TY - JOUR
T1 - A multi-level tonal interval space for modelling pitch relatedness and musical consonance
AU - Bernardes, Gilberto
AU - Cocharro, Diogo
AU - Caetano, Marcelo
AU - Guedes, Carlos
AU - Davies, Matthew E.P.
PY - 2016/10/1
Y1 - 2016/10/1
N2 - In this paper we present a 12-dimensional tonal space in the context of the Tonnetz, Chew’s Spiral Array, and Harte’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.
AB - In this paper we present a 12-dimensional tonal space in the context of the Tonnetz, Chew’s Spiral Array, and Harte’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.
KW - consonance
KW - tonal hierarchy
KW - tonal pitch space
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U2 - 10.1080/09298215.2016.1182192
DO - 10.1080/09298215.2016.1182192
M3 - Article
AN - SCOPUS:84970016307
VL - 45
SP - 281
EP - 294
JO - Journal of New Music Research
JF - Journal of New Music Research
SN - 0929-8215
IS - 4
ER -