The torii of phases

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 7937 LNAI, Issue , 2013, Pages 1-18

  Amiot, Emmanuel ^a  

^a Classes Préparatoire Aux Grandes Ecoles   (France)

Author keywords

DFT; Fourier; phase; scales; Tonnetz; torus; triads

Indexed keywords

DFT; FOURIER; PHASE; SCALES; TONNETZ; TORUS; TRIADS;

ARTIFICIAL INTELLIGENCE; COMPUTER SCIENCE;

FOURIER ANALYSIS;

EID: 84884489558     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/978-3-642-39357-0_1     Document Type: Conference Paper

References (21)

1. Quinn, I.: A Unified Theory of Chord Quality in Equal Temperaments. Ph.D. dissertation, Eastman School of Music (2004)
2. Quinn, I.: General Equal Tempered Harmony. Journal of Music Theory 44(2)-45(1) (2006-2007)
3. Amiot, E.: David Lewin and Maximally Even Sets. Journal of Mathematics and Music 1(3), 157-172 (2007)
4. Tymoczko, D.: Three Conceptions of Musical Distance. In: Chew, E., Childs, A., Chuan, C.-H. (eds.) MCM 2009. CCIS, vol. 38, pp. 258-272. Springer, Heidelberg (2009)
5. Callender, C.: Continuous Harmonic Spaces. Journal of Music Theory 51(2), 277-332 (2007)
6. Hoffman, J.: On Pitch-Class Set Cartography Relations between Voice-Leading Spaces and Fourier Spaces. Journal of Music Theory 52(2) (2008)
7. Krumhansl, C.: Cognitive Foundations of Musical Pitch. Oxford University Press, New York (1990)
8. Tymoczko, D.: Geometrical Methods in Recent Music Theory. Music Theory Online 16(1) (2010), http://www.mtosmt.org/issues/mto.10.16.1/mto.10.16.1. tymoczko.html
9. Tymoczko, D.: The Geometry of Music. Oxford University Press, New York (2011)
10. Tymoczko, D.: Set-Class Similarity, Voice Leading, and the Fourier Transform. Journal of Music Theory 52(2), 251-272 (2008)
11. Mazzola, G., Andreatta, M.: Diagrams, Gestures and Formulae in Music. Journal of Mathematics and Music 1(1), 23-46 (2007)
12. Lewin, D.: Generalized Musical Intervals and Transformations. Yale University Press, New Haven (1987)
13. Peck, R.W.: N th Roots of Pitch-Class Inversion. In: Agon, C., Andreatta, M., Assayag, G., Amiot, E., Bresson, J., Mandereau, J. (eds.) MCM 2011. LNCS, vol. 6726, pp. 196-206. Springer, Heidelberg (2011)
14. Mandereau, J., Ghisi, D., Amiot, E., Andreatta, M., Agon, C.: Discrete Phase Retrieval in Musical Structures. Journal of Mathematics and Music 5(2), 83-98 (2011)
15. Douthett, J., Steinbach, P.: Parsimonious Graphs: A Study in Parsimony, Contextual Transformations, and Modes of Limited Transposition. Journal of Music Theory 42(2), 241-263 (1998)
16. Plotkin, R.: Cardinality Transformations in Diatonic Space. In: Agon, C., Andreatta, M., Assayag, G., Amiot, E., Bresson, J., Mandereau, J. (eds.) MCM 2011. LNCS, vol. 6726, pp. 207-219. Springer, Heidelberg (2011)
17. Amiot, E., Sethares, B.: An Algebra for Periodic Rhythms and Scales. Journal of Mathematics and Music 5(3), 149-169 (2011)
18. Baroin, G.: The Planet-4D Model: An Original Hypersymmetric Music Space Based on Graph Theory. In: Agon, C., Andreatta, M., Assayag, G., Amiot, E., Bresson, J., Mandereau, J. (eds.) MCM 2011. LNCS, vol. 6726, pp. 326-329. Springer, Heidelberg (2011)
19. Carlé, M., Hahn, S., Matern, M., Noll, T.: Presentation of Fourier Scratching at MCM 2009, New Haven (2009), http://www.supercollider2010.de/ images/papers/fourier-scratching.pdf
20. Milne, A.J., Carlé, M., Sethares, W.A., Noll, T., Holland, S.: Scratching the Scale Labyrinth. In: Agon, C., Andreatta, M., Assayag, G., Amiot, E., Bresson, J., Mandereau, J. (eds.) MCM 2011. LNCS (LNAI), vol. 6726, pp. 180-195. Springer, Heidelberg (2011)
21. Callender, C., Quinn, I., Tymoczko, D.: Generalized Voice Leading Spaces. Science 320, 346-348 (2008)