论文标题
三色调和四色调和弦的小组理论分类
A group-theoretical classification of three-tone and four-tone harmonic chords
论文作者
论文摘要
我们根据作用于十二个色调的和弦的对称组的亚组对三色调和四色和弦进行分类。这些动作是反转，主要二元性和增强二元性的二元性。这些动作与对称群体的要素相对应，也对应于音乐和谐理论中的直觉概念。我们制作了这些动作如何将不同的第七和弦联系起来的图表，这些和弦暗示了和谐理论中的距离概念。
We classify three-tone and four-tone chords based on subgroups of the symmetric group acting on chords contained within a twelve-tone scale. The actions are inversion, major-minor duality, and augmented-diminished duality. These actions correspond to elements of symmetric groups, and also correspond directly to intuitive concepts in the harmony theory of music. We produce a graph of how these actions relate different seventh chords that suggests a concept of distance in the theory of harmony.
