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arxiv: 2604.15278 · v1 · submitted 2026-04-16 · 💻 cs.SD · eess.AS

A Manual Bar-by-Bar Tempo Measurement Protocol for Polyphonic Chamber Music Recordings: Design, Validation, and Application to Beethoven's Piano and Cello Sonatas

Ignasi Sole This is my paper

Pith reviewed 2026-05-10 09:15 UTC · model grok-4.3

classification 💻 cs.SD eess.AS
keywords tempo measurementmanual annotationpolyphonic recordingsBeethoven sonatasperformance analysisexpressive timinghistorical audiochamber music
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The pith

A cumulative lap-timer protocol produces bar-by-bar beats-per-minute data with millisecond resolution from polyphonic historical recordings.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

Standard automated beat-detection tools fail on historical polyphonic chamber music because they cannot handle multiple simultaneous voices or expressive deviations such as rubato and fermatas. The paper introduces a manual protocol based on cumulative timestamps that records running time totals to each bar boundary, yielding precise BPM values while preventing error buildup and allowing internal checks. This approach was applied to more than one hundred movement-level recordings of Beethoven's five piano and cello sonatas spanning 1930 to 2012. The resulting dataset supports visualizations including tempographs, histograms, and ridgeline plots that reveal tempo distributions and performance variations. A reader would care because the method supplies a replicable way to study expressive timing in music where computational tools fall short.

Core claim

The protocol yields bar-level beats-per-minute data with millisecond resolution, permits internal self-validation, and captures expressive timing phenomena (rubato, fermatas, accelerandi, ritardandi) that automated tools systematically suppress or misread. It rests on a cumulative timestamp architecture developed in collaboration with an engineer, includes a derived BPM formula and spreadsheet structure, and was used to process duo recordings of Beethoven's piano and cello sonatas from 1930 to 2012.

What carries the argument

The cumulative timestamp architecture that records running totals to each bar boundary, preventing error accumulation during manual annotation of polyphonic audio.

If this is right

  • The mathematical derivation of the BPM formula and the spreadsheet data structure enable direct replication on additional recordings.
  • The generated dataset supports quantitative comparisons of tempo across performers and eras through tempographs and ridgeline plots.
  • The protocol records expressive features such as accelerandi and ritardandi that would otherwise be lost in automated analysis of chamber music.
  • Public release of the dataset and analysis code allows extension to other movements or similar polyphonic works.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same cumulative timestamp approach could be tested on other historical polyphonic genres, such as string quartets, to check whether it remains effective beyond duo sonatas.
  • Running the protocol on modern studio recordings of the same works would allow direct comparison of expressive timing differences between eras.
  • Adding a second annotation layer for dynamics or articulation at the same bar points might produce richer performance datasets with minimal extra effort.
  • Statistical measures of agreement across multiple annotators could be added to quantify the reliability of the bar-boundary identifications.

Load-bearing premise

Human annotators can consistently and accurately identify bar boundaries in polyphonic historical audio without introducing systematic bias or fatigue-related errors that the cumulative timestamp architecture cannot fully mitigate.

What would settle it

Independent runs of the protocol by two different annotators on the same recordings, followed by direct comparison of the resulting per-bar BPM sequences, would show whether timings and values match within acceptable error bounds.

Figures

Figures reproduced from arXiv: 2604.15278 by Ignasi Sole.

Figure 1
Figure 1. Figure 1: Overlay of five representative cellists’ tempo [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 3
Figure 3. Figure 3: Ridge plot of per-performance tempo distribu [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
read the original abstract

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.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 0 minor

Summary. The paper introduces a formal manual protocol for bar-by-bar tempo measurement in polyphonic historical chamber music recordings, using a cumulative timestamp (lap-timer) architecture to achieve millisecond-resolution BPM data. It documents the systematic failure of automated beat-detection tools on Beethoven piano-cello sonata recordings, derives the BPM formula mathematically, characterises errors, applies the method to over 100 movement-level recordings (1930–2012), generates visualisations (tempographs, ridgeline plots, etc.), and releases the full dataset and analysis code publicly. The central claim is that this manual approach is a principled solution for capturing expressive timing (rubato, fermatas, accelerandi) that automation suppresses.

