1. He found that the interval of an octave is rooted in the ratio 2:1, that of the fifth in 32, that of the fourth in 4:3.and that of the whole tone in9:8.the phthagoreans applied these ratios to lengths of a string on an instrument called a canon, or monochord(a board with two bridges between which a string is stretched and a third bridge that divide the string in two partsand thereby were able to determine mathematically the intonation of an entire musical system.
毕达哥拉斯将这些弦长比例应用于一种叫做卡农的乐器上，卡农也可以称之为单弦琴或者单弦音响测定器（是一个由两个码构成的木板，码子之间有一条被拉伸的琴弦，第三个码子位于琴弦两端的码子之间），因此能够用数学的方法测定整个音乐系统的音调。
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2. Monochord: Traditional Chinese Monochord, also named duxian paoqin in Chinese, is a kind of traditional instrument handed down from ancient China.
独弦琴：又名独弦匏琴，是我国古代流传下来的一种乐器，据有文字记载可追溯到殷代，详见中国独弦琴网。