贝多芬钢琴与大提琴奏鸣曲的演奏速度有三种稳定传统，非单一演变。
Coexisting Tempo Traditions in Beethoven's Piano and Cello Sonatas: A K-means Clustering Analysis of Recorded Performances, 1930-2012
- 用K均值聚类分析100多个录音的每小节速度数据
- 发现慢、中、快三种速度传统共存且长期稳定，中速占55%-70%
- 速度传统不随时代、国籍或师承变化，体现个人诠释选择
对1930至2012年间超过一百个贝多芬五首钢琴与大提琴奏鸣曲（作品Op. 5 Nos. 1&2；Op. 69；Op. 102 Nos. 1&2）录音的巴级节拍数据进行k-means聚类（k=3）分析，揭示每个乐章至少存在两种、通常为三种独立的演奏速度传统（慢速、中速、快速）。各传统内部的速度趋势斜率极小（除一例外所有R²≤0.25），表明其在八十年间保持稳定。中速传统在所有乐章中占主导（55%-70%）。快速性格乐章（如Op. 5回旋曲、Op. 69谐谑曲）中无慢速传统，反映对乐曲特征的共同修辞共识。仅在Op. 102 No. 1 Allegro con brio中观察到显著内部漂移（R²=0.246，p=0.013），表现为中速组整体约3.2 BPM的缓慢下降。集群归属与演奏者世代、国籍或教学背景无相关性，说明速度传统源于个体诠释而非集体文化传承。论文提出生态式风格演变模型：多种传统并存且相对流行度变化，而非单一传统线性演化。此框架对实证演奏研究具有广泛意义。
原文摘要 · Abstract (English)
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.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。