Strips, clocks and donughts: a journey through contemporary mathemusical research

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1 Strips, clocks and donughts: a journey through contemporary mathemusical research Moreno Andreatta Equipe Représentations Musicales IRCAM/CNRS/UPMC & IRMA/GREAM/USIAS

2 The musical and scientific research at IRCAM...

3 ... at the interface between art and popular music MusiqueLab 2 OMAX (computer-aided impro)

4 The Society for Mathematics and Computation in Music Conferences: 2007 Technische Universität (Berlin, Allemagne) 2009 Yale University (New Haven, USA) 2011 IRCAM (Paris, France) 2013 McGill University (Canada) 2015 Queen Mary University (Londres) 2017 UNAM (Mexico City) Official Journal and MC code (00A65: Mathematics and Music) Journal of Mathematics and Music, Taylor & Francis (Editors: Th. Fiore, C. Callender Associate eds.: E. Amiot, J. Yust) Books Series: Computational Music Sciences Series, Springer (G. Mazzola & M. Andreatta eds. 12 books published (since 2009) Collection Musique/Sciences, Ircam-Delatour France (J.-M. Bardez & M. Andreatta dir. 16 books published (since 2006) European Training Network on Computational and Mathematical Music Analysis and Generation ( InForMusic ) (Aalborg Universitet, City, University of London, Universiteit Utrecht, Aristotelio Panepistimio Thessalonikis, IRISA (UMR 6074), IRMA (UMR 7501), STMS (UMR 9912), Vrije Universiteit Brussel + Sony Europe Ltd, Chordify, Melodrive, Steinberg) Under reviewing

5 Mathemusical research at the interface of three disciplines MATHEMATICS mathematical statement generalization general theorem COMPUTER SCIENCE formalization application MUSIC musical problem music analysis composition music theory

A historical example of mathemusical problem 2 1 1 1 2 1 1 2 2 2 2

6 A historical example of mathemusical problem HOMOMETRY Hexachord Theorem M. Babbitt

7 Aperiodic Rhythmic Tiling Canons (Vuza Canons) Dan Vuza Anatol Vieru

8 A short catalogue of mathemusical problems M. Andreatta : Mathematica est exercitium musicae, Habilitation Thesis, IRMA University of Strasbourg, 2010 Tiling Rhythmic Canons Z relation and homometry Transformational Theory Music Analysis, SC and FCA Diatonic Theory and ME-Sets Periodic sequences and FDC Block-designs in composition Rhythmic Tiling Canons Z-Relation and Homometric Sets Neo-Riemannian Theory and Spatial Computing Finite Difference Calculus Set Theory, andtransformation Theory Diatonic Theory and ME-Sets Block-designs

9 A short catalogue of mathemusical problems M. Andreatta : Mathematica est exercitium musicae, Habilitation Thesis, IRMA University of Strasbourg, 2010 Tiling Rhythmic Canons Z relation and homometry Transformational Theory Music Analysis, SC and FCA Diatonic Theory and ME-Sets Periodic sequences and FDC Block-designs in composition Rhythmic Tiling Canons Z-Relation and Homometric Sets Neo-Riemannian Theory and Spatial Computing Finite Difference Calculus UNIVERSITÀ DEGLI STUDI DI PADOVA Dipartimento di Matematica Corso di Laurea Triennale in Matematica Tesi di Laurea ON SOME ALGEBRAIC ASPECTS OF ANATOL VIERU PERIODIC SEQUENCES APPLIED TO MUSIC CANONS Set Theory, andtransformation Theory Diatonic Theory and ME-Sets Relatore: Dott.ssa LUISA FIOROT Laureando: NICOLÒ ANCELLOTTI MATRICOLA: ANNO ACCADEMICO dicembre2015

