音樂內涵分析(content-based music analysis)是近年來在多媒體訊號處理與音樂理論兩個領域中重要的研究議題。隨著電腦音樂內涵分析技術的進步，使得傳統上必須透過人工方式進行的音樂表現分析，逐漸轉變為可以使用電腦來協助進行大規模的自動化音樂表現比較與分析。音樂表現分析研究的核心是探討演奏家如何將音樂作品中的情感傳達給聆聽者，而音樂表現之體現的主要方式是力度(dynamics)和速度。雖然目前已經有不少音樂內涵分析的相關論文，但是力度表現的分析方法卻鮮少有研究探討。本文提出一種自動化樂音響度等化與力度表現轉換與分析方法，此方法可以針對某一演奏家的演奏作品訓練樣本建立其力度表現側寫，再透過此表現側寫，可以將一首演奏作品的錄音檔，自動計算出每個音的表現力度強弱，提供做為進一步大規模不同演奏作品的表現比較分析之用。

Content-based Music Analysis is the important research discussion in recent years. The core of the research of music expression analysis is discussed how performers communicate the emotion in music to listeners. The main ways to represent music expression are dynamics and tempo. We introduce a new technology to automatic equalization of loudness of music tones and the analysis of music dynamics, which can buit the music dynamics profile of any performer. Through the music expression profile, the system can automatic calculate the music dynamics of every tone in record.

1. 緒論 ....................................................................................................................... 1
2. 相關研究 ............................................................................................................... 3
2.1. 起音點偵測之相關研究 ........................................................................... 3
2.2. 音樂表現分析之相關研究 ....................................................................... 5
2.3. 響度計算之相關研究 ............................................................................... 9
2.4. 等響度曲線之相關研究 ......................................................................... 11
2.5. 力度模型之相關研究 ............................................................................. 15
3. 響度與力度的涵義 ............................................................................................. 17
3.1. 聲音強度的定義與涵義 ......................................................................... 17
3.2. 響度的定義與涵義 ................................................................................. 21
3.3. 力度的定義與涵義 ................................................................................. 23
4. 音樂演奏力度表現比較分析系統架構 ............................................................. 25
5. 力度表現分析方法 ............................................................................................. 27
6. 實驗 ..................................................................................................................... 33
6.1. 實驗一：RWC樂器資料庫中不同樂器之等響度曲線量測 ............... 33
6.2. 實驗二：真實演奏的力度側寫 ............................................................. 46
7. 結論 ..................................................................................................................... 56
參考文獻 ..................................................................................................................... 57
附錄A. 實驗樣本資訊 ......................................................................................... 65
附錄B. 新葛羅夫音樂辭典有關力度的定義之原文 ......................................... 87
附錄C. Zwicker與Moore之穩態聲音的響度計算方法 .................................. 91
附錄D. Zwicker與Moore之隨時間變化的聲音響度計算方法 ...................... 97
附錄E. 本論文之純音響度實驗數據 ............................................................... 100

[1] Adli, A., Z. Nakao, T. Yokoda and Y. Nagata, “Piano Sound Characteristics: a Study on Some Factors Affecting Loudness in Digital and Acoustic Pianos,” ICICIC, Japan, 2007.
[2] ANSI S3.4, “Procedure for the Computation of Loudness of Steady Sounds,” 2007.
[3] Boon, J. P. Noullez, A. and C. Mommen, “Complex Dynamics and Musical Structure,” J. New. Mus. Res., Vol. 19, No. 3, 1990.
[4] Boon, J. P. and O. Decroly, “Dynamical Systems Theory for Music Dynamics,” Chaos 5, pp.501-505, 1995.
[5] Berndt, A. and T. Hähnel, “Modelling Musical Dynamics,” in Audio Mostly 2010: 5th Conf. on Interaction with Sound, pp.134-141, Sweden, 2010.
[6] Bellmann, M. A., Mellert, V., Reckhardt, C., and Remmers, H., ‘‘Perception of Sound and Vibration at Low Frequencies,’’ Joint meeting of ASA and EAA: Forum Acusticum integrating German Acoustics DAGA Conference 1999, Berlin, Germany, 1999.
[7] Betke, K., and Mellert, V., ‘‘New Measurements of Equal-loudness Level Contours,’’ Proc. Inter-noise 89, pp. 793–796, 1989.
[8] Bello, J. P., C. Duxbury, M. Davies and M. B. Sandler, “On the Use of Phase and Energy for Musical Onset Detection in the Complex Domain,” IEEE Signal Processing Letters, Vol. 11, No. 6, 2004.
