第五章 第五章、 、 、 、 實驗 實驗 實驗 實驗
在實驗方面，我們從三個面向作實驗效果的評估：一、調性辨識率；二、動 機變化是否明顯；三、產生的音樂是否好聽。由於本系統提供調性及非調性的選 項來產生音樂，若能分辨出調性音樂，則表示我們的研究方法是有用的。而在動 機變化方面，如果能讓受試者聽出明顯變化，也顯示在結構上的成功。實驗的受 試者為十四位，其中七位為未受過音樂訓練，七位有受過音樂訓練，而這七位受 過音樂訓練者之中，學習音樂達十年以上者有四人，五年以上有一人，三至五年 有二人，顯示的比例如圖 5.1 所示。
圖圖
圖圖 5.1 受試者受過音樂訓練時間比例受試者受過音樂訓練時間比例受試者受過音樂訓練時間比例受試者受過音樂訓練時間比例圖圖圖 圖
接著我們調查接觸過非調性音樂者的比例，其中有八位受試者接觸過非調性 音樂，比例為 57% ，沒接觸過的受試者為六位，比例為 43% ，未受過音樂訓練 的受試者中 (7 位)，有一位接觸過非調性音樂，比例為 14%。圖 5.2 為受試者接 觸過非調性音樂的比例圖。
圖 圖 圖
圖 5.2 受試者接觸過非調性音樂受試者接觸過非調性音樂受試者接觸過非調性音樂受試者接觸過非調性音樂比例圖比例圖比例圖 比例圖
38
表
40
第 第
第 第六 六 六章 六 章 章、 章 、 、 、 結論與未來研究 結論與未來研究 結論與未來研究 結論與未來研究
6.1 結論結論結論結論
本論文中，我們以音高類集為理論基礎來作自動作曲的研究。在結構上，系 統達到動機變化及主題發展的功能，動機的長度為兩小節，由一組特定的節奏及 音高組成，主題則包含動機及動機變化，長度為八小節，我們提供簡單的曲式以 三段式為例 ABA’ ，亦即主題 A 為第一至第八小節，第九至十六小節為主題 B ， 接著是主題 A 發展；在有調音樂中，除了 24 個大小調外，還加入終止式以加強 和聲結構；在節奏部分，我們嘗試加入複雜度的概念來增加各種節奏的組合；而 最重要的音高部分，為了增加其變化，我們使用音高類集理論中的 Prime Form ， 其變化有 Transposition 、 Inversion 及 TnI 共 24 種，在無調性音樂中， Prime Form 的 24 種變化皆可使用，但到了有調音樂中，為了符合調性音樂的特性，系統使用 filter 機制來篩選出可用的 Prime Form 組合，再搭配終止式而成。
而根據三個實驗的結果，有調的調性辨識率平均為 78.25%，非調性的調性辨 識率平均為 52.75% ，表示非調性音樂較不容易辨識；動機辨識率及喜好程度的 平均分數以 Likert 5-point Scale 計算，動機辨識率的平均分數為 3.5，結果在平均 之上；喜好程度的整體平均分數為 2.975，其中，有調音喜好程度的平均分數為 3.29 ，非調音樂喜好程度的平均分數為 2.66 ，顯示大部分受試者對於系統產生 的有調音樂是可接受的。
6.2 未來研究未來研究未來研究未來研究
在未來的研究中，我們考慮加入三個方向來改進本論文的系統：
一、風格分析：現在的系統只具備基礎的自動作曲功能，因此曲風聽起來都 是差不多的，若能加入風格的選項，則能增加更多可能性，因此可以藉由分析大 量不同風格的樂曲，歸納出不同種風格的音高組成、節奏變化、和聲搭配及結構 規則等，如此便可產生變化更多的樂曲。
二、加入更多樂理分析：系統產生出的樂曲中，對於音與音之間的跳動程度 並無加以研究，例如： Leap 、 Stepwise 、 Arpeggio 等，若能分析以上三者在 樂曲中出現的比例，並加入系統中加以運用，必能在旋律的流暢度上有更多幫助。
三、使用馬可夫鏈：由於本系統在和聲方面只使用終止式，對於和聲的變化 不大，因此在未來考慮加入馬可夫鏈，來增加和聲變化的可能性，也可產生出更 多樣的樂曲。
42 Tutorial”, Leonardo, vol. 22, no. 2, pp. 175—187, 1989.
[2] Cambouropoulos, E., “Markov Chains as an Aid to Computer Assisted Composition”, Musical Praxis, vol. 1, no. 1, pp. 41—52, 1994.