The interplay between algebra and geometry in

fr Concerning music, it takes place in time, like

In mathematics, there is this fundamental duality

corresponds to the visual arts, an immediate

that is very close to the language, and which has

10 The interplay between algebra and geometry in music è Concerning music, it takes place in time, like algebra. In mathematics, there is this fundamental duality between, on the one hand, geometry which corresponds to the visual arts, an immediate intuition and on the other hand algebra. This is not visual, it has a temporality. This fits in time, it is a computation, something that is very close to the language, and which has its diabolical precision. [...] And one only perceives the development of algebra through music (A. Connes). è

11 The galaxy of geometrical models at the service of music

12 The galaxy of geometrical models at the service of music

13 Bach s enigmatic canons and geometry Do

14 My end is my beginning (but twisted!)

16 The galaxy of geometrical models at the service of music

17 The galaxy of geometrical models at the service of music

18 The galaxy of geometrical models at the service of music

19 Music and mathematics: «prima la musica»! I. Xenakis Pythagoras and the monochord, VI th -V th Century B.C. Mersenne and the musical clock, 1648 Euler and the Speculum musicum, 1773

The circular representation of the pitch space Marin Mersenne la # la 10 9 8 sol # sol si 11 7 do 0 6 fa # 1 2 fa

20 The circular representation of the pitch space Marin Mersenne la # la sol # sol si 11 7 do 0 6 fa # 1 2 fa Harmonicorum Libri XII, 1648 re mi dodo# re re# mi fa fa# sol sol# la la# si 5 do # 3 4 re # do

re re# mi fa fa# sol sol# la la# si 5 do

21 The circular representation of the pitch space Marin Mersenne la # la sol # sol si 11 7 do 0 6 fa # 1 2 fa Harmonicorum Libri XII, 1648 re mi dodo# re re# mi fa fa# sol sol# la la# si 5 do # 3 4 re # do è DEMO

22 The circle: a model for periodic rhythms Bembé B C D 12 A E G F Dinner Table Problem Abadja ou Bembé

23 African-cuban ME-rhythms El cinquillo El trecillo 8 8

24 The geometry of African-Cuban rhythms Z 16 ( )

25 Odditive property of orally-trasmitted practices Z 24 Simha Arom Marc Chemillier ( )

26 Olivier Messiaen s non-invertible rhythms Olivier Messaien ( ) Alain Connes

27 Palindromic structures in Steve Reich s music Clapping Music de Steve Reich (1972)

28 The circle and its canonic rotations Clapping Music (1972)

29 The circle and its canonic rotations Clapping Music (1972) Gerubach's Scrolling Score Project

30 Permutational melodies in contemporary (art) music Marin Mersenne, Harmonicorum Libri XII, 1648 do mi b mi Six Bagatelles (G. Ligeti, 1953) sol

31 Permutational melodies in song writing Se telefonando, 1966 (Maurizio Costanzo/Ennio Morricone) / Mina The harmonic do space do# si b la sol# sol fa fa# fa Chord progression (min ) Ennio Morricone F# B B b m E b m B C# F# E b m B b m B C# F# B b E b Dm Gm E b F B b Gm Dm Gm E b F B b D b = (C#)

32 The Tonnetz (Network of Tones) Leonhard Euler Speculum Musicum (1773) è DEMO

33 From the Tonnetz to the dual one (and vice-versa) [Sonia Cannas, 2018]

34 Gilles Baroin è

35 The Tonnetz, its symmetries and its topological structure P R L Minor third axis transposition Axe de tierces mineures R as relative? P as parallel L = Leading Tone

36 The Tonnetz, its symmetries and its topological structure R P L Minor third axis transposition Axe de tierces mineures R as relative P as parallel è Source: Wikipedia L = Leading Tone

LACL, 2013 Assembling chords related by some equivalence relation

37 The Tonnetz as a simplicial complex L. Bigo, Représentation symboliques musicales et calcul spatial, PhD, Ircam / LACL, 2013 Assembling chords related by some equivalence relation Transposition/inversion: Dihedral group action on P(Z n ) C E Intervallic structure major/minor triads B F A G K TI [3,4,5] C# F# B

