和弦辨識方法可以分為和弦偵測與產生和弦配置。和弦偵測的目標是預測和弦序列並自動標記，產生和弦配置則是產生和弦序列以建議伴奏及和弦的安排。一般而言，和弦偵測會有標準答案，產生和弦配置則沒有標準答案。由於單音音樂比複音音樂包含較少的音樂資訊，所以產生和弦序列的難度也較高。
在本論文中，我們使用和弦偵測及調性偵測的相關技術建立一個產生和弦配置的系統。我們利用和弦轉移機率和弦與旋律的相關度進行動態時間校準來產生和弦配置。其中，和弦與旋律相關度的計算分別使用餘弦相似度與高斯混合模型計算。實驗顯示，使用高斯混合模型計算兩向量文件相關度的方法會優於使用餘弦相似度的方法。且使用轉移機率方法能有效產生更佳的和弦序列。另外，使用前n名的調性偵測結果，其正確率與調性正確時的結果均非常接近。因此，我們建置包含了和弦偵測與調性偵測兩個階段的和弦配置系統。

Chord recognition includes chord detection and chord arrangement. The purpose of chord detection is to predict chord sequences for music, which could be used to tagging music automatically. Chord arrangement, on the other hand, aims to generate chord sequences for the purpose of accompaniment or arrangement. In general, chord detection will be given the ground truths while the chord arrangement won’t, and it is more difficult to produce the chord sequences for monophonic music than polyphonic music because the former contains less information.
In this thesis, we build a chord arrangement system for monophonic music based on key detection and chord detection techniques. We utilize a dynamic programming model for chord detection, which contains n-gram distribution of chord transition and chord-melody correlation. The chord-melody correlation can be computed based on the cosine similarity between the chord and the melody, or based on Gaussian mixture model (GMM) of melody for given chord. The n-gram distribution and the GMMs are trained and tested with 55 contemporary hymns under two segmentation schemes: full measure (a chord per measure) and semi measure (two chord per measure). Experimental results show that, for both segmentation schemes, GMM model can achieve better performance than cosine similarity, and the chord transition n-gram is useful for producing better chord sequences. In addition, using the n-best results of key detection, the accuracy of the chord detection for the music is very close to the result when the key is correctly assigned. Therefore, a two-stage chord arrangement system is built by combining key detection and chord detection.

[1] Fujishima, T., “Realtime Chord Recognition of Musical Sound: A System Using Common Lisp Music”, ICMC, pp. 464–467, 1999.
[2] Longuet-Higgins and M. J. Steedman., “On Interpreting Bach”, Machine Intelligence, 6:221.Edinburgh University Press, 1971.
[3] Carol L. Krumhansl., “Cognitive Foundations of Musical Pitch”, Oxford University Press, New York, NY, 1990.
[4] Carol L. Krumhansl Edward J. Kessler, “Tracing the Dynamic Changes in Perceived Tonal Organization in a Spatial Representation of Musical Keys”, Psychological Review, Vol. 89, No. 4, 334-368, 1982.
[5] Emilia Gómez, “Tonal Description of Music Audio Signals”, PhD Thesis, Universitat Pompeu Fabra, Barcelona, Spain, 2006.
[6] David Temperley., “What's Key for Key? The Krumhansl-Schmuckler Key-Finding Algorithm Reconsidered”, Music Perception, 17(1):65–100, 1999.
[7] W. Bas de Haas, José Pedro Magalhães and Frans Wiering, “Improving Audio Chord Transcription by Exploiting Harmonic and Metric Knowledge”, ISMIR, 2012.
[8] Judith C. Brown, “Calculation of a constant Q spectral transform”, J. Acoust. Soc. Am., 89(1):425–434, 1991.
[9] David Temperley, “A Bayesian Approach to Key-Finding”, ICMAI 2002, LNAI 2445, pp. 195-206, 2002.
[10] H. Sakoe and S. Chiba, “Dynamic programming algorithm optimization for spoken word recognition”, IEEE Transactions on Acoustics, Speech, and Signal Processing, vol. ASSP-26, no. 1, pp.43-49, 1978.
[11] D.A. Reynolds and R.C. Rose, “Robust text-independent speaker identification using Gaussian mixture speaker models”, IEEE Transaction on Speech Audio Process, vol. 3, pp. 72–83, 1995.
[12] Da-chuan Wei, “Recognition Algorithm of Musical Chord Based on Keynote-Dependent HMM”, TMEE, pp.2504-2507, 2011.
[13] Cheng-Jian Lin, Chin-Ling Lee and Chun-Cheng Peng, “Chord Recognition Using Neural Networks Based on Particle Swarm Optimization”, IEEE, pp.821-827, 2011.
[14] Kyogu Lee, “Automatic Chord Recognition from Audio Using Enhanced Pitch Class Profile”, ICMC, 2006.
[15] Laurent Oudre, Yves Grenier, Cedric F ´ evotte ´, “Chord Recognition using Measures of Fit, Chord Templates and Filtering Methods”, IEEE, pp.9-12, 2009.
[16] Yushi Ueda, Yuki Uchiyama, Takuya Nishimoto, Nobutaka Ono and Shigeki Sagayama, “HMM-Based Approach for Automatic Chord Detection using Refined Acoustic Features”, ICASSP, pp.5518-5521, 2010.
[17] Wang Feng, Xue-ying Zhang, Bing-nan Li, “Research of Chord Recognition Based On MPCP”, IEEE, vol.4, pp.76-79, 2010.
[18] N. Boulanger-Lewandowski, Y. Bengio, and P. Vincent, “Audio chord
recognition with recurrent neural networks,” in Proc. ISMIR, pp.335-340, 2013.
[19] Thomas Rocher, Matthias Robine, Pierre Hanna, Laurent Oudre “Concurrent Estimation of Chords and Key from Audio” in Proc. ISMIR, pp.141-146, 2010.
[20] Ricardo Scholz and Geber Ramalho, “COCHONUT: Recognizing Complex Chords from Midi Guitar Sequences”, in Proc. ISMIR, pp.27-32, 2008.
[21] Aiko Uemura and Jiro Katto, “Chord Recognition using Double Nested Circle of Fifths”, ICASSP, pp.449-452, 2012.
[22] Satoru Fukayama, Kazuyoshi Yoshii, Masataka Goto, “Chord-Sequence-Factory: A Chord Arrangement System Modifying Factorizes Chord Sequence Probabilities”, in Proc. ISMIR, pp.84-89, 2013.
[23] Sheh, A. and Ellis, D.P.W. “Chord Segmentation and Recognition Using EM-Trained Hidden Markov Models,” In Proc. ISMIR, 2003.
[24] J.P. Bello and J. Pickens. “A robust mid-level representation for harmonic content in music signals”, in Proc. ISMIR, pp.304-311, 2005.
[25] Kouhei Sumi, Katsutoshi Itoyama, Kazuyoshi Yoshii, Kazunori Komatani, Tetsuya Ogata, and Hiroshi G. Okuno, “Automatic Chord Recognition based on A Probabilistic Integration of Chord Transition and Bass Pitch Estimation”, in Proc. ISMIR, pp.39-44, 2008.
[26] http://lilypond.org/
[27] 飛躍青年傳愛中心(2006)。Faith in God：飛躍詩集.IV。新北市新店區：校園書房。
[28] http://www.music-ir.org/mirex/wiki/MIREX_HOME