[9] Böck, S., F. Krebs and M. Schedl, “Evaluating the Online Capabilities of Onset Detection Methods,” in Proc. ISMIR, pp.49-54, 2012.
[10] Bello, J. P., L. Daudet, S. Abdallah, C. Duxbury, M. Davies and M. B. Sandler, “A Tutorial on Onset Detection in Music Signals,” IEEE Transactions on Speech and Audio Processing, Vol. 13, No. 5, 2005.
58
[11] Cambouropoulos, E., S. Dixon and W. Goebl, “Human Preferences for Tempo Smoothness,” Proc. of the International Symposium on Systematic and Comparative Musicology, pp. 18-26, 2001.
[12] Churcher, B. G. and A. King, “The Performance of Noise Meters in Terms of the Primary Standard,” J. Inst. Electr. Eng., 1937.
[13] Dixon, S., W. Goebl and G. Widmer, “Real Time Tracking and Visualisation of Musical Expression,” ICMAI, 2002.
[14] Dixon, S., “An Interactive Beat Tracking and Visualization System,” Proc. of the International Computer Music Conference, pp.215-218,2001.
[15] DIN 45631, “Berechnung des Lautstärkepegels und der Lautheit aus dem Geräuschspektrum,” 2008.
[16] Fabiani, M., “A Method for The Modification of Acoustic Instrument Tone Dynamics,” Proc. of the 12th Int. Conference on Digital Audio Effects, Italy, 2009.
[17] Fletcher, H. and W. Munson, “Loudness, Its Definition, Measurement and Calculation,” J. Acoust. Soc. Am., Vol. 82, No. 5, pp.82-108, October, 1933.
[18] Fastl, H., Jaroszewski, A., Schorer, E., and Zwicker, E., ‘‘Equal Loudness Contours Between 100 and 1000 Hz for 30, 50, and 70 phon,’’ Acustica 70, 197–201, 1990.
[19] Goto, M., “An Audio-based Real-time Beat Tracking System for Music With or Without Drum-sounds,” J. New Music Res., Vol. 30, No. 2, 2001.
[20] Goto, M. and S. Hayamizu, “A Real-time Music Scene Description System: Detecting Melody and Bass Lines in Audio Signals,” Proc. of the 1999 International Joint Conference on AI Workshop on Computational Auditory Scene Analysis, pp.31-40, 1999.
[21] Goto, M., “A Real-time Music-Scene-Description System: Predominant-F0 Estimation for Detecting Melody and Bass Lines in Real-World Audio Signals,”
59
ISCA Journal, Vol. 43, No. 4, 2004.
[22] Goebl, W., E. Pampalk and G. Widmer, “Exploring Expressive Performance Trajectories: Six Famous Pianists Play Six Chopin Pieces,” Proc. of the 8th ICMPC, Evanston, Illinois, 2004.
[23] Grachten, M. and G. Widmer, “Explaining Musical Expression as a Mixture of Basis Functions,” Proceedings of the SMC 2011: The 8th Sound and Music Computing Conference (submitted), Italy, 2011.
[24] Genesis, S., “History and Description of Loudness Models,” GENESIS, 2009.
[25] Glasberg, B. and B. C. J. Moore, “A Model of Loudness Applicable to Time-varying Sounds,” J. Audio Eng. Soc, Vol. 50, No. 5, 2002.
[26] Goto, M., H. Hashiquchi, T. Nishimura and R. Oka, “RWC Music Database: Music Genre Database and Musical Instrument Sound Database,” in PROC. 4th International Conference on Music Information Retrieval, 2003.
[27] Huron, D., “The Ramp Archetype: A Score-Based Study of Musical Dynamics in 14 Piano Composers,” Psychology of Music and Music Education, Vol. 19, No. 1, pp.33-45, 1991.
[28] Hansen, C., “Occupational Exposure to Noise: Evaluation, Prevention and Control,” Department of Mechanical Engineering, University of Adelaide.
[29] ISO 532, “Method for calculating loudness level,” J. Acoust. Soc., 1975.
[30] ISO 226, “Acoustics: Normal Equal-loudness-level Contours,” 2003.
[31] Juslin, P. N., “Five Facets of Musical Expression: a Psychologist’s Perspective on Music Performance,” Psychology of Music, Vol. 31, No. 3, 2003.
[32] Kirk, B., ‘‘Loudness and Annoyance from Infrasound,’’ Institute of Electronic Systems, Aalborg University, Aalborg, Denmark, pp. 1–111, 1983.
[33] Klapuri, A. P.,“Sound Onset Detection by Applying Psychoacoustic Knowledge,”
60
in Proceedings of IEEE International Conference on Acoustics, Speech and Signal Processing, Vol. 6, pp. 3089-3092, 1999.
