基於曲調輪廓能量守恆的單聲部音高之演算法作曲

在眾多已提出的演算法作曲手段中，主音式的創作技巧與符號式的音級理論主宰了大部分的研究。然而，和聲乃由共生的曲調所構築；曲調線條才是西洋藝術音樂的根本法則。此外，當今的音樂科技，以低層內容為中心之方法與以高層後設資料為基礎之途徑間，兩者的橋樑正在萌芽。本論文從聲響頻率上的簡單比例出發，結合古典力學裡能量守恆的定律，再據以設計出相應的模型，來操縱曲調輪廓以及單旋律音高的運動。其描繪了音高間具體且可辨的能量比例，並反映了能量消耗與生成的物理現象。該創新模型能夠利用至符號式的記譜系統之外，以聲響頻率的原始資料作為輸出輸入。本研究實作出小型的視窗程式，能夠根據使用者參數自動產生出大致符合旋律創作之普遍性法則的單聲部連續音高。實驗結果展示出合理的曲調輪廓，亦即高度可唱的性質。未來期望能透過類似的能量概念，推導出適用於節奏與聲部間音程關係的演算法。

關鍵字

演算法作曲；音高頻率；能量；曲調；輪廓

並列摘要

In numerous methods of algorithmic composition of melody which have been proposed, techniques of homophonic composing and theories of symbolic pitch-class dominate most research. Nevertheless, harmony is constituted by symbiosis melodies; melodic lines are the fundamentals of western art music. Moreover, bridges between low-level content-centric methods and high-level metadata-based ones are just germinating in music technology nowadays. This thesis starts by the simple ratio of audio frequencies combining with the law of conservation of energy in classical dynamics and then devises a corresponding model in order to manipulate the melodic contour and motions of monophonic melody pitches. It represents the concrete and sensible energy ratio between each pitch as well as reflects the physical phenomenon of energy consumption and production. With the raw data of audio frequencies as input and output, that innovative model is able to be utilized beyond the system of symbolic notation. A small windows program is implemented in this research. It can automatically generate a series of monophonic pitches which roughly obeys the general rules of melody composing. Experimental results demonstrate reasonable melodic contour, i.e. a highly singable character. Through similar concepts of energy, an inference about the algorithm which is applicable to rhythms and relationship of intervals between voices could be expected in the future.

並列關鍵字

algorithmic composition ； pitch frequency ； energy ； melody ； contour

參考文獻

Adiloglu, Kamil, and Ferda N. Alpaslan. “A Machine Learning Approach to Two-Voice Counterpoint Composition.” Knowledge-based Systems 20, no. 3 (2007): 300-09.

Aguilera, Gabriel, José Luis Galán, Rafael Madrid, Antonio Manuel Martínez, Yolanda Padilla, and Pedro Rodríguez. “Automated Generation of Contrapuntal Musical Compositions Using Probabilistic Logic in Derive.” Mathematics and Computers in Simulation 80, no. 6 (2010): 1200-11.

Balaban, Mira, Kemal Ebcioglu, and Otto Laske, eds. Understanding Music with Ai: Perspectives on Music Cognition. Cambridge, MA: The MIT Press, 1992.

Bobbitt, Richard. “The Physical Basis of Intervallic Quality and Its Application to the Problem of Dissonance.” Journal of Music Theory 3, no. 2 (1959): 173-207.

Brower, Candace. “Paradoxes of Pitch Space.” Music Analysis 27, no. 1 (2008): 51-106.

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基於曲調輪廓能量守恆的單聲部音高之演算法作曲

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