothesis has not previously been tested at scale in real‑world performance data, making it a natural candidate for a large‑scale replication.

Key overlap ratio (KOR): To study articulation, we investigated the key overlap ratio originally proposed by Repp (1995) and also used by Bresin and Battel (2000). First, we measured the key overlap time (KOT), which is the amount of overlap time between successive piano tones that belong to the same perceptual stream, e.g., the melody line. Since post‑key press sound decays over time, brief key overlap is typically perceived not as simultaneity but as increased continuity. The KOR measures the amount of KOT in terms of the IOI between the same respective adjacent notes, and therefore presents a unit‑less, numerical measure of their relationship. As KOT is dependent on the interval size between the notes and varies with IOI (Repp, 1995), it is more natural to account for the ratio and investigate KOR in the setting of diverse datasets (Bresin and Battel, 2000). In short, the greater the KOR, the more legato‑like two adjacent notes will be perceived. Staccato notes, on the other hand, have a negative KOR. Figure 2 illustrates both measures: the top figure shows two legato‑marked notes, which have a KOT of $0.43$ ms, an IOI of $0.57$ ms, and correspondingly a KOR of $\frac{KOT}{IOI}=\frac{0.43}{0.57}=0.75$. For the bottom figure, a negative KOT for a staccato‑marked note results in a KOR of $\frac{-0.27}{0.57}=-0.47$.

Figure 2

Since our analysis relies on score‑voicing information, we chose to include the Vienna4×22, Batik, Magaloff, and Zeilinger datasets, where the source score editions are either explicitly known or have undergone careful editorial scrutiny. In contrast with Bresin and Battel (2000), who examined the full right hand, and Repp (1995), who selected individual voices, we restricted our analysis to note transitions in the melody voice. This choice is motivated by the fact that the melody voice typically forms a continuous sequence of successive notes, making note‑to‑note overlap measures well‑defined and interpretable. Other voices, such as bass or inner voices, often contain sustained tones or discontinuous entries, where key overlap is less interpretable.

While the original KOR analysis by Bresin and Battel (2000) focused on the finger and key actions in their articulation, we augmented our analysis with sound‑off articulation, which computes the prolonged note offset resulting from sustained pedal usage. For datasets where MIDI sustain control (CC64) is available and reliable (Vienna4×22, Batik, and Magaloff)⁴, we determined a dataset‑specific sound‑off threshold—the CC 64 value at which the dampers make contact with the strings.

The sound‑off threshold corresponds to a physically fixed position for a given piano: the point at which dampers touch the strings when the pedal is partially depressed. To estimate this position, we aggregated all CC 64 values recorded across all pieces (and pianists) in each dataset and inspected the resulting histogram (Figure 3). During legato re‑pedaling, the performer briefly holds the pedal at the damping position before re‑pressing; this creates a characteristic accumulation—a local mode—in the intermediate range of the CC 64 distribution, between the dominant peak at the resting position (CC $\approx$ 0 for Batik and Magaloff; CC $\approx$ 15 for Vienna4$\times$22, whose Bösendorfer CEUS sensor records an analog signal rather than a binary on/off) and the fully‑pressed peak at CC 127. We identify the threshold as the modal value of the lightly smoothed histogram of control values within the intermediate range 50–100, yielding dataset‑specific thresholds of 76 (Vienna4$\times$22), 75 (Batik), and 60 (Magaloff). Notes whose key offsets occur while the pedal control remains above this threshold are treated as acoustically sustained, and their effective note offsets are extended until the subsequent pedal‑release timestamp, identified as a time point where the CC 64 signal exhibits a large decrease (i.e., decreasing pedal values). KOR is then computed as described above, with statistics reported separately for note transitions occurring under pedal‑off and pedal‑on conditions.

Figure 3

6.3 Results

We begin by analyzing the KOR of notes based on their articulation score markings (legato and staccato), following Bresin and Battel (2000). For the Batik and Magaloff datasets, we lacked information about the specific score editions used by the pianists and whether they differ from our reference scores (the Henle Urtext Edition for Magaloff and the New Mozart Edition for Batik). However, it is reasonable to assume that the majority of articulation markings align across carefully edited scores used by professional pianists; hence, with few exceptions, the annotations in the performers’ scores likely match ours.

Articulation distinctions such as legato and staccato are, in theory, conveyed through variations in the amount of note overlap between adjacent notes. Figure 4 illustrates the distribution of note‑level KORs using violin plots, comparing legato and staccato markings. For the staccato group, we include notes marked with staccato and staccatissimo dots, while the legato group includes notes covered by slurs (excluding the last note of a slur group).

Figure 4

Overall, the differences between the legato and staccato groups are significant for all datasets: Vienna4$\times$22 ($F(1,5492)=142.0$, $P<0.05$), Batik ($F(1,11957)=537.3$, $P<0.05$), and Magaloff ($F(1,55651)=152.1$, $P<0.05$). These results indicate a consistent articulation‑dependent effect on KOR under the sound‑off (pedal‑released) condition. The Batik dataset shows the strongest distinction, suggesting that the performer interprets Mozart’s articulation markings with particularly clear differentiation between legato and staccato passages, while Magaloff shows the least‑pronounced differences between articulation groups.

