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Conchord: An Application for Generating Musical Harmony by Navigating in the Tonal Interval Space

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Music, Mind, and Embodiment (CMMR 2015)

Part of the book series: Lecture Notes in Computer Science ((LNISA,volume 9617))

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Abstract

We present Conchord, a system for real-time automatic generation of musical harmony through navigation in a novel 12-dimensional Tonal Interval Space. In this tonal space, angular and Euclidean distances among vectors representing multi-level pitch configurations equate with music theory principles, and vector norms acts as an indicator of consonance. Building upon these attributes, users can intuitively and dynamically define a collection of chords based on their relation to a tonal center (or key) and their consonance level. Furthermore, two algorithmic strategies grounded in principles from function and root-motion harmonic theories allow the generation of chord progressions characteristic of Western tonal music.

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Notes

  1. 1.

    Sheppard [36] and Kruskal [37] first used this method, which has been extensively applied to visualise representations of multidimensional pitch structures [38, 39]. Briefly, nonmetric MDS attempts to transform a set of n-dimensional vectors, expressed by their distance in the item-item matrix, into a spatial representation that exposes the interrelationships among a set of input cases. We use the smacof library [40] from the statistical analysis package ‘R’ to compute dimensionality reduction using a nonmetric MDS algorithm. More specifically, we use the function smacofSym, with ‘ordinal’ type and ‘primary’ ties.

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Acknowledgments

This research is financed by National Funds through the FCT - Fundação para a Ciência e a Tecnologia within post-doctoral grants SFRH/BPD/109457/2015 and SFRH/BPD/88722/2012.

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Authors and Affiliations

  1. Sound and Music Computing, INESC TEC, Porto, Portugal

    Gilberto Bernardes, Diogo Cocharro, Carlos Guedes & Matthew E. P. Davies

  2. New York University Abu Dhabi, Abu Dhabi, United Arab Emirates

    Carlos Guedes

Authors
  1. Gilberto Bernardes
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  2. Diogo Cocharro
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  3. Carlos Guedes
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  4. Matthew E. P. Davies
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Correspondence to Gilberto Bernardes .

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Editors and Affiliations

  1. CNRS - LMA, Marseille Cedex 20, France

    Richard Kronland-Martinet

  2. CNRS - LMA, Marseille, France

    Mitsuko Aramaki

  3. CNRS - LMA, Marseille, France

    Sølvi Ystad

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Bernardes, G., Cocharro, D., Guedes, C., Davies, M.E.P. (2016). Conchord: An Application for Generating Musical Harmony by Navigating in the Tonal Interval Space. In: Kronland-Martinet, R., Aramaki, M., Ystad, S. (eds) Music, Mind, and Embodiment. CMMR 2015. Lecture Notes in Computer Science(), vol 9617. Springer, Cham. https://doi.org/10.1007/978-3-319-46282-0_15

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  • DOI: https://doi.org/10.1007/978-3-319-46282-0_15

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