[34] Langner, J. and W. Goebl, “Visualizing Expressive Performance in Tempo-Loudness Space,” Journal of Computer Music, Forthcoming, 2003.
[35] Lund, T., “Control of Loudness in Digital TV,” in Proc. of the NAB Engineering Conference, pp.57-65, 2006.
[36] Lund, T., “Control of Loudness Across Broadcast Platforms,” in Proc. of the NAB Engineering Conference, 2009.
[37] Lydolf, M., and Møller, H., ‘‘New Measurements of the Threshold of Hearing and Equal-loudness Contours at Low Frequencies,’’ in Proceedings of the 8th International Meeting on Low Frequency Noise and Vibration, Gothenburg, Sweden, pp. 76–84, 1997.
[38] Leisinger, U., H. Scholz and R. D. Levin, “Wolfgang Amadeus Mozart: Klavierson Piano Sonatas / Sonates pour Piano,” Wiener Urtext Edition, Schott / Universal Edition, 2004.
[39] Masri, P., “Computer Modeling of Sound for Transformation and Synthesis of Musical Signals,” PhD thesis, University of Bristol, UK, 1996.
[40] Moore, B. C. J. and B. R. Glasberg, “A Revision of Zwicker’s Loudness Model,” Acustica, Vol. 82, pp. 335-345, 1996.
[41] Møller, H., and Andresen, J., ‘‘Loudness at Pure Tones at Low and Infrasonic Frequencies,’’ J. Low Freq. Noise. Vib. 3, 78–87, 1984.
[42] Meyer, J., “Acoustics and the Performance of Music,” Springer, 5 Edition, 2009.
[43] Mion, L. and G. Poli, “Score-Independent Audio Features for Description of Music Expression,” IEEE Transactions on Audio, Speech, and Language Processing, Vol. 16, No. 2, 2008.
61
[44] Pampalk, E., P. Herrera and M. Goto, “Computational Models of Similarity for Drum Samples,” IEEE Transaction on Audio, Speech, and Language Processing, Vol. 16, No. 2, 2008.
[45] Poulsen, T., and Thøgersen, L., ‘‘Hearing Threshold and Equal Loudness Level Contours in a Free Sound Field for Pure Tones from 1 kHz to 16 kHz,’’ Proc. Nordic Acoust. Meeting, pp. 195–198, 1994.
[46] Repp, B., “The Dynamics of Expressive Piano Performance: Schumann’s “Träumerei” Revisited,” J. Acoust. Soc. Am., Vol. 100, No. 1, 1996.
[47] Rossing, T., “Springer Handbook of Acoustics,” Springer, LLC, New York, 2007.
[48] Robinson, D. and R. Dadson, “A Re-determination of the Equal-loudness Relations for Pure Tones,” Br. J. Appl. Phys., 1956.
[49] Serway, R. and J. Jewett, “Physics for Scientists and Engineers,” Belmont, 6 Edition.
[50] Srinivasan, S. H., “Characterizing Music Dynamics for Improvisation,” in Proc. of the 2004 IEEE International Conference on Multimedia and Expo, pp.1339-1342, 2004.
[51] Sandvold, V. and P. Herrera, “Towards a Semantic Descriptor of Subjective Intensity in Music,” in Proc. of the ICMC, 2005.
[52] Skovenborg, E. and S. Nielsen, “Evaluation of Different Loudness Models with Music and Speech Material,” in Proc. of the 117th Convention of the Audio Engineering Society, San Francisco, CA, USA, 2004.
[53] Skovenborg, E., R. Quesnel and S. Nielsen, “Loudness Assessment of Music and Speech,” in Proc. of the 116th Convention of the Audio Engineering Society, 2004.
[54] Skovenborg, E. and S. Nielsen, “Real-Time Visualisation of Loudness Along Different Time Scales,” in Proc. of the 10th Int. Conference on Digital Audio Effects
62
(DAFx-07), Bordeaux, France, 2007.
[55] Skovenborg, E. and T. Lund, “Loudness Descriptors to Characterize Programs and Music Tracks,” in Proc. of the 125th Convention of the Audio Engineering Society, San Francisco, CA, USA, 2008.
[56] Suzuki, Y. and H. Takeshima, “Equal-Loudness-Level Contours for Pure Tones,” J. Acoust. Soc. Am., Vol. 116, No. 2, pp.918-933, 2004.
[57] Sadie, S., et al., “The New Grove Dictionary of Music and Musicians,” Macmillan, London, 2001.
