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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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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
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We'll be talking about the fact that this is an interval of a third; it spans three letter names a little bit later on.
我们以后会谈到,这其实是个三度音程,它跨越了三个音名
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Well, we've got a skippy Beethoven music but here with Tchaikovsky he's coming down, just straight down, down consecutive intervals there for the most part.
我们听过贝多芬的曲子,非常跳跃,但在柴可夫斯基的乐曲里,音高急转直下,动机部分连续出现音程下降
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Then the next pitch on the trumpet is actually an interval of a fifth.
然后下一个音高在小号那里,实际上是一个五度音程
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One more time and we need- we're going to get our third in.
再来一次,我们把三度音程加进去
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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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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
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