The article aims to draw attention to the diatonic algorithm, a simple numerical algorithm, by which musical scales and intervals can be described, if they fit to the staff notation of the European tradition. The essential concept for this non-Pythagorean algorithm was developed by Gottfried Wilhelm Leibniz (1646–1716) in his manuscripts and in his correspondence with Conrad Henfling (1648–1716) under the heading “Harmonic Equations.” In the field of music, the algorithm can be used to bring order and clarity into the domain of historical interval systems and temperaments. From a modern point of view, it can be formulated more concisely using elementary matrix calculation, and it might therefore also be of some interest to mathematicians.

本文旨在引起人们对全音阶算法的关注，全音阶算法是一种简单的数值算法，如果符合欧洲传统的工作人员表示法，则可以用其描述音阶和音程。这种非毕达哥拉斯算法的基本概念是由Gottfried Wilhelm Leibniz（1646–1716）在他的手稿以及与Conrad Henfling（1648–1716）的书信中以“谐波方程”提出的。在音乐领域，该算法可用于将顺序和清晰度带入历史音程系统和气质的领域。从现代的角度来看，可以使用基本矩阵计算更简洁地表述它，因此它可能也引起数学家的兴趣。