The present article introduces the notion of smoothness of rhythm and proposes a unified method that transforms an arbitrary rhythm into a smooth one. The method employs a self-map Rav, discrete average map, on the space of rhythms of arbitrary length with a fixed number of onsets. It is shown that, for any rhythm $\mathit{a}$ in the space, the iterations $Ra{v}^k\left(\mathit{a}\right)$ become eventually periodic, and that the final cycle consists only of smooth rhythms. The discrete average map leads naturally to a finite directed graph, which visualizes the realm of smooth rhythms in the whole world of rhythms. This article has an Online Supplement, in which we give detailed proof of the main result.

本文介绍了节奏平滑的概念，并提出了一种将任意节奏转换为平滑节奏的统一方法。该方法在具有固定数量起始点的任意长度节奏空间上采用自映射Rav离散平均映射。结果表明，对于任何节奏$\mathit{一个}$在空间中，迭代$R\mathrm{一个}{v}^{ķ}\left(\mathit{一个}\right)$最终变成周期性的，并且最后的循环仅由平滑的节奏组成。离散平均图自然地导致有限有向图，它可视化了整个节奏世界中平滑节奏的领域。本文有一个在线补充，我们在其中给出了主要结果的详细证明。