For thousands of years 人 have tried to 用 数学 to 描述 and 理解 樂/乐
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和谐 and Strings

The 古 Greeks 已有 that some 声 fitted together well and that others did 不 The Greek 词 和谐 literally 中项 to fit well together So 和谐 声 are 声 that fit well together

They 已有 that changing the 长 of a plucked string 影响 the 音高 of the resulting 声波 Two 弦 of exactly the same 长 产生 the same 音高 and a string half the 长 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 and 理解 the Universe

The Greeks used 数学 to try and 解释 the 关系 of 声 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 樂/乐 of the Spheres’

In the early 20th Century composers decided to apply 类似 rules to all 樂/乐 参数 时间 时值 and 音高 Using these mathematical rules all 声 could be 相等 The 樂/乐 that they 创作 was called Serial 樂/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 樂/乐


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


Keywords
频率 音高