TY - GEN
T1 - Interval cycles, affinity spaces, and transpositional networks
AU - Martins, José Oliveira
PY - 2011
Y1 - 2011
N2 - The paper proposes a framework that coordinates several models of pitch space whose constructive features rely on the concept of interval cycles and transpositional relations. This general model brings under a focused perspective diverse pitch structures such as Tonnetze, affinity spaces, Alban Berg's "master array" of interval-cycles, and several types of transpositional networks (T-nets). This paper argues that applying incremental changes on some of the constructive features of the generic Tonnetz (Cohn 1997) results in a set of coherent and analytically versatile transpositional networks (T-nets), here classified as homogeneous, progressive, and dynamic. In this context, several properties of the networks are investigated, including voice-leading and common-tone relations. The paper also explores the music-modeling potential of progressive and dynamic T-nets by attending to characteristic compositional deployments in the music of Witold Lutosławski and György Kurtág.
AB - The paper proposes a framework that coordinates several models of pitch space whose constructive features rely on the concept of interval cycles and transpositional relations. This general model brings under a focused perspective diverse pitch structures such as Tonnetze, affinity spaces, Alban Berg's "master array" of interval-cycles, and several types of transpositional networks (T-nets). This paper argues that applying incremental changes on some of the constructive features of the generic Tonnetz (Cohn 1997) results in a set of coherent and analytically versatile transpositional networks (T-nets), here classified as homogeneous, progressive, and dynamic. In this context, several properties of the networks are investigated, including voice-leading and common-tone relations. The paper also explores the music-modeling potential of progressive and dynamic T-nets by attending to characteristic compositional deployments in the music of Witold Lutosławski and György Kurtág.
KW - Affinity spaces
KW - Dasian
KW - Interval cycles
KW - neo-Riemannian theory
KW - Network
KW - T-nets
KW - Tonnetz
KW - Transposition
UR - http://www.scopus.com/inward/record.url?scp=79959595331&partnerID=8YFLogxK
U2 - 10.1007/978-3-642-21590-2_10
DO - 10.1007/978-3-642-21590-2_10
M3 - Conference contribution
AN - SCOPUS:79959595331
SN - 9783642215896
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 126
EP - 139
BT - Mathematics and Computation in Music - Third International Conference, MCM 2011, Proceedings
T2 - 3rd International Conference on Mathematics and Computation in Music, MCM 2011
Y2 - 15 June 2011 through 17 June 2011
ER -