重新定义音乐音阶：从统计规律出发，跨文化可计算
What is a Musical Scale? Regularity and Convention in the Organization of Pitch
- 用音高分布的统计规律定义音阶，不依赖传统理论
- 发现音阶本质是调性中心的音高组织规律，可从录音中计算
- 揭示音阶含多重含义，适合跨文化音乐研究者参考
音阶在人类音乐中近乎普遍，但学界对其定义缺乏共识。本文指出‘音阶’实指多种相关概念：规范性抽象、乐器调音、演奏音高的统计规律、感知范畴与社会惯例。作者提出一种基于实证的定义：音阶是相对于主音的音高组织中的统计规律，该定义可在不同传统间通用且可从录音中计算。这一核心虽具客观性，但仍有惯例参与判断哪些音属于某音阶。进一步将音阶归类为命名类别，则是另一层社会约定，本文通过原型理论及爱尔兰音乐实例加以说明。厘清这些层次，为音阶的跨文化与实证研究奠定基础。
原文摘要 · Abstract (English)
Musical scales are near-universal in human music, and most readers will feel they already know what a scale is. On closer inspection, however, the literature lacks a consensus definition: which conditions are necessary and sufficient shifts across disciplines and traditions, and the term turns out to cover several distinct objects. I argue this is less a failure of rigour than a sign that ``scale'' names several related objects: prescriptive abstractions, instrument tunings, statistical regularities in performed pitch, perceptual categories, social conventions. I adopt an empirical definition -- a scale as a statistical regularity in pitch organisation relative to a tonic -- that is portable across traditions and computable from recordings, and situate it alongside the other senses of the term. Even this empirical core is not purely observational, as convention enters in deciding which pitches belong to a scale. And a further step of grouping scales into named categories is a separate convention, which I approach through prototype theory and illustrate with examples from Irish music. Separating these layers provides a basis from which scales can be re-examined empirically and cross-culturally.
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