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当音阶在空间中翻转重叠,几何的结构性和音乐的结构性重合了
18世纪下半叶以降,欧洲的数学有了巨大的发展,音乐则处在一个多种风格涌动的局面,法国和意大利风格,古代风格和“现代”风格(比如法国理论家和作曲家拉莫为代表)共存。这个时期,热爱音乐并从中获得研究方向的数学家和科学家不止一位,比如瑞士数学巨匠欧拉。本来,音乐只是消遣,不过数学本能让他在音乐中也开始思考数学。从十几岁的时候,他就发表了关于“声音传播”的论文,此后几十年都经常回到对音乐的思考中。1730 ...
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