節奏複雜度之分析與應用 － 以北管與京劇為例

本研究探討北管與京劇的鑼鼓節奏，利用off-beatness、Keith’s measure、Weighted Note-to-Beat Distance等方法分析出節奏複雜度，得到節奏複雜度數據後，進一步利用curve fitting分析出線性圖表與數學多項式，經過比較整理，找出鑼鼓節奏的特性與異同，最後應用在自動作曲的節奏產生上，另外加上對北管與京劇的音高作馬可夫鍊統計出機率，最終建立傳統音樂的自動作曲，嘗試產生具特殊風格的自動作曲，期望有助於自動作曲在節奏上的產生與傳統音樂方面的應用，提供作參考。

關鍵字

節奏複雜度；自動作曲；北管鑼鼓；京劇鑼鼓

並列摘要

This research study on the rhythm of Bei Guan music and Peking Opera music. This research Use three way of rhythm complexity analyses - off-beatness, Keith’s measure and Weighted Note-to-Beat Distance to find out the complexity of these two traditional music. Moreover, use these analyzed complexity data to do curve fitting, generate linear graph and polynomial. After find out rhythm’s similarities and characteristic, apply properties and polynomials to rhythm generator of algorithmic composition. In addition, use the Markov Chain Model to find out the probability of pitches in Bei Guan music and Peking Opera music. Finally this research builds up algorithmic composition of traditional music, and composes music with special style. Hope this research can help algorithmic composition to generate rhythm in different ways and reach the field of traditional music.