In addition to score markings, consonance is another factor influencing the overlap between neighboring notes. Figure 5 shows the distribution of KORs for neighboring note pairs, grouped by interval. We computed intervals in semitone steps modulo 12 and analyzed them separately by direction (upward or downward). The interval groups, ranging from unison to tritone, are ordered by increasing levels of dissonance according to Western common‑practice harmony.

Figure 5

None of the performances in the datasets analyzed support the premise that consonant note pairs overlap more than dissonant ones. While ANOVA tests indicate significant differences in mean KOR across interval groups, Pearson’s correlation coefficient between mean KOR and consonance level (with unison = $8$ and tritone = $0$) reveals an insignificant negative trend: $r(6)=-0.50,P=0.21$ for upward intervals and $r(5)=-0.54,P=0.21$ for downward intervals. However, it is important to note that these interval categories are highly unbalanced in the performed repertoire.

In terms of the impact of direction, we also found that upward transitions generally contain more overlaps than downward transitions among all datasets, with the difference being significant for all intervals. The interval with the largest difference is the perfect fourth, a historically controversial interval with regard to consonance, where upward leaps have an average KOR (with pedal sustain) of $0.72\pm 1.35$ compared to $0.46\pm 1.26$ for downward leaps, resulting in a 56% difference. This observation may imply that the upward intervals sound more stable than the downward intervals, leading to the articulation choice of a longer overlap.

Building on the findings of Repp (1995), we investigated how key overlap varies with register in performed notes. His scale‑listening experiment demonstrated that increased overlap in the upper register was associated with improved legato perception, while the lower register tolerated less overlap, presumably due to the instrument’s inherent acoustic decay. However, in Repp’s pianist performance experiment, no significant effects of register were found. We investigated this relationship in a real‑world performance context by categorizing melody note KORs based on the octave register of both notes (with A0 marking the pitch class A in register 0).

As shown in Figure 6, our analysis reveals an overall positive relationship between register and overlap articulation. In the Magaloff dataset, the Pearson correlation between register and the mean KOR computed for each register is $r(5)=0.96,P<0.05$. The Zeilinger ($r(3)=0.83,P=0.08$) and Vienna4×22 ($r(1)=0.26,P=0.83$) datasets, which contain compositions within a narrower register range, also show a weak, nonsignificant positive trend. In contrast, the Batik dataset defies this pattern, showing a significant negative correlation ($r(4)=-0.90,P=0.02$) between register and overlap time.

Figure 6

Treating octave register as a categorical factor, a one‑way ANOVA reveals significant differences in mean KOR across registers ($F=173.4$, $P<{10}^{-200}$). Post‑hoc Holm‑corrected pairwise comparisons indicate that these differences are systematic across register pairs, despite substantial imbalance in register sample sizes.

Overall, these findings suggest that, in real‑world piano performances, higher registers tend to encourage more overlapping articulation, potentially compensating for the faster decay of high‑pitched notes. However, this positive relationship is only statistically significant for the Magaloff dataset ($r(5)=.96,p<.05$); the Batik dataset shows a significant negative register–KOR relationship ($r(4)=-0.90,P=0.02$), reflecting a repertoire‑specific effect, while the Zeilinger and Vienna4×22 datasets show nonsignificant correlations, indicating that this relationship is likely influenced by repertoire characteristics and individual performer interpretation, rather than being a universal performance rule.

7.1 Hypothesis

Building on prior work (see Section 2.3), we investigate the following hypotheses on asynchrony: H1 (Metrical hierarchy): Asynchrony magnitude increases on metrically stronger positions, with downbeats showing the largest root mean squaree (RMS) values, followed by beats, and off‑beats. H2 (Tempo hypothesis): RMS asynchrony decreases with faster tempi. H3 (Texture hypothesis): RMS asynchrony decreases in pieces with higher chordal density. H4 (Voice‑specific asynchrony hypothesis): Melody notes systematically precede other voices (melody lead), while bass patterns vary by metrical position, with bass anticipation most pronounced on downbeats. H5 (Velocity hypothesis): Observed asynchronies arise from dynamic accentuation rather than intentional timing, such that melody asynchrony correlates positively with velocity differences between melody and accompaniment voices.

7.2 Method

We restricted our analysis to polyphonic score events where at least three non‑grace or non‑ornamental notes are performed simultaneously. For each such event, we calculated the pairwise onset time differences between all notes and computed the RMS of these differences as a measure of overall asynchrony (Palmer, 1989). Specifically, for a chord with $n$ notes, we computed all $(\genfrac{}{}{0.0pt}{}{n}{2})$ pairwise differences, squared them, took their mean, and extracted the square root. This RMS measure, expressed in milliseconds, captures the overall temporal spread of notes within a chord, regardless of voice assignment.

