Nelias Corentin, Geisel Theo
Max Planck Institute for Dynamics and Self-Organization, 37077, Göttingen, Germany.
Bernstein Center for Computational Neuroscience Göttingen, Georg August University Göttingen, 37073, Göttingen, Germany.
Nat Commun. 2024 Oct 28;15(1):9280. doi: 10.1038/s41467-024-53155-y.
Musical sequences are correlated dynamical processes that may differ depending on musical styles. We aim to quantify the correlations through power spectral analysis of pitch sequences in a large corpus of musical compositions as well as improvised performances. Using a multitaper method we extend the power spectral estimates down to the smallest possible frequencies optimizing the tradeoff between bias and variance. The power spectral densities reveal a characteristic behavior; they typically follow inverse power laws (1/f -noise), yet only down to a cutoff frequency, where they end in a plateau. Correspondingly the pitch autocorrelation function exhibits slow power law decays only up to a cutoff time, beyond which the correlations vanish. We determine cutoff times between 4 and 100 quarter note units for the compositions and improvisations of the corpus, serving as a measure for the degree of persistence and predictability in music. The histogram of exponents β for the power law regimes has a pronounced peak near β = 1 for classical compositions, but is much broader for jazz improvisations.
音乐序列是相互关联的动态过程，可能因音乐风格而异。我们旨在通过对大量音乐作品以及即兴表演中的音高序列进行功率谱分析来量化这些相关性。使用多窗口方法，我们将功率谱估计扩展到尽可能小的频率，优化偏差和方差之间的权衡。功率谱密度揭示了一种特征行为；它们通常遵循反幂律（1/f噪声），但仅到截止频率，在那里它们以平台期结束。相应地，音高自相关函数仅在截止时间之前表现出缓慢的幂律衰减，超过该时间相关性消失。我们为语料库中的作品和即兴表演确定了4到100个四分音符单位之间的截止时间，作为音乐中持续性和可预测性程度的一种度量。对于幂律 regime，指数β的直方图在古典作品中β = 1附近有一个明显的峰值，但对于爵士即兴表演则要宽得多。
