什么是调音与调律
保证若干个乐音合在一起听起来悦耳的两个方面。调音保证一对音调合成得好听;调律则与调音达成某种妥协以保证任何一对以及所有各对音调能合成出悦耳的声音。如果两根弦的长度之比可以用两个小的整数来表示,那麽它们一起振动时发出的声音就最好听。如果两根弦以2:1的比例振动,那麽这两种振动将总是协调一致并互相加强的。但如果它们以197:100(非常接近2:1)的比例振动,那麽每秒钟内它们会彼此抵销掉三次,产生可以听得出来的「拍」。这些拍就造成一些「不协和」的声音。因为由一种比例所产生的音调并不一定与重复应用的另一种比例所产生的相同音调一致,所以必须要麽使某些音程失调以使其他的音程完美地和谐,要麽将所有的音程都稍作失调。1700年以前,使用的是在前一种妥协基础上的若干系统,包括「精确转调」(just intonation);而1700年以後,由「平均律」(equal temperament)代表的这种妥协占了优势,其中每对相邻的音所代表的比例都是一样的。
tuning and temperament
Two aspects of assuring that musical tones sound well together. Tuning assures a good sound for a given pair of tones; temperament compromises the tuning to assure a good sound for any and all pairs of tones. Two vibrating strings sound best together if the ratio between their lengths can be expressed by two small whole numbers. If two strings vibrate in a ratio of 2:1, the vibrations will always coincide and so reinforce each other. But if they vibrate in a ratio of 197:100 (very close to 2:1), they will cancel each other out three times per second, creating audible “beats.” These beats are what make something sound “out of tune.” Since a tone produced by one ratio will not necessarily agree with the same tone created by repeatedly applying another ratio, either some intervals must be mistuned to allow for the perfect tuning of others or all intervals must be slightly mistuned. Before 1700, several systems were used based on the former compromise, including “just intonation”; since then, the compromise represented by “equal temperament,” in which the ratios represented by each pair of adjacent notes are identical, has prevailed.
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