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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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We're going to start here and we have this pattern of the major that goes whole, whole, half, whole, whole, whole, half step.
我们从这里开始,大调模式是这样,它经过,全音,全音,半音,全音,全音,全音,半音级
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So halfway is the right thing to do, because at each step, I'm guaranteed to throw away at least half the list. Right? And that's nice.
一半以上的元素，对不对？，这很棒，好，大家猜猜这个算法的增长率是多少？,为什么？太对了。
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It's always a half step--always a half step-- seventh degree, right below, right below the tonic.
它总是一个半音级,总是如此,第七级刚好在主音下面
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So, flats are below, sharps take you up a half step.
降调是下降半音级,而升调是上升半个
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Then the first time so he came up a major third there and then quickly backed off with just a half step below it, which completely gave it a different feel.
于是开始的时候,乐曲中出现一个大三和弦,然后快速地降低了半个音,这种变化给人完全不同的感受
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I need a half step above G.
上面应该是个半音级
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Now, I have a half step.
然后是一个半音级
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Up--just D. Now, we need, according to our pattern, to go up just a half step.
是D,接下来,根据小调的模式,只要上升半音级
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And the last one in the major pattern is a half step from B to C.
大调模式的最后,是一个从B到C的半音级
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I got to go up just a half step there, I'm on E.
上升半音级到E
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The first step is divide them in half. All right? I'm not sure how to mark it here, remember I need to come back there. I'm not yet done. What do I do?
我不能确定如何,在这里进行标记,记住我会回这里进行讲解,我还没做完呢？
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But it's just--F is just a half step away, so that's good.
也只是半音级的距离,很好
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All right, so there we are, but is this, from D to E, a half step?
好了,明白了,但这里,从D到E,是个半音级吗
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What we've written is a whole step, so we've got to indicate that this is just a half step away in that fashion, D to E-flat.
而这里写的是一个全音级,所以我们要在这里标出,从D到降E只有半音级
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What's a half step above G?
比G高半音级是什么
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Because if b was odd, then b minus one is even which means on the next step, I can cut the problem in half again.
这意味着我在下一步里解决的问题,规模要小了一半，好，课堂材料的第三题。
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What's a half step above D?
上升半音级是什么
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What am I going to write here? From G I need a half step.
在这里要写什么,过G之后是个半音级
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But in one step, I've reduced this problem in half.
我就将这个问题的规模减半了，我不仅仅是缩小了问题的规模。
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Getting rid of half at each step.
每一步把空间缩小一半。
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Well, a whole step here--there's one half, there's another half, would take us to F, whole step above F, would take us to G.
是一个全音级,这里是半个,这里是另外半个,这就到了F,F之后一个全音级,就到了G
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With this, if I can assume that accessing the i'th element of a list is constant, then you can't see that the rest of that analysis looks just like the log analysis I did before, and each step, no matter which branch I'm taking, I'm cutting the problem down in half.
读取数组中的第i个元素,是个常量时间的操作的话，我也就能像以前那样得到,这个算法是对数级复杂度的分析,并且每一步不管我选择哪个区间，我都可以把问题的规模缩小一半。
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