38 Classifying Chord Complexes L. Bigo, Représentation symboliques musicales et calcul spatial, PhD, Ircam / LACL, 2013 Complexes enumeration in the chromatic system C E B A F G C# F# B ß0=1 ß1=2 ß2=1

39 Classifying Chord Complexes L. Bigo, Représentation symboliques musicales et calcul spatial, PhD, Ircam / LACL, 2013 The search of the optimal space C E B G B (2,3,7) (3,4,5)

40 Classifying Chord Complexes L. Bigo, Représentation symboliques musicales et calcul spatial, PhD, Ircam / LACL, 2013 The search of the optimal space C E B G B (2,3,7) (3,4,5)

41 The panoply of Tonnetze at the service of the analyst (1,1,10) 10 9 (2,1,9)

The geometric character of musical logic 0,5 Johann

T[2,3,7] T[3,4,5] 0 K[1,1,10] K[1,2,9] K[1,3,8] K[1,4,7]

K[2,4,6] random chords K[2,5,5] K[3,3,6] K[3,4,5] K[4,4,4]

2-compactness 0,5 0,25 Schönberg - Pierrot Lunaire -

K[2,2,8] K[2,3,7] K[2,4,6] K[2,5,5] K[3,3,6] K[3,4,5]

K[1,2,9] K[1,3,8] K[1,4,7] K[1,5,6] K[4,4,4] Schönberg -

Andreatta, «Musical analysis with simplicial chord spaces»,

42 The geometric character of musical logic 0,5 Johann Sebastian Bach - BWV compactness 0,25 T[2,3,7] T[3,4,5] 0 K[1,1,10] K[1,2,9] K[1,3,8] K[1,4,7] K[1,5,6] K[2,2,8] Johann Sebastian Bach - BWV 328 K[2,3,7] K[2,4,6] random chords K[2,5,5] K[3,3,6] K[3,4,5] K[4,4,4] 0,5 Claude Debussy - Voiles 2-compactness 0, compactness 0,5 0,25 Schönberg - Pierrot Lunaire - Parodie K[1,1,10] K[1,2,9] K[1,3,8] K[1,4,7] K[1,5,6] K[2,2,8] K[2,3,7] K[2,4,6] K[2,5,5] K[3,3,6] K[3,4,5] K[4,4,4] Claude Debussy - Voiles random chords 0 K[1,1,10] K[1,2,9] K[1,3,8] K[1,4,7] K[1,5,6] K[2,2,8] K[2,3,7] K[2,4,6] K[2,5,5] K[3,3,6] K[3,4,5] K[4,4,4] Schönberg - Pierrot Lunaire - Parodie random chords Bigo L., M. Andreatta, «Musical analysis with simplicial chord spaces», in D. Meredith (ed.), Computational Music Analysis, Springer, 2015

43 The musical style...is the space! 3 2

44 Symmetries in Paolo Conte s Madeleine La b Re b Si b Mi b Si Mi Re b Fa # Re Sol Mi La Re La b Re b Do Mi b Almost total covering of the major-chords space!

45 Gilles Baroin è

46 Harmonic progressions as spatial trajectories L R è Source :

47 Gilles Baroin è

48 Reading Beethoven backwards time

49 The collection of 124 Hamiltonian Cycles! G. Albini & S. Antonini, University of Pavia, 2008

Hamiltonian cycles with inner periodicity L P L P L R... P L P L R L... L P L R L P... P L R L P L... L R L P L P... R L P L P L.

1 02 La sera non è più la tua canzone, è questa roccia d ombra traforata dai lumi e dalle voci senza fine, la quiete d una cosa già pensata.

perduta. R L P Music: M. Andreatta Arrangement and mix: M. Bergomi & S. Geravini (Perfect Music Production) Mastering: A.

