Abstract
This study aims at identifying the chord functions by statistical machine learning. Those functions found in the traditional harmony theory are not versatile for the various music styles, and we envisage that the statistical method would more faithfully reflect the music style we have targeted. In machine learning, we adopt hidden Markov models (HMMs); we evaluate the performance by perplexity and optimize the parameterization of HMM for each given number of hidden states. Thereafter, we apply the acquired parameters to the detection of modulation. We evaluate the plausibility of the partitioning by modulation by the likelihood value. As a result, the six-state model achieved the highest likelihood value both for the major keys and for the minor keys. We could observe finer-grained chord functions in the six-state models, and also found that they assigned different functional roles to the two tonalities.
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Notes
- 1.
The set partitioning model is a sort of the linear programming.
- 2.
In this paper, a phrase means a section divided by fermatas.
- 3.
Fermata is a notation which usually represents a grand pause. However, in the chorale pieces, it represents the end of a lyric paragraph.
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Acknowledgments
This research has been supported by JSPS KAHENHI Nos. 16H01744 and 19K20340.
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Uehara, Y., Nakamura, E., Tojo, S. (2021). Chord Function Identification with Modulation Detection Based on HMM. In: Kronland-Martinet, R., Ystad, S., Aramaki, M. (eds) Perception, Representations, Image, Sound, Music. CMMR 2019. Lecture Notes in Computer Science(), vol 12631. Springer, Cham. https://doi.org/10.1007/978-3-030-70210-6_12
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