什麼是調音與調律

保證若干個樂音合在一起聽起來悦耳的兩個方面。調音保證一對音調合成得好聽；調律則與調音達成某種妥協以保證任何一對以及所有各對音調能合成出悦耳的聲音。如果兩根弦的長度之比可以用兩個小的整數來表示，那麼它們一起振動時發出的聲音就最好聽。如果兩根弦以2:1的比例振動，那麼這兩種振動將總是協調一致並互相加強的。但如果它們以197:100（非常接近2:1）的比例振動，那麼每秒鐘內它們會彼此抵銷掉三次，產生可以聽得出來的「拍」。這些拍就造成一些「不協和」的聲音。因為由一種比例所產生的音調並不一定與重複應用的另一種比例所產生的相同音調一致，所以必須要麼使某些音程失調以使其他的音程完美地和諧，要麼將所有的音程都稍作失調。1700年以前，使用的是在前一種妥協基礎上的若干系統，包括「精確轉調」（just intonation）；而1700年以後，由「平均律」（equal temperament）代表的這種妥協佔了優勢，其中每對相鄰的音所代表的比例都是一樣的。

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.