@article{02f9111ba1e34a14b55d804692a29e9d,
title = "A multi-level tonal interval space for modelling pitch relatedness and musical consonance",
abstract = "In this paper we present a 12-dimensional tonal space in the context of the Tonnetz, Chew{\textquoteright}s Spiral Array, and Harte{\textquoteright}s 6-dimensional Tonal Centroid Space. The proposed Tonal Interval Space is calculated as the weighted Discrete Fourier Transform of normalized 12-element chroma vectors, which we represent as six circles covering the set of all possible pitch intervals in the chroma space. By weighting the contribution of each circle (and hence pitch interval) independently, we can create a space in which angular and Euclidean distances among pitches, chords, and regions concur with music theory principles. Furthermore, the Euclidean distance of pitch configurations from the centre of the space acts as an indicator of consonance.",
keywords = "consonance, tonal hierarchy, tonal pitch space",
author = "Gilberto Bernardes and Diogo Cocharro and Marcelo Caetano and Carlos Guedes and Davies, {Matthew E.P.}",
note = "Funding Information: This research was supported by the Project “NORTE-01-0145-FEDER-000020”, financed by the North Portugal Regional Operational Programme (NORTE 2020), under the PORTUGAL 2020 Partnership Agreement, and through the European Regional Development Fund (ERDF) and by the Portuguese Foundation for Science and Technology under the post-doctoral grants SFRH/BPD/109457/2015 and SFRH/BPD/88722/2012. Funding Information: This research was supported by the Project ?NORTE-01-0145-FEDER-000020?, financed by the North Portugal Regional Operational Programme (NORTE 2020), under the PORTUGAL 2020 Partnership Agreement, and through the European Regional Development Fund (ERDF) and by the Portuguese Foundation for Science and Technology under the post-doctoral grants SFRH/BPD/109457/2015 and SFRH/BPD/88722/2012. Publisher Copyright: {\textcopyright} 2016 Informa UK Limited, trading as Taylor & Francis Group.",
year = "2016",
month = oct,
day = "1",
doi = "10.1080/09298215.2016.1182192",
language = "English (US)",
volume = "45",
pages = "281--294",
journal = "Journal of New Music Research",
issn = "0929-8215",
publisher = "Taylor and Francis Ltd.",
number = "4",
}