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有两种相反的意见:一种认为音乐既然是建立在数理基础上的艺术,则数理原则即是音乐的准绳,应尽量按此准绳行事,另一种则认为音乐既然是艺术,就不能受数理规律的束缚,而应尽可能远避那些僵化的数理原则,否则,就不成其为艺术。 究竟谁是谁非?究竟应如何正确认识音乐中的数理因素呢? 不同的律制取决于不同的生律方法,不同的生律方法表现为不同的数学途径;如由三分损益法得五度相生律,而由求等比级数则得平均律。没有律制就没有音准的标尺,从而也就失去了音乐艺术的重要基础,故律制不可缺少。 在律制的研究中,人们不厌其繁地力求精微,小心谨慎地计算其精确频率数据,而在艺术实践中,有时力求律制的统一,但在另外一些场合,却又故意模糊不同律制的界限,造成诸律混用的局面。如铜管乐器,往往是根据共振原理运用“超吹法”演奏。以圆号的a音为例,既可在F基音上超吹大三度而得,又可在A基音上超吹八度而得,亦可在D基音上超吹五度而得。这三种奏法,只有超吹八度符合于平均律,而其余两种均与平均律相悖。但事实上以平均律制作的钢琴常在管弦乐队中使用,效果不错。
There are two opposing opinions: one is that since music is art based on mathematical principles, the principle of mathematics is the standard of music, and should try its best to follow this principle. The other is that since music is art, it can not be affected Mathematical laws, but as far as possible to avoid those rigid mathematical principles, otherwise, it is not art. Who exactly is who? How to correctly understand the mathematical factors in music? Different legal system depends on different methods of life, different methods of life performance of the law for different mathematics; Degree of law, but by the same order than the average law. There is no standard tone of the scale, which also lost an important basis for the art of music, so the system of law indispensable. In the study of the system of law, people did not tire of trying hard and meticulously to calculate precise frequency data. In artistic practice, however, they sometimes sought the unification of the law. However, on other occasions, they deliberately obscured different systems of law The boundaries, resulting in mixed use of the law situation. Such as brass instruments, often based on the principle of resonance using the “blowing method” play. Take the alpha of the French horn as an example. It can be obtained by blowing the third major over the F base sound, blowing over the octave at the A fundamental sound, and blowing over the fifth at the D base sound. Of these three methods, only the super-blow eight is in line with the law of averages, while the other two are contrary to the law of averages. But in fact the average law of the piano often used in the orchestra, the effect is good.