[3] Farbood, M., Schoner, B., “Analysis and Synthesis of Palestrina-Style Counterpoint Using Markov Chains”, the International Computer Music Conference, September in Havana, Cuba, pp. 18—22, 2001.
[4] Wiggins, G., Papadopoulos, G., Phon-Amnuaisuk S., Tuson, A., “Evolutionary Methods for Musical Composition”, Partial Proceedings of the 2nd International Conference CASYS’98 on Computing Anticipatory Systems, Liège, Belgium, pp.
10—14, 1998.
[5] Moroni, A., Manzolli, J., Zuben, F. V., Gudwin, R., “Evolutionary Computation applied to Algorithmic Composition”, Evolutionary Computation, 1999. CEC 99.
Proceedings of the 1999 Congress on, 1999.
[6] Povel, D.J., “Melody Generator: A Device for Algorithmic Music Construction”, Journal of Software Engineering & Applications, 3, 683-695, 2010.
[7] Temperley, D., “A Probabilistic Model of Melody Perception”, Cognitive Science, vol.32, no.2, pp418—444, 2008.
[8] 張錦鴻，基礎樂理，大陸書店，民國八十五年。
[9] Straus, J.N., Introduction to Post-Tonal Theory, Prentice Hall, Englewood Cliffs, New Jersey, 1990.
[10] Schuijer, M., Analyzing Atonal Music: Pitch-Class Set Theory and Its Contexts, Eastman Studies in Music 60. Rochester, NY: University of Rochester Press, 2008.
[11] Nelson, P., Pitch Class Sets, Revised on January 20 2007, http://composertools.com/Theory/PCSets/, accessed April 08, 2011.
[12] Schoenberg, A., Stein, L., Fundamentals of Music Composition, faber and faber, LONDON．BOSTON, 1967.
[13] Stein, L.: Structure & Style: The Study and Analysis of Musical Forms, Summy-Birchard Music, 1979.
[14] 黎翁斯坦 (Leon Stein) 著，音樂的結構與風格，康謳主譯，全音樂譜出版社，
1974。
[15] Gehrkens, K.W., The Project Gutenberg eBook, Music Notation and Terminology, 2006.
[16] Scruton, R., The Aesthetics of Music, Oxford: Clarendon Press, 1997.
[17] Thul, E., Toussaint, G. T., “Rhythm complexity measures: A comparison of mathematical models of human perception and performance”, In Proc. 9th International Conference on Music Information Retrieval, Philadelphia, USA, September, pp. 14—18, 2008.
[18] Shmulevich, I., Povel, D.-J., Complexity measures of musical rhythms', in Rhythm Perception and Production, Eds. Desain, P. and Windsor, W.L. (Lisse: Swets &
Zeitlinger), pp. 239--244, 2000.
[19] Longuet-Higgins, H., Lee, C., “The rhythmic interpretation of monophonic music”, Music Perception, Vol. 1, No. 4, pp. 424—441, 1984.
[20] Fitch, W. T., Rosenfeld, A. J.: Perception and production of syncopated rhythms, Music Perception, Vol. 25, No. 1, pp. 43—58, 2007.
[21] Smith, L., Honing, H.: Evaluating and extending computational models of rhythmic syncopation in music, in Proceedings of the International Computer Music Conference, pp. 688—691, 2006.
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ACM, New York, NY, USA, pp. 1--9, 2008.
