Abstract
We propose structural similarity of two melodies based on sub-trees from the time-span tree provided by the Generative Theory of Tonal Music. The structural distance of the tree was previously defined and called the “maximal time-span distance,” and experimental results showed to some extent a correspondence between the maximal time-span distance and psychological similarity. However, there is a big problem in that almost all pairs of melodies are not similar on the basis of the maximal time-span distance because the definition of the similarity is too strict. Therefore, we attempt to express a melodic structural similarity by using the coincidence rate of time-span sub-trees to weaken the condition for calculating similarity. We have set up three experimental conditions and compared their results.
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- 1.
This definition of similarity is different from general definitions such as of the Jaccard coefficient, the Simpson coefficient, and Dice coefficient in that we independently normalize \(P-P \sqcap Q\) and \(Q-P \sqcap Q\); otherwise, only one melody is influential when one melody has a lot of notes and the other has little numbers of notes.
- 2.
The distance by maximal time-span has been improved in [6], however, we here omit its detail by our limited space. We will compare this improved distance by maximal time-span with our sub-tree similarity in future.
References
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Acknowledgments
This work was supported in part by JSPS KAKENHI Grant Numbers 23500145, 25330434, and 25700036 and PRESTO, JST.
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Hamanaka, M., Hirata, K., Tojo, S. (2015). Structural Similarity Based on Time-Span Sub-Trees. In: Collins, T., Meredith, D., Volk, A. (eds) Mathematics and Computation in Music. MCM 2015. Lecture Notes in Computer Science(), vol 9110. Springer, Cham. https://doi.org/10.1007/978-3-319-20603-5_19
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DOI: https://doi.org/10.1007/978-3-319-20603-5_19
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