Metaphors involving motion and forces are a source of inspiration for understanding tonal music and tonal harmonies since ancient times. Starting with the rise of quantum cognition, the modern interactional conception of forces as developed in gauge theory has recently entered the field of theoretical musicology. We develop a gauge model of tonal attraction based on SU(2) symmetry. This model comprises two earlier attempts, the phase model grounded on U(1) gauge symmetry, and the spatial deformation model derived from SO(2) gauge symmetry. In the neutral, force-free case both submodels agree and generate the same predictions as a simple qubit approach. However, there are several differences in the force-driven case. It is claimed that the deformation model gives a proper description of static tonal attraction. The full model combines the deformation model with the phase model through SU(2) gauge symmetry and unifies static and dynamic tonal attraction.

自古以来，涉及运动和力量的隐喻一直是理解音调音乐和音调和声的灵感之源。从量子认知的兴起开始，规范理论中发展起来的现代的相互作用力概念最近进入了理论音乐学领域。我们基于SU（2）对称性开发了一个音调吸引的量表模型。该模型包括两个较早的尝试，基于U（1）规范对称性的相位模型，以及从SO（2）规范对称性推导的空间变形模型。在中性，无力的情况下，两个子模型都一致，并产生与简单的qubit方法相同的预测。但是，在强制驱动情况下存在一些差异。据称，变形模型给出了静态色调吸引的正确描述。