And so in theory after just 2 or 3 steps you were in order of magnitude farther along in this counting process than I would be because I'd still be on person literally 3 or 4.

因此从理论上说,经过这样短短的两三个步骤,你们就有了分级次序，比我数数快多了,因为我才数到第三四个人。

哈佛公开课 - 计算机科学课程节选

So, they had the ratio of two to one, which gave them the octave, and three to two, which gave them the fifth, and four to three, which gave them the fourth.

他们发现,八度音程中,呈现的是二比一的比例,而五度音程中呈现三比二的比例,在四度音程中则呈现四比三的比例

耶鲁公开课 - 聆听音乐课程节选

What we've got here is the following, this idea of partials that Eva was talking about with ratios, two to one, three to two, four to three, five to four, six to five and so on, and the point here is that the way we differentiate between instruments.

接下来,我们要讲的是,伊娃刚谈到的泛音的高低比率,二比一,三比二,四比三,五比四,六比五,等等,这里我要讲的是,我们区分乐器的方式

耶鲁公开课 - 聆听音乐课程节选

They're irrational numbers and these irrational numbers like to move to rational numbers; they like to move to consonances; they like to move to intervals that are based on things such as two to one and three to two or maybe four to three.

它们是无理数,而这些无理数想要变为有理数,它们想变成和谐音,就要根据一些比率改变音程,比如二比一,三比二,或四比三的比率

耶鲁公开课 - 聆听音乐课程节选