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1 . 中西方音乐的不同发展与其对音阶的研究有密切的关系,中国传统音阶是五声音阶:宫、商、角、徵、羽;西方音阶是七声音阶“Do、Re、Mi、Fa、Sol、La、Si”.它们虽然不同,却又极其相似,最终发展的结果均是将一个完整的八度音阶分成了12个半音,即“十二平均律”.从数学的角度来看,这12个半音的频率成公比为
的等比数列.已知两个音高
,
的频率分别为
,
,且满足函数关系:
,已知两个纯五度音高的频率比
,则它们相差的半音个数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ee45266ffc6178562cfd7aef7158505.png)
________ .(其中
,
,结果四舍五入保留整数部分).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6baeba79bded20a82228fea93f37d4ae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3b9e816b14051f785aa5aae72b8eed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/226e10b63b42fd5b695db882fe6f48a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2187a1a0f3baa9ace0f3aa7efa9cd794.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32e22d049686a15333e378b9a7b90a5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9239ccaa786ff0a227bfb097277c0657.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ee45266ffc6178562cfd7aef7158505.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45a6b35cb73b548ea5a143ea464133db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9c1ae3913d38516521f0ae5cbebcfdc.png)
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