西方音乐的数学式探索与形而上诉求

自毕达哥拉斯开始,西方人便发现了音响背后的数量关系,并通过这种关系的掌握而制造乐音。于是,在可被感知的音乐背后,发现一种可被计算的数量关系,进而获得超验主宰的形而上意蕴,便成为无数西方音乐家的共同追求。然而,正像哲学的发展经历了一个从宗教哲学、理性哲学到非理性哲学的过程一样,数学的发展经历了一个从认识有理数到理解无理数再到利用无理数的过程,音乐的发展也经历了一个从追求和谐到利用不和谐再到肯定不和谐的过程。如果说从巴洛克到古典主义,西方的音乐家们都在竭尽全力地寻找着音乐背后的数理逻辑,并通过这一逻辑的运用而企及上帝的和谐或理性的本体,那么从浪漫主义到印象派,西方的音乐家们则是在将和谐的技法运用圆熟之后,转而利用不和谐的音响来补充和谐的内容,从而使音乐变得更加丰富多彩并具有个性,而20世纪以来的西方音乐家则企图全面颠覆传统的理性法则和数学逻辑,标新立异地创作着无调性、没旋律、不和谐的音乐。

The Mathematical Explorations and Metaphysical Concerns in Western Music

Since Pythagoras the underlying numerical relations of musical notes have been discovered and used to reform music in the West,whereupon the numerical relations behind perceptible music with their transcendent metaphysical meanings have become the common goals for numerous musicians.However,just as philosophy has experienced a course from the religious to rational and irrational,and mathematics a course from the understanding of rational numbers to that of irrational numbers and the application of irrationa...