To examine melody (bass) asynchronies specifically, we computed the onset timing difference between the melody (bass) voice and the mean onset time of all remaining notes in the chord. Where voice annotations are unavailable, we followed the common heuristic of assigning the highest and lowest pitch notes to the melody and bass voices, respectively (Palmer, 1989).

To distinguish temporal accentuation from the velocity hypothesis, which suggests that asynchronies arise mechanically from dynamic differences rather than intentional timing displacement, we computed the velocity difference between the melody note and the mean velocity of the remaining notes at each onset and measured the correlation between these timing and velocity differences.

7.3 Results

With respect to H1 (metrical hierarchy), as a general measure of temporal variability across staves, Figure 7 shows mean asynchrony measured in milliseconds (lower x‑axis) for selected composers, grouped by metrical position. The upper x‑axis shows polyphonic density—that is, the proportion of events at each metrical position that contain three or more simultaneous notes, providing textural context for interpreting asynchrony patterns. To address potential transcription artifacts while preserving performance variability, we excluded polyphonic events with RMS asynchrony values exceeding 200 ms.

Figure 7

RMS asynchrony is comparable on downbeat and beat positions but less pronounced on off‑beat positions. Similarly, chordal density is comparable on downbeat and beat positions, particularly for Romantic compositions, and lower on off‑beat positions across all compositional periods. Across all metrical positions, performances of works by Chopin and Schubert exhibit the greatest degree of asynchrony.

To address H2 and H3, we performed two separate linear regression analyses. For H2 (tempo effects), we use estimated tempo (in BPM) as the independent variable and asynchrony as the dependent variable. For H3 (texture effects), we used texture density (proportion of joint note onsets with three or more non‑grace notes, over all onsets in a given piece) as the independent variable and asynchrony as the dependent variable. We conducted these analyses at the performer level for performer‑specific datasets and at the piece level for multi‑performer datasets, and we assessed statistical significance at $P<0.05$.

For tempo effects on overall asynchrony, we found $76$ (out of $248$) significant tempo–asynchrony relationships. Of these, 43 were negative (mean slope = $-0.0007$) and $33$ were positive (mean slope = $0.0019$). These slopes are very small, indicating that the overall influence of performed tempo on asynchrony is negligible, even when significant.

Looking at the effect of musical texture, we found only $11$ (out of $248$, or 4.4%) regressions to be statistically significant, which is close to the rate of Type I errors. Moreover, the large magnitude of regression coefficients suggests numerical instability in the model. When analyzing texture effects for each hand separately, we found $67$ significant relationships for the right hand (staff 1: $21$ positive with mean slope = $0.0035$; $46$ negative with mean slope = $-0.0007$) and $64$ for the left hand (staff $2$: $29$ positive with mean slope = $0.0007$; $35$ negative with mean slope = $-0.0007$). Overall, the results indicate that the influence of texture on asynchrony is slightly negative and generally negligible.

With respect to H4 (voice‑specific asynchrony hypothesis), we investigated melody and bass note timing with respect to their tendency to lead or lag at different metrical positions. Bass notes tend to lag (59.81%) more often than they lead (39.29%). Across all datasets and metrical positions, bass lags have a mean magnitude of approximately 14.9 ms (SD = 18.1 ms), with comparable values observed at downbeat, beat, and offbeat positions. Bass leads are slightly larger in magnitude, averaging 21.8 ms (SD = 35.3 ms). Lead time magnitudes are greatest at downbeat positions (mean = 28.8 ms) and decrease at weaker metrical positions (beats and offbeats).

Melody notes tend to lead more often than they lag, with an approximate 70:30 lead‑to‑lag ratio when measured relative to all (both hand) accompaniment notes and roughly 80:20 relative to right‑hand accompaniment notes only. Lead‑time magnitudes are similar in magnitude across all metrical positions, and, on average, amount to 17.39 ms (SD = 18.13 ms) across both hands and 16 ms (SD = 17.99 ms) within the right hand. Lag times are greater at downbeat positions when measured across both hands, and less so when measured within the right hand only.

Addressing H5 (velocity hypothesis), Figure 8 illustrates the relationship between melody lead (as the timing difference between the melody voice and the mean onset time of other notes at the same onset, measured in milliseconds) and MIDI velocity differences (binned into four‑unit bins), within the right hand (top) and across both hands (bottom), grouped by metrical position (columns), for a subset of our analyzed corpora (ATEPP, (n)ASAP, and Vienna4×22). Note that this figure only includes polyphonic events with positive velocity differences. Across all datasets, cases where the melody note is played softer than the accompanying notes is relatively rare, accounting for between 2% and 16% of polyphonic events across hands and between 2% and 13% within the right hand. The lowest rates are observed in Vienna4×22 and Batik, while the higher proportions occur in (n)ASAP and ATEPP. As can be seen in Figure 8, both within‑hand and cross‑hand melody leads show a positive correlation with velocity differences (as computed on raw, unbinned velocity difference values), consistent with the velocity hypothesis that timing deviations between melodic and accompanying notes at shared score onsets may reflect dynamic accentuation strategies.

Figure 8