strips, clocks and donughts: a journey through contemporary...
TRANSCRIPT
![Page 1: Strips, clocks and donughts: a journey through contemporary ...repmus.ircam.fr/_media/moreno/andreatta_padova_19-04...2018/04/19 · Strips, clocks and donughts: a journey through](https://reader033.vdocuments.net/reader033/viewer/2022051921/600e0418ba578c159c7736b4/html5/thumbnails/1.jpg)
Strips, clocks and donughts: a journey through contemporary
‘mathemusical’ research
Moreno AndreattaEquipe Représentations Musicales
IRCAM/CNRS/UPMC & IRMA/GREAM/USIAShttp://repmus.ircam.fr/moreno/smir
![Page 2: Strips, clocks and donughts: a journey through contemporary ...repmus.ircam.fr/_media/moreno/andreatta_padova_19-04...2018/04/19 · Strips, clocks and donughts: a journey through](https://reader033.vdocuments.net/reader033/viewer/2022051921/600e0418ba578c159c7736b4/html5/thumbnails/2.jpg)
www.ircam.fr
The musical and scientific research at IRCAM...
![Page 3: Strips, clocks and donughts: a journey through contemporary ...repmus.ircam.fr/_media/moreno/andreatta_padova_19-04...2018/04/19 · Strips, clocks and donughts: a journey through](https://reader033.vdocuments.net/reader033/viewer/2022051921/600e0418ba578c159c7736b4/html5/thumbnails/3.jpg)
OMAX (computer-aided impro)
MusiqueLab 2
www.ircam.fr
... at the interface between art and popular music
![Page 4: Strips, clocks and donughts: a journey through contemporary ...repmus.ircam.fr/_media/moreno/andreatta_padova_19-04...2018/04/19 · Strips, clocks and donughts: a journey through](https://reader033.vdocuments.net/reader033/viewer/2022051921/600e0418ba578c159c7736b4/html5/thumbnails/4.jpg)
The Society for Mathematics and Computation in MusicConferences:• 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)
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)
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)
Under reviewing…
![Page 5: Strips, clocks and donughts: a journey through contemporary ...repmus.ircam.fr/_media/moreno/andreatta_padova_19-04...2018/04/19 · Strips, clocks and donughts: a journey through](https://reader033.vdocuments.net/reader033/viewer/2022051921/600e0418ba578c159c7736b4/html5/thumbnails/5.jpg)
MUSIC
MATHEMATICS
musicalproblem
mathematicalstatement
generaltheoremgeneralization
musicanalysis
musictheory
composition
application
form
aliza
tion
COMPUTERSCIENCE
‘Mathemusical’ research at the interface of three disciplines
![Page 6: Strips, clocks and donughts: a journey through contemporary ...repmus.ircam.fr/_media/moreno/andreatta_padova_19-04...2018/04/19 · Strips, clocks and donughts: a journey through](https://reader033.vdocuments.net/reader033/viewer/2022051921/600e0418ba578c159c7736b4/html5/thumbnails/6.jpg)
1 1 1 1 1 1 1 1
1
1
1
1
11
1
1
2 2 2
2
2
2
2
2
2
22
2
A historical example of “mathemusical” problem
HexachordTheorem
HOMOMETRY
M. Babbitt
![Page 7: Strips, clocks and donughts: a journey through contemporary ...repmus.ircam.fr/_media/moreno/andreatta_padova_19-04...2018/04/19 · Strips, clocks and donughts: a journey through](https://reader033.vdocuments.net/reader033/viewer/2022051921/600e0418ba578c159c7736b4/html5/thumbnails/7.jpg)
Aperiodic Rhythmic Tiling Canons (Vuza Canons)
Dan Vuza
Anatol Vieru
![Page 8: Strips, clocks and donughts: a journey through contemporary ...repmus.ircam.fr/_media/moreno/andreatta_padova_19-04...2018/04/19 · Strips, clocks and donughts: a journey through](https://reader033.vdocuments.net/reader033/viewer/2022051921/600e0418ba578c159c7736b4/html5/thumbnails/8.jpg)
Set Theory, andTransformation Theory
Finite Difference Calculus
Diatonic Theory and ME-Sets Block-designs
Rhythmic TilingCanons
Z-Relation and Homometric Sets
A short catalogue of mathemusical problems
Neo-Riemannian Theoryand Spatial Computing
• 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
M. Andreatta : Mathematica est exercitium musicae, Habilitation Thesis, IRMA University of Strasbourg, 2010
![Page 9: Strips, clocks and donughts: a journey through contemporary ...repmus.ircam.fr/_media/moreno/andreatta_padova_19-04...2018/04/19 · Strips, clocks and donughts: a journey through](https://reader033.vdocuments.net/reader033/viewer/2022051921/600e0418ba578c159c7736b4/html5/thumbnails/9.jpg)
Set Theory, andTransformation Theory
Finite Difference Calculus
Diatonic Theory and ME-Sets
Rhythmic TilingCanons
Z-Relation and Homometric Sets
A short catalogue of mathemusical problems
Neo-Riemannian Theoryand Spatial Computing
