This paper investigates the processes leading to musical fame or obscurity, whether for composers, performers, or works themselves. It starts from the observation that the patterns of success, across many historical music datasets, follow a similar mathematical relationship known as a power law, often with an exponent approximately equal to two. It presents several simple models which can produce power law distributions. An examination of these models' transience characteristics suggests parallels with some historical music examples, giving clues to the ways that success and obscurity might emerge in practice and the extent to which success might be influenced by inherent musical quality. These models can be seen as manifestations of a more fundamental process resulting from the law of maximum entropy, subject to a constraint on the average value of the logarithm of the success measure. This implies that musical success is a multiplicative quality, and suggests that musical markets operate to strike a balance between familiarity (socio-cultural importance) and novelty (individual importance). The common power law exponent of two is seen to emerge as a consequence of the tendency for musical activity to be spread evenly across the log-success bands.

中文翻译：

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音乐史上的名望，晦涩和幂律

本文研究了无论对于作曲家，表演者还是作品本身，导致音乐成名或默默无闻的过程。从观察开始，在许多历史音乐数据集中，成功的模式遵循着称为幂律的相似数学关系，通常具有近似等于2的指数。它提出了几种可以产生幂律分布的简单模型。对这些模型的瞬态特性的研究表明，它与一些历史音乐实例具有相似之处，为在实践中可能出现成功和晦涩的方式以及内在音乐品质对成功的影响程度提供了线索。这些模型可以看作是最大熵定律所导致的更基本过程的体现，受制于成功度量的对数平均值的约束。这意味着音乐的成功是一种乘数性质，并表明音乐市场的运作是在熟悉度（社会文化重要性）和新颖性（个体重要性）之间取得平衡。由于音乐活动趋向于在对数成功频带内平均分布的趋势，因此出现了2的幂次幂指数。