音网谱系考

Genealogies of Tonnetz

在19世纪的调性和声理论发展中,音网一直扮演着举足轻重的角色。至20世纪末,音网更是新里曼理论特有的呈现形式。作为音高关系建构的几何象征,音网形式的更迭折射出音乐理论的演变轨迹。在几何形式、音程构建、律制等方面,19世纪音网具有明确的谱系脉络,瑙曼、厄廷根等理论家的音网一脉相承,最终汇聚成里曼音网,完成了从“音关系网”向“和弦关系网”的扩展。音网成为调性与和弦的空间象征后,暗示了和弦进行的多重路径。音网上的和弦进行拥有比调性和声系统内更高的自由度。这也有助于认识19世纪至今非功能性的和弦转换现象。

In terms of geometric form,interval construction,temperament system,etc.,the19th-century tone network has a clear genealogical context,and the tone network of theorists such as those by Naumann and Oettingen is in the same vein,and finally converges into the form of the Riemann tone network,completing the expansion from the“tone network”to the“chord network”.Chord progressions in the tone network have a higher degree of freedom than within tonality and tone systems,which helps to understand the phenomenon of non-functional chord transitions from the 19th century to the present.