• 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
M. Andreatta : Mathematica est exercitium musicae, Habilitation Thesis, IRMA University of Strasbourg, 2010
UNIVERSITA DEGLI STUDI DI PADOVA
Dipartimento di Matematica
Corso di Laurea Triennale in Matematica
Tesi di Laurea
ON SOME ALGEBRAIC ASPECTS OFANATOLVIERU PERIODIC SEQUENCES
APPLIED TO MUSIC CANONS
Relatore: Laureando:
Dott.ssa LUISA FIOROT NICOLO ANCELLOTTIMATRICOLA:1052827
ANNO ACCADEMICO 2014-20154 dicembre 2015
![Page 10: Strips, clocks and donughts: a journey through contemporary ...repmus.ircam.fr/_media/moreno/andreatta_padova_19-04...2018/04/19 · Strips, clocks and donughts: a journey through](https://reader033.vdocuments.net/reader033/viewer/2022051921/600e0418ba578c159c7736b4/html5/thumbnails/10.jpg)
The interplay between algebra and geometry in music
�Concerning music, it takes place in time, like algebra. In mathematics, there is this fundamental dualitybetween, on the one hand, geometry – whichcorresponds 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 whichhas its diabolical precision. [...] And one only perceivesthe development of algebra through music�(A. Connes).
è http://videotheque.cnrs.fr/
è http://agora2011.ircam.fr
![Page 11: Strips, clocks and donughts: a journey through contemporary ...repmus.ircam.fr/_media/moreno/andreatta_padova_19-04...2018/04/19 · Strips, clocks and donughts: a journey through](https://reader033.vdocuments.net/reader033/viewer/2022051921/600e0418ba578c159c7736b4/html5/thumbnails/11.jpg)
The galaxy of geometrical models at the service of music
![Page 12: Strips, clocks and donughts: a journey through contemporary ...repmus.ircam.fr/_media/moreno/andreatta_padova_19-04...2018/04/19 · Strips, clocks and donughts: a journey through](https://reader033.vdocuments.net/reader033/viewer/2022051921/600e0418ba578c159c7736b4/html5/thumbnails/12.jpg)
The galaxy of geometrical models at the service of music
![Page 13: Strips, clocks and donughts: a journey through contemporary ...repmus.ircam.fr/_media/moreno/andreatta_padova_19-04...2018/04/19 · Strips, clocks and donughts: a journey through](https://reader033.vdocuments.net/reader033/viewer/2022051921/600e0418ba578c159c7736b4/html5/thumbnails/13.jpg)
Do
Bach’s enigmatic canons and geometry
![Page 14: Strips, clocks and donughts: a journey through contemporary ...repmus.ircam.fr/_media/moreno/andreatta_padova_19-04...2018/04/19 · Strips, clocks and donughts: a journey through](https://reader033.vdocuments.net/reader033/viewer/2022051921/600e0418ba578c159c7736b4/html5/thumbnails/14.jpg)
…
My end is my beginning (but twisted!)
![Page 15: Strips, clocks and donughts: a journey through contemporary ...repmus.ircam.fr/_media/moreno/andreatta_padova_19-04...2018/04/19 · Strips, clocks and donughts: a journey through](https://reader033.vdocuments.net/reader033/viewer/2022051921/600e0418ba578c159c7736b4/html5/thumbnails/15.jpg)
http://www.josleys.com/Canon/Canon.html
![Page 16: Strips, clocks and donughts: a journey through contemporary ...repmus.ircam.fr/_media/moreno/andreatta_padova_19-04...2018/04/19 · Strips, clocks and donughts: a journey through](https://reader033.vdocuments.net/reader033/viewer/2022051921/600e0418ba578c159c7736b4/html5/thumbnails/16.jpg)
The galaxy of geometrical models at the service of music
![Page 17: Strips, clocks and donughts: a journey through contemporary ...repmus.ircam.fr/_media/moreno/andreatta_padova_19-04...2018/04/19 · Strips, clocks and donughts: a journey through](https://reader033.vdocuments.net/reader033/viewer/2022051921/600e0418ba578c159c7736b4/html5/thumbnails/17.jpg)
The galaxy of geometrical models at the service of music
![Page 18: Strips, clocks and donughts: a journey through contemporary ...repmus.ircam.fr/_media/moreno/andreatta_padova_19-04...2018/04/19 · Strips, clocks and donughts: a journey through](https://reader033.vdocuments.net/reader033/viewer/2022051921/600e0418ba578c159c7736b4/html5/thumbnails/18.jpg)
The galaxy of geometrical models at the service of music
![Page 19: Strips, clocks and donughts: a journey through contemporary ...repmus.ircam.fr/_media/moreno/andreatta_padova_19-04...2018/04/19 · Strips, clocks and donughts: a journey through](https://reader033.vdocuments.net/reader033/viewer/2022051921/600e0418ba578c159c7736b4/html5/thumbnails/19.jpg)
Euler and the Speculum musicum, 1773
Mersenne and the ‘musical clock’, 1648
Pythagoras and the monochord, VIth-Vth Century B.C.
