With dissonant intervals they tend to be frequencies that are sounding right next to each other, very close-by frequencies.

这些不协调音程的频率,听起来彼此很相似,频率很相近

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We can just play with that particular interval to change entirely the way we feel about particular melodies.

我们只需关注这一特别的音程,是如何彻底改变我们对某些旋律的感受的

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Generally speaking, dissonant intervals have ratios such as nine to eight for the whole step or seventeen to sixteen for the half step.

一般而言,不和谐音程是有比率的,全音的情况下为九比八,半音的情况下为十七比十六

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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

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If you allow a little bit of spacing, a little more space between your frequencies, they're a little bit farther apart, then you can move from closeness plays to spacing and you get the consonance.

如果让频率间有点间隔,给频率间多一点空间,让它们彼此远离一些,从密集的音高,转向有间距的音程,就能得到和谐音

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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

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