For thousands of years 人 have tried to 使用 数学 to 描述 and 理解 音乐
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和声 and Strings

The 古代 Greeks 已有 that some 声音 fitted together well and that others did 不 The Greek 词 和声 literally 手段(意味着) to fit well together So 和谐 声音 are 声音 that fit well together

They 已有 that changing the 长度 of a plucked string 影响 the 音高 of the resulting 声音 Two 弦（乐） of exactly the same 长度 产生 the same 音高 and a string half the 长度 创作 the same 音符 but an 倍频程（八度） 较高

By doing many calculations the Greeks worked out the first 音高 scales with a 系统 of rules for 音符 that would 作品 well together and those that they felt did 不


理解 声音 and 理解 the Universe

The Greeks used 数学 to try and 解释 the 关系 of 声音 to one another because they believed that this would help them to 理解 the universe In the middle ages 人 描述 the 关系 between planets as ‘The 音乐 of the Spheres’

In the early 20th Century 作曲者 decided to apply 类似 rules to all 音乐 参数 时间 时值 and 音高 Using these mathematical rules all 声音 could be 相等 The 音乐 that they 创作 was called Serial 音乐

A 现代 Greek called Iannis Xenakis used 数学 to 创作 beautiful parabolic curves these were then translated into both 结构 and 音乐


Fact
The crisp snack “Pringles” have an interesting 形状 These are parabolic curves


Keywords
频率 音高