I. Xenakis
Music and mathematics: « prima la musica »!
![Page 20: Strips, clocks and donughts: a journey through contemporary ...repmus.ircam.fr/_media/moreno/andreatta_padova_19-04...2018/04/19 · Strips, clocks and donughts: a journey through](https://reader033.vdocuments.net/reader033/viewer/2022051921/600e0418ba578c159c7736b4/html5/thumbnails/20.jpg)
do…
do# re# fa# sol# la#re mi fa sol la si
0 1 2 3 4 5 6 7 8 9 10 11 12
do…
Marin Mersenne
Harmonicorum Libri XII, 1648
The circular representation of the pitch space
do
re
mi
fasol
la
si0 1
2
3
45
678
9
1011
do#
re#
fa#
sol#
la#
![Page 21: Strips, clocks and donughts: a journey through contemporary ...repmus.ircam.fr/_media/moreno/andreatta_padova_19-04...2018/04/19 · Strips, clocks and donughts: a journey through](https://reader033.vdocuments.net/reader033/viewer/2022051921/600e0418ba578c159c7736b4/html5/thumbnails/21.jpg)
do…
do# re# fa# sol# la#re mi fa sol la si
0 1 2 3 4 5 6 7 8 9 10 11 12
do…
Marin Mersenne
Harmonicorum Libri XII, 1648
The circular representation of the pitch space
do
re
mi
fasol
la
si0 1
2
3
45
678
9
1011
do#
re#
fa#
sol#
la#
è DEMO
![Page 22: Strips, clocks and donughts: a journey through contemporary ...repmus.ircam.fr/_media/moreno/andreatta_padova_19-04...2018/04/19 · Strips, clocks and donughts: a journey through](https://reader033.vdocuments.net/reader033/viewer/2022051921/600e0418ba578c159c7736b4/html5/thumbnails/22.jpg)
Bembé
Abadja ou Bembé
Dinner Table Problem
C
D
E
FG
A
B
The circle: a model for periodic rhythms
12
![Page 23: Strips, clocks and donughts: a journey through contemporary ...repmus.ircam.fr/_media/moreno/andreatta_padova_19-04...2018/04/19 · Strips, clocks and donughts: a journey through](https://reader033.vdocuments.net/reader033/viewer/2022051921/600e0418ba578c159c7736b4/html5/thumbnails/23.jpg)
El cinquillo El trecillo
African-cuban ME-rhythms
8 8
![Page 24: Strips, clocks and donughts: a journey through contemporary ...repmus.ircam.fr/_media/moreno/andreatta_padova_19-04...2018/04/19 · Strips, clocks and donughts: a journey through](https://reader033.vdocuments.net/reader033/viewer/2022051921/600e0418ba578c159c7736b4/html5/thumbnails/24.jpg)
The geometry of African-Cuban rhythms
Z16
(3 3 4 3 3)
![Page 25: Strips, clocks and donughts: a journey through contemporary ...repmus.ircam.fr/_media/moreno/andreatta_padova_19-04...2018/04/19 · Strips, clocks and donughts: a journey through](https://reader033.vdocuments.net/reader033/viewer/2022051921/600e0418ba578c159c7736b4/html5/thumbnails/25.jpg)
Odditive property of orally-trasmitted practices
Simha Arom Marc Chemillier
(3 2 2 2 2 3 2 2 2 2 2)
Z24
![Page 26: Strips, clocks and donughts: a journey through contemporary ...repmus.ircam.fr/_media/moreno/andreatta_padova_19-04...2018/04/19 · Strips, clocks and donughts: a journey through](https://reader033.vdocuments.net/reader033/viewer/2022051921/600e0418ba578c159c7736b4/html5/thumbnails/26.jpg)
Olivier Messiaen’s non-invertible rhythms
Olivier Messaien
(3 2 2 2 2 3 2 2 2 2 2)
Alain Connes
![Page 27: Strips, clocks and donughts: a journey through contemporary ...repmus.ircam.fr/_media/moreno/andreatta_padova_19-04...2018/04/19 · Strips, clocks and donughts: a journey through](https://reader033.vdocuments.net/reader033/viewer/2022051921/600e0418ba578c159c7736b4/html5/thumbnails/27.jpg)
