五度圈中的音、音列、音阶及其数理关系

Tones,Serials and Scales in the Circle of Fifth and Their Mathematical Relation

对五度圈中的音、音列、音阶及其内在的数理逻辑关系进行探讨,指出了从五度圈中相邻音中所取的数量及其作为不同音级的可能性之间和所含"宫音"数量之间的规律。前者可用"鱼合八""鱼合七""鱼合六"加以说明,后者则可用"x(音列或音阶中音的数量)-4=宫音数量"的公式进行概括。

The article explores the tones, serials and scales in the circle of fifth and their mathematical logic rela- tion. It identifies how the number of the adjacent tones is related with the possibilities of the tones to be different scale degrees, and the regularity between the number of the adjacent tones and the number of ＂Gong tone＂ （ notes of ancient Chinese pentatonic scale）. The former can be indicated by the structure pattern ＂Yuheba Yuheqi＂ ＂Yuheliu＂, and the latter be deduced by the equation X （the number of tones in the serial or scale） -4 = the number of Gong tone.