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Location Constraints for Repetition-Based Segmentation of Melodies

Part of the Lecture Notes in Computer Science book series (LNAI,volume 9110)


Repetition-based modelling of melody segmentation relies on identifying and selecting repetitions of melodic fragments. At present, automatic repetition identification results in an overwhelmingly large number of repetitions, requiring the application of constraints for selecting relevant repetitions. This paper proposes constraints based on the locations of repetitions, extending existing approaches on constraints based on repetition length and frequency, and the temporal overlap between repetitions. To test our constraints, we incorporate them in a state-of-the-art repetition-based segmentation model. The original and constraint-extended versions of the model are used to segment 400 (symbolically encoded) folk melodies. Results show the constraint-extended version of the model achieves a statistically significant 14 % average improvement over the model’s original version.


  • Melody segmentation
  • Similarity matrix
  • Symbolic music processing

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Fig. 1.


  1. 1.

    Since \(\sigma \in \mathbb {R}_{\ge 0}\), normalisation of the \(\lambda _1\) values is required.

  2. 2.

    While theoretically \(\lambda _2 \in [0,1]\), considering \(\lim _{\mathcal {O}\rightarrow N} \lambda _2(\mathcal {O})=1\), in practice the values of \(\lambda _2\) will never reach the maximum of the function’s range, and so re-scaling is required.

  3. 3.

  4. 4.

  5. 5.

    Vocal music has dominated previous evaluations of melodic segmentation (especially large-scale evaluations), which might give an incomplete picture of the overall performance and generalisation computational segmentation models.

  6. 6.

    The samples are taken randomly from the EFSC and LC. However, following the corpus cleaning procedures of [18], we filtered out melodies which contained rests at annotated phrase markings, and also excluded melodies with just one phrase. The reason to exclude melodies with rests at annotated phrase markings is that, according to transcription research, sometimes musicologists transcribing the folk melodies would use rests at phrases as ‘breath marks’, regardless of whether performers would actually take breaths or not, making these rests an artefact of the transcription process (for a more detailed discussion on this topic see [18]).

  7. 7.

    Instructions to annotate boundaries were related to performance practice (e.g. “where would you change the movement of the bow”). The annotators agreed on a single segmentation, so no inter-annotator-agreement analysis is possible.

  8. 8.

    We tested both standard thresholding and the thresholding method provided in the SM toolbox (with the default parameters). We also tested Gaussian smoothing with window sizes \(\in \{2,3,6\}\) notes.


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We thank the anonymous reviewers for the useful comments on earlier drafts of this document. Marcelo Rodríguez López and Anja Volk are supported by the Netherlands Organization for Scientific Research (NWO-VIDI grant 276-35-001).

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Correspondence to Marcelo E. Rodríguez-López .

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Rodríguez-López, M.E., Volk, A. (2015). Location Constraints for Repetition-Based Segmentation of Melodies. In: Collins, T., Meredith, D., Volk, A. (eds) Mathematics and Computation in Music. MCM 2015. Lecture Notes in Computer Science(), vol 9110. Springer, Cham.

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