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44
count Forte code Prime form Inverted form Sets of 0 pitch classes, 0 intervals (1 vector, 1 quality, 1 total)
<000000> (1) (){silence}
Sets of 1 pitch classes, 0 intervals (1 vector, 1 quality, 12 total)
<000000> (12) (0){single-note}
Sets of 2 pitch classes, 1 intervals (6 vectors, 6 qualities, 66 total)
<100000> (12) (0,1){half-step}
<010000> (12) (0,2){whole-step}
<001000> (12) (0,3){minor-third}
<000100> (12) (0,4){major-third}
<000010> (12) (0,5){perfect}
<000001> (6) (0,6){tritone}
Sets of 3 pitch classes, 3 intervals (12 vectors, 19 qualities, 220 total)
<210000> (12) 3-1: (0,1,2)
Sets of 4 pitch classes, 6 intervals (28 vectors, 43 qualities, 495 total)
<321000> (12) 4-1: (0,1,2,3)
Interval Vector
count Forte code Prime form Inverted form
<110121> (24) 4-16: (0,1,5,7) [0,2,6,7]
<021030> (12) 4-23: (0,2,5,7){quar-4}
<020301> (12) 4-24: (0,2,4,8){7+5}
<020202> (6) 4-25: (0,2,6,8){fr.,7-5}
<012120> (12) 4-26: (0,3,5,8){min7,maj6}
<012111> (24) 4-27: (0,2,5,8){hd7} [0,3,6,8]{dom7}
<004002> (3) 4-28: (0,3,6,9){dd7}
Sets of 5 pitch classes, 10 intervals (35 vectors, 66 qualities, 792 total)
<432100> (12) 5-1: (0,1,2,3,4)
46
Interval Vector
count Forte code
Prime form Inverted form
<122230> (24) 5-27: (0,1,3,5,8) [0,3,5,7,8]{min9}
<122212> (24) 5-28: (0,2,3,6,8) [0,2,5,6,8]
<122131> (24) 5-29: (0,1,3,6,8) [0,2,5,7,8]
<121321> (24) 5-30: (0,1,4,6,8) [0,2,4,7,8]
<114112> (24) 5-31: (0,1,3,6,9) [0,2,3,6,9]{7-9}
<113221> (24) 5-32: (0,1,4,6,9) [0,2,5,6,9]{7+9}
<040402> (12) 5-33: (0,2,4,6,8){9+5,9-5}
<032221> (12) 5-34: (0,2,4,6,9){dom9}
<032140> (12) 5-35: (0,2,4,7,9){pentatonic,Quar-5}
Sets of 6 pitch classes, 15 intervals (35 vectors, 80 qualities, 924 total)
<543210> (12) 6-1: (0,1,2,3,4,5)
Interval Vector
count Forte code
Prime form Inverted form
<233241> (48) 6-Z25: (0,1,3,5,6,8) [0,2,3,5,7,8]
<143250> (12) 6-32: (0,2,4,5,7,9){min11}
<143241> (24) 6-33: (0,2,3,5,7,9) [0,2,4,6,7,9]{dom11}
<142422> (24) 6-34: (0,1,3,5,7,9) [0,2,4,6,8,9]
<060603> (2) 6-35: (0,2,4,6,8,A){wholetone}
Sets of 7 pitch classes, 21 intervals (35 vectors, 66 qualities, 792 total)
<654321> (12) 7-1: (0,1,2,3,4,5,6)
7-Z36: (0,1,2,3,5,6,8) [0,2,3,5,6,7,8]
<443532> (24) 7-13: (0,1,2,4,5,6,8) [0,2,3,4,6,7,8]
<434442> (48) 7-Z18: (0,1,4,5,6,7,9) [0,2,3,4,5,8,9]
7-Z38: (0,1,2,4,5,7,8) [0,1,3,4,6,7,8]
<434343> (24) 7-19: (0,1,2,3,6,7,9) [0,1,2,3,6,8,9]
<433452> (24) 7-20: (0,1,2,4,7,8,9) [0,1,2,5,7,8,9]
<424641> (24) 7-21: (0,1,2,4,5,8,9) [0,1,3,4,5,8,9]
<424542> (12) 7-22: (0,1,2,5,6,8,9){hungar-min}
<354351> (24) 7-23: (0,2,3,4,5,7,9) [0,2,4,5,6,7,9]
<353442> (24) 7-24: (0,1,2,3,5,7,9) [0,2,4,6,7,8,9]
48
Interval Vector
count Forte code
Prime form Inverted form
<345342> (24) 7-25: (0,2,3,4,6,7,9) [0,2,3,5,6,7,9]
<335442> (24) 7-32: (0,1,3,4,6,8,9){harm-min} [0,1,3,5,6,8,9]
