Natural harmonics, i.e. partials and their harmonic series, may be isolated on a vibrating string by lightly touching specific points along its length. In addition to the two endpoints, stationary nodes for a given partial n present themselves at n − 1 locations along the string, dividing it into n parts of equal length. It is not the case, however, that touching any one of these nodes will necessarily isolate the nth partial and its integer multiples. The subset of nodes that will activate the nth partial (termed playable nodes by the authors) may be derived by following a mathematically predictable pattern described by so-called Farey sequences. The authors derive properties of these sequences and connect them to physical phenomena. This article describes various musical applications: locating single natural harmonics, forming melodies of neighbouring harmonics, sounding multiphonic aggregates, as well as predicting the relative tuneability of just intervals.

中文翻译：

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FAREY SEQUENCES 将可播放节点映射到字符串上

自然谐波，即分音和它们的谐波系列，可以通过沿着其长度轻轻触摸特定点而在振动的弦上被隔离。除了两个端点，静止的节点对于给定的部分n展示自己n− 沿字符串的 1 个位置，将其划分为n等长的部分。然而，触摸这些节点中的任何一个节点都不一定会隔离nth 部分及其整数倍。将激活的节点子集n部分（称为可玩节点作者）可以通过遵循所谓的数学上可预测的模式得出法雷序列. 作者推导出这些序列的特性并将它们与物理现象联系起来。本文描述了各种音乐应用：定位单个自然泛音、形成相邻泛音的旋律、发声多音集合，以及预测音程的相对可调性。