After the Greeks laid out their fifths and fourths and whole steps, they had these little leftovers.

当希腊人安排好,五度音程,四度音程和全音级后,他们还有一些剩余

耶鲁公开课 - 聆听音乐课程节选

That's a fourth but it happens to produce an octave against that.

这个是四度,但它碰巧产生一个八度音阶,与另一个形成对比

耶鲁公开课 - 聆听音乐课程节选

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

They filled in the octave up above and then they filled in the fifth and then they filled in the fourth and then they came down a whole step and then they went up a fourth from that whole step and then up a fourth from that, and they were filling in in this fashion.

他们填写了八度音程,然后填写了五度音程,又填写了四度音程,然后下降一个全音级,又从那个全音级上升四度音程,然后再上升四度音程,他们就是照这样填写

耶鲁公开课 - 聆听音乐课程节选