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Learning metrics on spectrotemporal modulations reveals the perception of musical instrument timbre


Humans excel at using sounds to make judgements about their immediate environment. In particular, timbre is an auditory attribute that conveys crucial information about the identity of a sound source, especially for music. While timbre has been primarily considered to occupy a multidimensional space, unravelling the acoustic correlates of timbre remains a challenge. Here we re-analyse 17 datasets from published studies between 1977 and 2016 and observe that original results are only partially replicable. We use a data-driven computational account to reveal the acoustic correlates of timbre. Human dissimilarity ratings are simulated with metrics learned on acoustic spectrotemporal modulation models inspired by cortical processing. We observe that timbre has both generic and experiment-specific acoustic correlates. These findings provide a broad overview of former studies on musical timbre and identify its relevant acoustic substrates according to biologically inspired models.

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Fig. 1: Two different approaches to investigate the auditory perception of musical instrument timbre.
Fig. 2: Replicability of the MDS-based approach.
Fig. 3: Correspondence between fitted metrics and standard deviations of the stimuli.
Fig. 4: Generalizability of the metrics learned for the different datasets.

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Data availability

The data that support the findings of this study are available from the corresponding author upon request and at

Code availability

Custom codes that support the findings of this study are available from the corresponding author upon request and at


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This work was supported by the Canadian Natural Sciences and Engineering Research Council awarded to S.M. (grant nos. RGPIN-2015-05280 and RGPAS 478121-15) and to P.D. (RGPIN- 2018-05662), as well as a Canada Research Chair (grant nos. 950-223484 and 950-231872) awarded to S.M. E.T. was funded through an ILCB/BLRI grant no. ANR-16-CONV-0002 (ILCB), ANR-11-LABX-0036 (BLRI) and the Excellence Initiative of Aix-Marseille University (A*MIDEX), B.C. was founded through EU Marie Skłodowska-Curie fellowship (Project MIM, H2020-MSCA-IF-2014, grant agreement no. 659232). B.C. acknowledges STMS IRCAM-CNRS-Sorbonne Université in Paris where he recieved support from a Marie Sklodowska Curie research fellowship at the beginning of the project. The funders had no role in study design, data collection and analysis, decision to publish or preparation of the manuscript. We thank the authors of the studies re-analysed for providing the stimuli and data from their experiments; G. Mestdagh, E. Ponsot and B. Morillon for helpful discussions on earlier versions of the manuscript; and M. Elhilali and D. Pressnitzer for help in the initial implementation of the optimization framework.

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Authors and Affiliations



E.T., B.C., P.D. and S.M. worked on the conceptualization and methodology, and also reviewed and edited the article. E.T. and B.C. worked on the software, formal analysis and the investigation. E.T. conducted data curation, wrote the original draft and worked on the visualization. SM. supervised the work, conducted project administration and obtained funding.

Corresponding author

Correspondence to Etienne Thoret.

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Peer review information Primary Handling Editor: Marike Schiffer.

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Extended data

Extended Data Fig. 1 Details of the datasets.

Summary of the properties of the 17 datasets from the 8 different studies: dataset name (when applicable), number of stimuli in the dataset (Nb Sounds), fundamental frequency of the stimuli in Hz (f0), number and type of participants, type of sounds, and supplemental information when applicable.

Extended Data Fig. 2 Multi-Dimensional Scaling analysis.

Spearman correlation (ρ2) of the LAT and SC values with the positions of stimuli along the first two dimensions of the timbre spaces using the same MDS method for all datasets. The full statistics are provided in the Supplementary Table 1.

Extended Data Fig. 3 Replicability of the MDS-based analyses.

Spearman correlations (ρ2) of LAT and SC with perceptual dimensions reported in the original studies and determined with the same MDS parameters here (see Methods). It is noticeable that for almost all datasets, the original correlations reported in the studies are quasi-systematically lower than those computed in this meta-analysis. The full statistics are reported in the Supplementary Table 1.

Extended Data Fig. 4 Cross-validation of the metrics.

For each dataset, the metrics were cross-validated to test their generalizability within the dataset. Explained variances (r2) of the human ratings by the cross-validated metrics for each dataset are presented for: the Training correlations (fitted on the N-1 sounds), the Testing correlations (tested on the removed sound), the within correlation between the N*(N-1)/2 metric pairs characterizing the Internal consistency of the fitted metrics in each dataset, and the average correlation (r2) with the metric Refitted on all sounds with those on the N-1 subsets showing the extent to which this metric is different from the cross-validated one. On median, the metrics were cross-validated with r2 = 0.51 on the testing sets. For each dataset, they are highly consistent within the N-folds (r2: Mdn=0.85), and they strongly correlate with the metric fitted on the whole dataset (r2: Mdn=0.92). For each dataset, the correlation of the refitted metric on whole sounds with those fitted for the cross-validation (last column) are high showing that the metric fitted on whole sounds can be used to perform the analyses.

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Supplementary Figs. 1–18 and Supplementary Tables 1–19.

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Thoret, E., Caramiaux, B., Depalle, P. et al. Learning metrics on spectrotemporal modulations reveals the perception of musical instrument timbre. Nat Hum Behav 5, 369–377 (2021).

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