[58] Stevens, S. S., “Calculation of the Loudness of Complex Noise,” J. Acoust. Soc., 1956.
[59] Suzuki, S., Suzuki, Y., Kono, S., Sone, T., Kumagai, M., Miura, H., and Kado, H., ‘‘Equal-loudness Level Contours for Pure Tone Under Free Field Listening Condition (I)—Some Data and Considerations on Experimental Conditions,’’ J. Acoust. Soc. Jpn. (E) 10, 329–338, 1989.
[60] Takeshima, H., Suzuki, Y., Ashihara, K., and Fujimori, T., ‘‘Equal-loudness Contours Between 1 kHz and 12.5 kHz for 60 and 80 phons,’’ Acoust. Sci. Tech. 23, 106–109, 2002.
[61] Takeshima, H., Suzuki, Y., Fujii, H., Kumagai, M., Ashihara, K., Fujimori, T., and Sone, T., ‘‘Equal-loudness Contours Measured by the Randomized Maximum Likelihood Sequential Procedure,’’ Acust. Acta Acust. 87, 389–399, 2001.
[62] Takeshima, H., Suzuki, Y., Kumagai, M., Sone, T., Fujimori, T., and Miura, H., ‘‘Equal-loudness Level Measured with the Method of Constant Stimuli—Equal-loudness Level Contours for Pure Tone Under Free-field Listening Condition (II),’’ J. Acoust. Soc. Jpn. (E) 18, 337–340, 1997.
[63] Todd, N. P. McA., “A Model of Expressive Timing in Tonal Music,” Music Percep.
63
3, 33-58, 1985.
[64] Todd, N. P. McA., “A Computational Model of tempo,” Contemp. Music Rev. 3, 69-88, 1989.
[65] Todd, N. P. McA., “Towards a Cognitive Theory of Expression: The Performance and Perception of Tempo,” Contemp. Music Rev. 4, 405-416, 1989.
[66] Todd, N. P. McA., “Computational Theory and Implementations of an Abstract Expression System: A Contribution to Computational Psychomusicology,” Ph .D. thesis, University of Exeter, 1989.
[67] Timoney, J., T. Lysaght and M. Schoenwiesner, “Implementing Loudness Models in Matlab,” in Proc. of the 7th Int. Conference on Digital Audio Effects (DAFx-04), Naples, Italy, October 5-8, 2004.
[68] Timmers, R., “Predicting the Similarity Between Expressive Performances of Music From Measurements of Tempo and Dynamics,” J. Acoust. Soc. Am., Vol. 117, No. 1, 2005.
[69] Todd, N. P. M., “The Dynamics of Dynamics: A Model of Musical Expression,” J. Acoust. Soc. Am., Vol. 91, No. 6, pp.3540-3550, 1992.
[70] Vickers, E., “Metrics for Quantifying Loudness and Dynamics,” in Proc. of the AES 129th Convention, San Francisco, 2010.
[71] Vines, B. W. Nuzzo, R. L. and D. J. Levitin, “Analyzing Temporal Dynamics in Music: Differential Calculus, Physics, and Functional Data Analysis Techniques,” Music Perception, Vol. 23, No. 2, pp.137-152, 2005.
[72] Vickers, E., “Automatic Long-Term Loudness and Dynamics Matching,” in Proc. of the AES 111th Convention, New York, 2001.
[73] Widmer, G., S. Dixon, W. Goebl, E. Pampalk and A. Tobudic, “In Search of the Horowitz Factor,” AI Magazine, Vol. 24, No. 3, 2003.
64
[74] Widmer, G. and A. Tobudic, “Playing Mozart by Analogy: Learning Multi-level Timing and Dynamics Strategies,” Journal of New Music Research, Vol. 32, No. 3, 2003.
[75] Watanabe, T., and Møller, H., ‘‘Hearing Threshold and Equal Loudness Contours in Free Field at Frequencies Below 1 kHz,’’ J. Low Freq. Noise Vib. 9, 135–148, 1990.
[76] Zwicker, E., “Subdivision of the Audible Frequency Range into Critical Bands,” Journal of the Acoustical Society of America (33):248-249, 1961.
[77] Zwicker, E. and H. Fastl, “Psychoacoustics: Facts and Models,” 2nd Edition, Springer-Verlag, Berlin, 1999.
[78] Zwicker, E. and R. Feldtkeller, “On the Loudness of Stationary Noises,” Acustica, 1955.
[79] 王小川, “語音訊號處理,” 全華, 修訂二版.
[80] 黃信夫, “人對基本幾何形狀面積知覺的研究,” 雲林科技大學, 2004.