用五种图表组合分析贝多芬钢琴与大提琴奏鸣曲演奏节奏，揭示单一图表无法展现的细节。
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
- 提出五种互补图表：时序图、平滑直方图、脊线图、堆叠条形图和组合图。
- 在1930–2012年两版《作品5号1》演奏数据中，发现节奏结构随时代变化。
- 适合音乐表演分析、数据可视化研究者，代码开源可复现。
在实证演奏分析中，可视化选择并非中立呈现，而是一种分析行为：不同图形形式揭示同一数据集的不同特征，依赖任一类型会系统性掩盖其他形式暴露的内容。本文提出并论证了一套五种互补的可视化工具：时序图（tempographs）、带样条平滑概率密度函数的直方图、脊线图、堆叠条形图和组合图。这些工具应用于1930–2012年间录制的贝多芬五首钢琴与大提琴奏鸣曲（作品5之1、2；作品69；作品102之1、2）的逐小节速度数据。每种工具均经正式描述、分析属性刻画、完整实现代码（Python与MATLAB）说明，并以两个相隔八十年的《作品5号1》录音（卡萨尔斯/霍尔佐夫斯基1930–39，伊瑟利斯/利文2012）为例展示其独特贡献。五合一复合图同时呈现五种图表，直观体现互补性：时序图揭示聚合统计忽略的瞬时结构相似性；样条平滑直方图暴露双峰及次级峰值，避免分箱伪影；脊线图将两版本置于整体分布空间中定位；堆叠条形图揭示相同乐章平均速度下段落节奏的分化；组合图整合平均速度、变异性与历史标记于一图。文中提出的样条累积分布函数平滑方法（三次样条插值，零斜率边界条件）为性能分析工具包新增技术贡献。全部实现代码公开可用。
原文摘要 · Abstract (English)
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pacing concealed by identical movement means; and the combination chart integrates mean tempo, variability, and historical reference marks in a single view.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.
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