Abstract
This paper describes a good way to put forward to a general public the relationship between maths and music: “concerférences”, a French term coined to designate anything between a talk cum music and a concert cum fairly detailed scientific explanations. This format of exposition is quite versatile, and the content can be adapted to a wide range of publics. It has shown considerable pedagogical promise, some possible reasons are explored with examples taken from actual practice.
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Notes
- 1.
See references in [2], which covers the subject in greater depth and shows a variety of topics appropriate for a variety of audiences. The present talk focuses more on the general concept of concerference and its pedagogical interest.
- 2.
A Shepard-Risset never-ending scale, played while a Penrose stair (or Escher fountain) is shown, can help drive the idea home.
- 3.
Its topological structure is quite easy to grab when the audience follows a sequence of chords/notes going through one side and turning up on the opposite one, and there is a wealth of interesting videos using this model. A fantastic pedagogical tool is Louis Bigo’s software HexaChord [3] which enables to follow chord progressions in real time.
- 4.
P, L, and R respectively exchange C major triad with C minor, E minor and A minor.
- 5.
In concerférences, we sometimes use G. Albini’s seminal variant https://youtu.be/rXR64vFcf-Q of Bach’s first cello Suite, Corale #4 which shows beautifully the parsimonious character of chord transitions. However, when I am privileged to share the stage with Gilles Baroin and Moreno Andreatta, the latter plays and sings live one of his own ‘Hamiltonian songs’ while the former projects his stunning graphics renderings in diverse geometrical models, for instance Aprile (https://www.youtube.com/watch?v=AB8By7ghTkU) on a moving poem by Gabriele d’Annunzio.
- 6.
See [4].
- 7.
- 8.
Recent experiments show particularly notable benefits for “lower performers” when subjected to artistic teachings [6].
- 9.
See examples with Paolo Conte or Frank Zappa at http://www.mathemusic4d.net/.
- 10.
For instance, if the concepts of musical inversions and retrogradations have been shown, students can be enticed to try them on their own musical compositions, for instance with synthesizers online like http://www.audiosauna.com/studio/.
- 11.
My usual answer to the teleological argument that Music, being the breath of Gods, is best left respectfully unstained by maths, is: “the better you know the person you love, the better you love him/her”. The argument is usually well received.
References
Albini, G., Antonini, S.: Hamiltonian cycles in the topological dual of the tonnetz. In: Chew, E., Childs, A., Chuan, C.-H. (eds.) MCM 2009. CCIS, vol. 38, pp. 1–10. Springer, Heidelberg (2009). https://doi.org/10.1007/978-3-642-02394-1_1
Amiot, E.: “Concerférences”, addressing different publics for mathemusical popularization. In: Montiel, M., Gómez, F. (eds.) Theoretical and Practical Pedagogy of Mathematical Music Theory, pp. 179–199. World Scientific Publishing (2019)
Bigo, L.: Hexachord, free software (Java). http://www.lacl.fr/~lbigo/hexachord
Cannas, S., Antonini, S., Pernazza, L.: On the group of transformations of classical types of seventh chords. In: Agustín-Aquino, O.A., Lluis-Puebla, E., Montiel, M. (eds.) MCM 2017. LNCS (LNAI), vol. 10527, pp. 13–25. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-71827-9_2. https://www.researchgate.net/publication/317218582_On_the_group_of_transformations_of_classical_types_of_seventh_chords
Cohn, R.: Maximally smooth cycles, hexatonic systems, and the analysis of late-romantic triadic progressions. Music Anal. 15(1), 9–40 (1996)
Klass, P.: Using Arts Education to Help Other Lessons Stick, NYT, 4th March 2019. https://www.nytimes.com/2019/03/04/well/family/using-arts-education-to-help-other-lessons-stick.html
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Amiot, E. (2019). “Concerférences”: of Music and Maths, for the Audience’s Delight. In: Montiel, M., Gomez-Martin, F., Agustín-Aquino, O.A. (eds) Mathematics and Computation in Music. MCM 2019. Lecture Notes in Computer Science(), vol 11502. Springer, Cham. https://doi.org/10.1007/978-3-030-21392-3_36
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