Ignasi Sole

Ignasi Sole

Empirical performance analysis depends on the accurate extraction of tempo data from recordings, yet standard computational tools, designed for monophonic audio or modern studio conditions, fail systematically when applied to historical polyphonic chamber music. This paper documents the failure of automated beat-detection software on duo recordings of Beethoven's five piano and cello sonatas (Op.~5 Nos.~1 and~2; Op.~69; Op.~102 Nos.~1 and~2), and presents a formalised manual alternative: a cumulative lap-timer protocol that yields bar-level beats-per-minute data with millisecond resolution. The protocol, developed in cross-disciplinary collaboration with an engineer specialising in VLSI design, rests on a cumulative timestamp architecture that prevents error accumulation, permits internal self-validation, and captures expressive timing phenomena (rubato, fermatas, accelerandi, ritardandi) that automated tools systematically suppress or misread. The mathematical derivation of the BPM formula, the spreadsheet data structure, and the error characterisation are presented in full. Applied to over one hundred movement-level recordings spanning 1930--2012, the protocol generated a dataset subsequently visualised through tempographs, histograms with spline-smoothed probability density functions, ridgeline plots, and combination charts. The paper argues that manual annotation is not a methodological retreat but a principled response to the intrinsic limitations of computational tools when faced with the specific challenges of polyphonic historical recordings. The complete dataset and analysis code are publicly available.

Ignasi Sole

Empirical studies of recorded performance have conventionally modelled tempo change as a unidirectional historical process, fitting linear regression lines to tempo data plotted against recording year. This paper argues that such approaches impose a false narrative of uniform stylistic evolution on what is, in fact, a plurality of coexisting interpretive traditions. Applying k-means clustering (k=3) to bar-level BPM data from over one hundred recordings of Beethoven's five piano and cello sonatas (Op. 5 Nos. 1 and 2; Op. 69; Op. 102 Nos. 1 and 2) spanning 1930-2012, this study reveals that every movement supports at least two, and usually three, discrete tempo traditions (slow, mid-range, and fast), whose internal regression slopes are negligible (R-squared <= 0.25 in all but one case), demonstrating that each tradition is independently stable across eight decades. The mid-range cluster dominates in all movements, typically comprising 55-70% of recordings. A slow cluster is absent from fast-character movements (Op. 5 Rondos, Op. 69 Scherzo), reflecting a shared rhetorical consensus about their character. The single case of significant intra-cluster drift (Op. 102 No. 1 Allegro con brio, R-squared=0.246, p=0.013) indicates a moderate mid-range deceleration of approximately 3.2 BPM across the study period. No correlation is found between cluster membership and performers' generational, national, or pedagogical backgrounds, suggesting that tempo tradition reflects individual interpretive choice rather than collective cultural inheritance. The paper proposes an ecological model of stylistic change - coexisting traditions shifting in relative prevalence rather than a single tradition evolving - and argues that this reframing has broad implications for how empirical performance studies interpret corpus-level tempo data.

Ignasi Sole

Portamento in string performance has been studied primarily as a binary presence-or-absence phenomenon, with existing research measuring frequency of occurrence and, less commonly, duration in milliseconds. This paper introduces a third quantitative descriptor; the spectrographic gradient of the portamento slide, measured in Hz/second, and demonstrates its measurement using a protocol combining Sonic Visualizer's melodic spectrogram layer, GIMP pixel analysis, and metric calibration against the spectrogram's known frequency axis. The gradient captures what duration alone cannot: the steepness of the pitch trajectory, which encodes the expressive character of the slide independently of its length. Applied to the opening measures of. Specifically because their monophonic texture permits reliable spectrographic pitch tracking. The method yields gradient values ranging from approximately 600~Hz/s in late-period recordings to over 4,000~Hz/s in early twentieth-century performances. The paper further documents a gain-recovery protocol that extends the analysable corpus to analogue recordings from the 1930s where portamento traces are faint in digital transfer. Applying the method to a corpus of 22 recordings spanning 1930--2012, the paper tests the hypothesis that gradient steepness correlates negatively with tempo: that slower performances produce steeper, longer slides while faster performances produce shallower slides or none at all. The results support this hypothesis, suggesting that the widely documented decline of portamento across the twentieth century is not a binary transition from presence to absence but a continuou

Ignasi Sole

Historical metronome indications for Beethoven's five piano and cello sonatas (as transmitted by Czerny, Moscheles, and Kolisch), have long been regarded as problematic by performers and scholars alike. This paper presents the first systematic empirical assessment of those indications against a corpus of over one hundred movement-level recordings spanning 1930--2012, encompassing first, second, and third movements across all five sonatas (Op.~5 Nos.~1 and~2; Op.~69; Op.~102 Nos.~1 and~2). The core findings are threefold. First, Czerny's and Moscheles's markings are consistently and substantially exceeded by the entire recording corpus: gaps of 15--39\% are documented across movements, with the largest divergences in slow Adagio movements and the smallest in fast Allegro finales. Second, Kolisch's 1943 markings align considerably more closely with recorded practice than either Czerny's or Moscheles's, a striking result given that Kolisch was reasoning without corpus data. Third, the central Allegro tempo traditions for each movement are stable across eight decades; not because all performers play alike, but because three coexisting slow, mid-range, and fast traditions persist simultaneously, with the mid-range dominant throughout. Building on these findings, this paper proposes a set of revised tempo indications grounded in the statistical modal tempi of the corpus, presented as ranges reflecting the documented spectrum of expert interpretive practice rather than single prescriptive values. These indications are offered not as claims about Beethoven's intentions but as evidence-based reference points for performers and scholars navigating the gap between historical prescription and performable reality.

Ignasi Sole

The choice of visualisation in empirical performance analysis is not a neutral presentation decision but an analytical one: different graphical forms reveal different features of the same dataset, and reliance on any single type systematically conceals what the others expose. This paper presents and argues for a suite of five complementary visualisation tools; tempographs, histograms with spline-smoothed probability density functions, ridgeline plots, stacked bar charts, and combination charts. These are applied to bar-level beats-per-minute data from recordings of Beethoven's five piano and cello sonatas (Op.~5 Nos.~1 and~2; Op.~69; Op.~102 Nos.~1 and~2) spanning 1930--2012. Each tool is described formally, its analytical properties characterised, its implementation detailed in working Python and MATLAB code, and its specific contribution demonstrated on a worked example using two recordings of Op.~5 No.~1 (Casals/Horszowski 1930--39 and Isserlis/Levin 2012) separated by eight decades. A five-panel composite figure applies all five tools to the same two recordings simultaneously, making the complementarity argument concrete: the tempograph reveals moment-to-moment structural parallels invisible in aggregate statistics; the spline-smoothed histogram exposes bimodality and secondary peaks suppressed by binning artefacts; the ridgeline plot positions both recordings within the full distributional space; the stacked bar chart shows divergent sectional pacing concealed by identical movement means; and the combination chart integrates mean tempo, variability, and historical reference marks in a single view. The spline-CDF smoothing method, applied to histogram data via cubic spline interpolation with zero-slope boundary conditions, is presented as a novel contribution to the performance analysis toolkit. Full implementation code is publicly available.