穿越五个世纪古典音乐的时间之箭
The arrow of time across five centuries of classical music
摘要：
时间序列不可逆性的概念--信号的统计数据在时间反演下不恒定的程度--自然出现在非平衡物理学中的静态系统中，这些系统远离平衡运行并产生熵。这个概念尚未被探索到目前为止，在乐谱领域，因为这些通常是短序列的时间可逆性估计可能会遭受强大的有限大小的影响，排除解释。在这里，我们表明，所谓的水平可见性图方法-最近被证明可以量化这种统计特性，即使在非平稳信号-是一种方法，可以估计时间可逆性的短符号序列，从而解锁的可能性，探索这些属性的背景下，音乐作品。因此，我们分析了从文艺复兴到现代早期的8000多首音乐作品，并证明，事实上，它们中的大多数都显示出时间不可逆性的明显特征。由于通过构造具有线性相关结构的随机过程（如1/f噪声）是时间可逆的，因此我们得出结论，音乐作品具有相当丰富的结构，这超出了由功率谱或类似方法检索的传统属性。我们还表明，音乐作品显示出强烈的非线性相关性的迹象，非线性相关的不可逆性，这些也与不对称的音乐间隔，我们联想到的叙事音乐作品的基础丰富。这些发现为音乐时期和作曲家的研究提供了工具，也为音乐欣赏和认知提供了标准。
英文摘要：
The concept of time series irreversibility -- the degree by which the statistics of signals are not invariant under time reversal -- naturally appears in non-equilibrium physics in stationary systems which operate away from equilibrium and produce entropy. This concept has not been explored to date in the realm of musical scores as these are typically short sequences whose time reversibility estimation could suffer from strong finite size effects which preclude interpretability. Here we show that the so-called Horizontal Visibility Graph method -- which recently was shown to quantify such statistical property even in non-stationary signals -- is a method that can estimate time reversibility of short symbolic sequences, thus unlocking the possibility of exploring such properties in the context of musical compositions. Accordingly, we analyse over 8000 musical pieces ranging from the Renaissance to the early Modern period and certify that, indeed, most of them display clear signatures of time irreversibility. Since by construction stochastic processes with a linear correlation structure (such as 1/f noise) are time reversible, we conclude that musical compositions have a considerably richer structure, that goes beyond the traditional properties retrieved by the power spectrum or similar approaches. We also show that musical compositions display strong signs of nonlinear correlations, that nonlinearity is correlated to irreversibility, and that these are also related to asymmetries in the abundance of musical intervals, which we associate to the narrative underpinning a musical composition. These findings provide tools for the study of musical periods and composers, as well as criteria related to music appreciation and cognition.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