<262623> (12) 7-33: (0,1,2,4,6,8,A)
<254442> (12) 7-34: (0,1,3,4,6,8,A)
<254361> (12) 7-35: (0,1,3,5,6,8,A){diatonic}
Sets of 8 pitch classes, 28 intvls (28 vectors, 43 qualities, 495 total)
<765442> (12) 8-1: (0,1,2,3,4,5,6,7)
<665542> (24) 8-2: (0,1,2,3,4,5,6,8) [0,2,3,4,5,6,7,8]
<656542> (12) 8-3: (0,1,2,3,4,5,6,9)
<655552> (24) 8-4: (0,1,2,3,4,5,7,8) [0,1,3,4,5,6,7,8]
<654553> (24) 8-5: (0,1,2,3,4,6,7,8) [0,1,2,4,5,6,7,8]
<654463> (12) 8-6: (0,1,2,3,5,6,7,8)
<645652> (12) 8-7: (0,1,2,3,4,5,8,9)
<644563> (12) 8-8: (0,1,2,3,4,7,8,9)
<644464> (6) 8-9: (0,1,2,3,6,7,8,9)
<566452> (12) 8-10: (0,2,3,4,5,6,7,9)
<565552> (24) 8-11: (0,1,2,3,4,5,7,9) [0,2,4,5,6,7,8,9]
<556543> (24) 8-12: (0,1,3,4,5,6,7,9) [0,2,3,4,5,6,8,9]
<556453> (24) 8-13: (0,1,2,3,4,6,7,9) [0,2,3,5,6,7,8,9]
<555562> (24) 8-14: (0,1,2,4,5,6,7,9) [0,2,3,4,5,7,8,9]
<555553> (48) 8-Z15: (0,1,2,3,4,6,8,9) [0,1,3,5,6,7,8,9]
8-Z29: (0,1,2,3,5,6,7,9) [0,2,3,4,6,7,8,9]
<554563> (24) 8-16: (0,1,2,3,5,7,8,9) [0,1,2,4,6,7,8,9]
<546652> (12) 8-17: (0,1,3,4,5,6,8,9)
<546553> (24) 8-18: (0,1,2,3,5,6,8,9) [0,1,3,4,6,7,8,9]
<545752> (24) 8-19: (0,1,2,4,5,6,8,9) [0,1,3,4,5,7,8,9]
<545662> (12) 8-20: (0,1,2,4,5,7,8,9)
<474643> (12) 8-21: (0,1,2,3,4,6,8,A)
<465562> (24) 8-22: (0,1,2,3,5,6,8,A) [0,1,3,4,5,6,8,A]
<465472> (12) 8-23: (0,1,2,3,5,7,8,A)
<464743> (12) 8-24: (0,1,2,4,5,6,8,A)
<464644> (6) 8-25: (0,1,2,4,6,7,8,A)
<456562> (12) 8-26: (0,1,2,4,5,7,9,A)
<456553> (24) 8-27: (0,1,2,4,5,7,8,A) [0,1,3,4,6,7,8,A]
<448444> (3) 8-28: (0,1,3,4,6,7,9,A){octatonic}
Sets of 9 pitch classes, 36 intervals (12 vectors, 19 qualities, 220 total)
<876663> (12) 9-1: (0,1,2,3,4,5,6,7,8)
<777663> (24) 9-2: (0,1,2,3,4,5,6,7,9) [0,2,3,4,5,6,7,8,9]
<767763> (24) 9-3: (0,1,2,3,4,5,6,8,9) [0,1,3,4,5,6,7,8,9]
Interval Vector
count Forte code Prime form Inverted form
<766773> (24) 9-4: (0,1,2,3,4,5,7,8,9) [0,1,2,4,5,6,7,8,9]
<766674> (24) 9-5: (0,1,2,3,4,6,7,8,9) [0,1,2,3,5,6,7,8,9]
<686763> (12) 9-6: (0,1,2,3,4,5,6,8,A)
<677673> (24) 9-7: (0,1,2,3,4,5,7,8,A) [0,1,3,4,5,6,7,8,A]
<676764> (24) 9-8: (0,1,2,3,4,6,7,8,A) [0,1,2,4,5,6,7,8,A]
<676683> (12) 9-9: (0,1,2,3,5,6,7,8,A)
<668664> (12) 9-10: (0,1,2,3,4,6,7,9,A)
<667773> (24) 9-11: (0,1,2,3,5,6,7,9,A) [0,1,2,4,5,6,7,9,A]
<666963> (4) 9-12: (0,1,2,4,5,6,8,9,A)
Sets of 10 pitch classes, 45 intervals (6 vectors, 6 qualities, 66 total)
<988884> (12) (0,1,2,3,4,5,6,7,8,9)
<898884> (12) (0,1,2,3,4,5,6,7,8,A)
<889884> (12) (0,1,2,3,4,5,6,7,9,A)
<888984> (12) (0,1,2,3,4,5,6,8,9,A)
<888894> (12) (0,1,2,3,4,5,7,8,9,A)
<888885> (6) (0,1,2,3,4,6,7,8,9,A) Sets of 11 pitch classes, 55 intervals (1 vector, 1 quality, 12 total)
<AAAAA5> (12) (0,1,2,3,4,5,6,7,8,9,A) Sets of 12 pitch classes, 66 intervals (1 vector, 1 quality, 1 total)
<CCCCC6> (1) (0,1,2,3,4,5,6,7,8,9,A,B) {chromatic}