論音樂與數學的交集—碎形音樂

A Discourse of the Interaction in Music and Mathematics - Fractal Music

吳鼎武．瓦歷斯(Walis Ding-Wuu Wu)

《中原學報》 32卷2期 (2004/06) Pp. 213-222

https://doi.org/10.6358/JCYU.200406.0213

摘要

自1950年代末期，電腦就已被作曲者用來創作音樂曲譜，在此同時電腦繪圖的技術亦同樣處於初步的應用階段，而對於電腦繪圖背後的複雜邏輯演算法與數學方程式（指的是矩陣、行列式與三角函數而言）皆是架構電腦之於視覺應用的最佳詮釋。同樣地，對於聽覺之音樂而言，亦是具有相同的轉喻應用。在眾多應用案例中，尤其以處理“數學影音化”最受矚目。一位出生於波蘭華沙的博學家兼數學家，祖籍是立陶宛猶太人的波努瓦．孟德布羅（Benoit．B Mandelbrot）發表了新的數學理論碎形幾何學（Fractal Geometry）。而其中的「瑪麗集合」（Marie Sets）即是藉助分析碎形函數，並轉換成相對應之音樂或動畫的演算程式來產生聲音與視覺影像，可說是最早結合音樂、動畫與碎形幾何數學的新影音實驗多媒體作品。「瑪麗集合」是於1987年首次發表於國際電腦音樂會議上，該會議對於從事電腦音樂與動畫媒體的創作者來說，是一項極大的激勵與鼓舞的推動力。

關鍵字

碎形幾何學 ； 碎形音樂 ； 電腦音樂

並列摘要

Since the end of 1950 era, Computer has been used for the creation in music composition by music composer. At the same time, the development of technology in computer graphics has the same initiate application level. For the complex logic algorithm and mathematics equation are the best adequate transformation for the application of visual computation. Similarly, for the sound of Music area, it also has the same metaphor. Therefore, in some examples, “Mathematics in visual-sound Transforming” especially is the best focusing. Benoit B. Mandelbrot, a famous mathematician, presented a new Mathematics theory of Fractal Geometry.「Marie Sets」is a function tool for analysis Fractal Function, to generate sound and visual image by transformed the mapping algorithm equation of music or animation, which is a brand new area of sound-music experimental multi-media work, which combined the music, animation and Fractal Geometry fields etc..「Marie Sets」is first presented at the Conference of International Computer Music in 1987, which is a great inspiration and implement for the people who are engaged in the creation of computer music and animation media. So, based on these reasons, within this paper I will find out a fairly discourse of the interaction in Music and Mathematics-a formation of Fractal Music.

並列關鍵字

Fractal Geometry ； Fractal Music ； Computer Music