50 Hamiltonian cycles with inner periodicity L P L P L R... P L P L R L... L P L R L P... P L R L P L... L R L P L P... R L P L P L... La sera non è più la tua canzone (Mario Luzi, 1945, in Poesie sparse) min La sera non è più la tua canzone, è questa roccia d ombra traforata dai lumi e dalle voci senza fine, la quiete d una cosa già pensata. Ah questa luce viva e chiara viene solo da te, sei tu così vicina al vero d una cosa conosciuta, per nome hai una parola ch è passata nell intimo del cuore e s è perduta. R L P Music: M. Andreatta Arrangement and mix: M. Bergomi & S. Geravini (Perfect Music Production) Mastering: A. Cutolo (Massive Arts Studio, Milan) Caduto è più che un segno della vita, riposi, dal viaggio sei tornata dentro di te, sei scesa in questa pura sostanza così tua, così romita nel silenzio dell essere, (compiuta). L aria tace ed il tempo dietro a te si leva come un arida montagna dove vaga il tuo spirito e si perde, un vento raro scivola e ristagna.

51 Gilles Baroin è

52 The use of constraints in arts OuLiPo (Ouvroir de Littérature Potentielle) Georges Perrec Cent mille milliards de poèmes, 1961 La vie mode d emploi, Raymond Queneau Italo Calvino Il castello dei destini incrociati, 1969

53 From the OuLiPo to the OuMuPo (ouvroir de musique potentielle) Valentin Villenave Mike Solomon M. Andreatta et al., «Music, mathematics and language: chronicles from the Oumupo sandbox», in Kapoula, Z., Volle, E., Renoult, J., Andreatta, M. (Eds.), Exploring Transdisciplinarity in Art and Sciences, Springer, 2018 Jean-François Piette Martin Granger Joseph Boisseau Moreno Andreatta Tom Johnson

54 Keeping the space...but changing the trajectory! è

55 Keeping the space...but changing the trajectory! Rotation (autour du do) Beatles, Hey Jude (orig. version) Beatles, Hey Jude (transformed version)

56 The SMIR Project: Structural Music Information Research Algebraic models Signal-based Music Information Retrieval Topological models Mathematical models Computational models Cognitive models Oleg Berg Structural Symbolic Music Information Research

57 Topological vs categorical construction of the Tonnetz Popoff A., C. Agon, M. Andreatta, A. Ehresmann (2016), «From K-Nets to PK-Nets: A Categorical Approach», PNM, 54(1) Popoff A., M. Andreatta, A. Ehresmann, «Relational PK-Nets for Transformational Music Analysis» (forthcoming in the JMM)

58 From K-Nets to category-based PK-Nets? Popoff A., M. Andreatta, A. Ehresmann, «A Categorical Generalization of Klumpenhouwer Networks», MCM 2015, Queen Mary University, Springer, p

Some cognitive implications of mathemusical research «La théorie des

macroscopique, et procède d étage en étage.

reprenant ellemême un principe constructeur présent dès le stade

Le style catégoriel qui est ainsi à l image d un aspect important de la

59 Some cognitive implications of mathemusical research «La théorie des catégories est une théorie des constructions mathématiques, qui est macroscopique, et procède d étage en étage. Elle est un bel exemple d abstraction réfléchissante, cette dernière reprenant ellemême un principe constructeur présent dès le stade sensorimoteur. Le style catégoriel qui est ainsi à l image d un aspect important de la genèse des facultés cognitives, est un style adéquat à la description de cette genèse» J. Piaget Jean Piaget, Gil Henriques et Edgar Ascher, Morphismes et Catégories. Comparer et transformer, 1990

60 THANK YOU FOR YOUR ATTENTION

Computational Musicology between scientific research and artistic practice

Computational Musicology between scientific research and artistic practice Collège Doctoral International Université de Strasbourg 23 January 2018 Moreno Andreatta Music Representations Team IRCAM/CNRS/UPMC