减七和弦六种解决的自然数理解读

On the nature of mathematical in six kinds of solution of Diminish seventh chord

俄罗斯强力集团作曲家里姆斯基·科萨科夫所撰写的《和声学实用教程》一书讲解了"减七和弦六种解决法",是和声学功能理论的一宗可贵财富。六种解决法从调式类型视角可分为大调与小调两个范围,从减七和弦与解决和弦的关系看,可分成三种样式:无共同音、有一个共同音、有两个共同音。减七和弦解决序进可以作逆向考察,借助逆向考察可发现大小三和弦衍生成减七和弦的衍生规律:由大三和弦衍生而成的减七和弦显示属功能动力。由小三和弦衍生而成的减七和弦显示下属功能动力。由此可发现"减七和弦两源生成"与"减七和弦功能两可"的和声学规律。这一规律可运用律学方法作出合乎数理、顺应自然的说明。

Six kinds of solutions of diminished seventh chord in Russian composer Rimsky- Korsakov's Practical Manual of Harmonyis a very precious treasure in functional harmony theory. Six methods can be divided into two ranges( major and minor),also can be divided into three waysin relation between diminished seventh chord and solution chord( no same tone,one same tone,two same tones). By backward process of solution of diminished seventh chord,the law which major or minor triad can derive diminished seventh chord will be presented. The diminished seventh chord was derived from major triad show the dominant function,and minor triad show the subdominantfunction. Therefore,the law which diminished seventh chord was derived from two way and show different function can be demonstrate in mathematical by temperament way.