以小節為基礎之譯譜演算法

本論文提出一套新的譯譜演算法，能夠處理多音的MIDI輸入並產生一有系統且便於閱讀的記譜方式。在所提出的演算法中，除了整體調性分析之外，所有的分析處理皆以小節為單位。這套演算法包含兩個部份：本調音的譯譜及變化音的譯譜。調性分析是本調音譯譜中最重要的環節，我們使用首調唱名的方法先列舉幾個可能的調性後，再以所提出的半圓轉調模型決定最後的調性。在變化音的譯譜上則使用一些通用法則並加入變異量評估。此演算法測試了貝多芬兩首奏鳴曲的兩個樂章及三首蕭邦的圓舞曲；總正確率為98.65% (8139個音中有110個錯誤)。

關鍵字

譯譜；階名唱法；樂器數位介面；調號；轉調

並列摘要

This paper describes a novel pitch spelling algorithm which can deal with polyphonic MIDI data and generate systematic and readable score notations. In the proposed algorithm, all the spelling processes are executed using a measure as a unit, except the global key analysis. Our spelling process includes two stages: diatonic spelling and chromatic spelling. Key analysis is the main concern in the diatonic spelling. We use solmization result to get the key candidates and apply the proposed Semicircle Key Modulation (SKM) model to further decide the key analysis result. In the chromatic spelling, we use general rules of notating chromatic notes and variance evaluation to decided notes which need accidentals under a specific key. The algorithm was tested under two movements of Beethoven’s Sonatas and three Chopin’s Waltzes, and reached an overall 98.65% (misspelled 110 of 8139 notes) correct rate.

並列關鍵字

pitch spelling ； solmization ； MIDI ； key signature ； key modulation

參考文獻

[3] H. C. Longuet-Higgins. The Perception of Melodies. In H. C. Longuet-Higgins, Mental Processes: Studies in Cognitive Science: MIT Press, London, England and Cambridge, Mass., 1987.

[4] E. Cambouropoulos, "Pitch Spelling: A Computational Model," Music Perception, vol. 20, pp. 411-429, 2003.

[5] D. Temperley, The Cognition of Basic Musical Structures: MIT Press, 2001.

[6] E. Chew and Y.-C. Chen, "Real-Time Pitch Spelling Using the Spiral Array," Computer Music Journal, vol. 29, pp. 61-76, 2005.

[9] A. K. Honingh, "Pitch Spelling Using Compactness," in Proceedings of the 9th International Conference on Music Perception & Cognition (ICMPC9) Bologna, 2006.

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以小節為基礎之譯譜演算法

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