Significance. If the protocol's claimed reliability holds, the work supplies a reproducible, high-resolution method for extracting expressive tempo data from polyphonic historical audio where current computational tools are inadequate, directly supporting empirical performance analysis. The public release of the complete dataset and code is a clear strength that enables independent verification and reuse.

major comments (1)
  1. [Abstract and error characterisation section] Abstract and error characterisation section: the paper asserts that the protocol 'permits internal self-validation' and presents 'the error characterisation ... in full,' yet no quantitative metrics are reported (e.g., inter-annotator agreement coefficients, repeated-annotation error rates, or comparison of annotated bar onsets against score-derived positions). This is load-bearing for the central claim, because the protocol's advantage over automated tools rests on demonstrating that human boundary placement is sufficiently consistent to avoid systematic bias or fatigue effects that would propagate into the BPM curves and tempographs.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their constructive and detailed review. We address the single major comment below and outline the revisions we will make.

read point-by-point responses

  1. Referee: [Abstract and error characterisation section] Abstract and error characterisation section: the paper asserts that the protocol 'permits internal self-validation' and presents 'the error characterisation ... in full,' yet no quantitative metrics are reported (e.g., inter-annotator agreement coefficients, repeated-annotation error rates, or comparison of annotated bar onsets against score-derived positions). This is load-bearing for the central claim, because the protocol's advantage over automated tools rests on demonstrating that human boundary placement is sufficiently consistent to avoid systematic bias or fatigue effects that would propagate into the BPM curves and tempographs.

    Authors: We agree that the absence of quantitative metrics is a gap. The internal self-validation arises from the cumulative timestamp (lap-timer) architecture, which makes any boundary inconsistency immediately visible in subsequent bar timings and prevents cumulative drift; this is described in the protocol section and error characterisation. The error characterisation section details qualitative sources of error (onset ambiguity in polyphonic textures, potential fatigue) and the design mitigations. However, no numerical coefficients or repeated-annotation statistics are provided. We will revise by re-annotating a stratified subset of at least 20 movements after a minimum one-month delay, compute bar-onset timing differences and derived BPM discrepancies, and report mean absolute error, standard deviation, and any systematic trends. We will also add a brief discussion of why direct comparison to score-derived onsets is limited for expressive historical performances. These quantitative results and the discussion will be added to the error characterisation section and referenced in the abstract. This revision directly addresses the load-bearing concern while preserving the protocol's core description. revision: yes

Circularity Check

0 steps flagged

No circularity: manual protocol and BPM derivation are independent of outputs

full rationale

The paper describes a cumulative lap-timer protocol for manual bar-boundary annotation in polyphonic recordings, with a standard BPM formula derived directly from measured timestamps (BPM = 60 / inter-bar interval in seconds, aggregated per bar). This is a direct calculation from human-placed timestamps rather than any fitted parameter, self-referential definition, or prediction that reduces to the input data by construction. No self-citations are invoked as load-bearing uniqueness theorems, no ansatz is smuggled, and no known empirical pattern is merely renamed. Internal self-validation refers to consistency checks on the cumulative timestamps themselves, not a redefinition of the measured quantities. The protocol stands as an independent measurement method whose outputs (BPM curves) are not presupposed in its design.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The protocol rests on the domain assumption that human perception can reliably segment bars in overlapping instrumental audio; no free parameters or invented entities are introduced in the abstract description.

axioms (1)
  • domain assumption Human listeners can accurately and consistently detect bar boundaries in polyphonic historical recordings
    Foundational to the manual protocol's validity and error characterisation claims

pith-pipeline@v0.9.0 · 5571 in / 1109 out tokens · 48301 ms · 2026-05-10T09:15:48.215231+00:00 · methodology

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Forward citations

Cited by 4 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Towards Revised Tempo Indications for Beethoven's Piano and Cello Sonatas: Czerny, Moscheles, Kolisch, and Recorded Practice 1930-2012

    cs.SD 2026-04 unverdicted novelty 7.0

    Historical tempo indications for Beethoven sonatas are exceeded by 15-39% in recordings, Kolisch's markings align better, and stable mid-range traditions support proposed revised tempo ranges reflecting actual perform...

  2. Spectrographic Portamento Gradient Analysis: A Quantitative Method for Historical Cello Recordings with Application to Beethoven's Piano and Cello Sonatas, 1930--2012

    cs.SD 2026-04 unverdicted novelty 6.0

    A spectrographic method quantifies portamento gradient in Hz/s and finds it correlates negatively with tempo across 22 historical recordings of Beethoven cello sonatas from 1930-2012.

  3. Coexisting Tempo Traditions in Beethoven's Piano and Cello Sonatas: A K-means Clustering Analysis of Recorded Performances, 1930-2012

    cs.SD 2026-04 unverdicted novelty 6.0

    K-means clustering of historical Beethoven sonata recordings identifies multiple stable tempo traditions per movement that persist independently over eight decades instead of showing uniform change.

  4. A Complementary Visualisation Suite for Empirical Performance Analysis: Tempographs, Histograms, Ridgeline Plots, Stacked Bar Charts, and Combination Charts Applied to Beethoven's Piano and Cello Sonatas

    cs.SD 2026-04 unverdicted novelty 4.0

    The paper introduces and demonstrates a complementary set of five visualizations including tempographs, spline-smoothed histograms, ridgeline plots, stacked bar charts, and combination charts for bar-level tempo data ...

Reference graph

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