Palindromic structures in Steve Reich’s music
Clapping Music de Steve Reich (1972)
![Page 28: Strips, clocks and donughts: a journey through contemporary ...repmus.ircam.fr/_media/moreno/andreatta_padova_19-04...2018/04/19 · Strips, clocks and donughts: a journey through](https://reader033.vdocuments.net/reader033/viewer/2022051921/600e0418ba578c159c7736b4/html5/thumbnails/28.jpg)
Clapping Music (1972)
The circle and its ‘canonic’ rotations
![Page 29: Strips, clocks and donughts: a journey through contemporary ...repmus.ircam.fr/_media/moreno/andreatta_padova_19-04...2018/04/19 · Strips, clocks and donughts: a journey through](https://reader033.vdocuments.net/reader033/viewer/2022051921/600e0418ba578c159c7736b4/html5/thumbnails/29.jpg)
Clapping Music (1972)
Gerubach's Scrolling Score Project http://www.gerubach.com
The circle and its ‘canonic’ rotations
![Page 30: Strips, clocks and donughts: a journey through contemporary ...repmus.ircam.fr/_media/moreno/andreatta_padova_19-04...2018/04/19 · Strips, clocks and donughts: a journey through](https://reader033.vdocuments.net/reader033/viewer/2022051921/600e0418ba578c159c7736b4/html5/thumbnails/30.jpg)
Marin Mersenne, Harmonicorum Libri XII, 1648
Six Bagatelles (G. Ligeti, 1953)
do
mib
mi
sol
Permutational melodies in contemporary (art) music
![Page 31: Strips, clocks and donughts: a journey through contemporary ...repmus.ircam.fr/_media/moreno/andreatta_padova_19-04...2018/04/19 · Strips, clocks and donughts: a journey through](https://reader033.vdocuments.net/reader033/viewer/2022051921/600e0418ba578c159c7736b4/html5/thumbnails/31.jpg)
Se telefonando, 1966 (Maurizio Costanzo/Ennio Morricone) / Mina do#
fasol#
Ennio Morricone
Chord progression
F# B Bbm Ebm B C#
fa#
do#
sol#
fa#
sib
Chord progression
F# B Bbm Ebm B C#F# Ebm Bbm B C# F#
do
la
fa
sib
Chord progression
F# B Bbm Ebm B C#F# Ebm Bbm B C# F#Bb Eb Dm Gm Eb F
do
la
fa
sib
sol
Chord progression
F# B Bbm Ebm B C#F# Ebm Bbm B C# F#Bb Eb Dm Gm Eb FBb Gm Dm Gm Eb F BbDb = (C#)
Permutational melodies in song writing
(min. 0’53’’)
The harmonic space
![Page 32: Strips, clocks and donughts: a journey through contemporary ...repmus.ircam.fr/_media/moreno/andreatta_padova_19-04...2018/04/19 · Strips, clocks and donughts: a journey through](https://reader033.vdocuments.net/reader033/viewer/2022051921/600e0418ba578c159c7736b4/html5/thumbnails/32.jpg)
Speculum Musicum (1773)
Leonhard Euler è DEMO
The Tonnetz(Network of Tones)
![Page 33: Strips, clocks and donughts: a journey through contemporary ...repmus.ircam.fr/_media/moreno/andreatta_padova_19-04...2018/04/19 · Strips, clocks and donughts: a journey through](https://reader033.vdocuments.net/reader033/viewer/2022051921/600e0418ba578c159c7736b4/html5/thumbnails/33.jpg)
43
7
5
From the Tonnetz to the dual one (and vice-versa)
[Sonia Cannas, 2018]
![Page 34: Strips, clocks and donughts: a journey through contemporary ...repmus.ircam.fr/_media/moreno/andreatta_padova_19-04...2018/04/19 · Strips, clocks and donughts: a journey through](https://reader033.vdocuments.net/reader033/viewer/2022051921/600e0418ba578c159c7736b4/html5/thumbnails/34.jpg)
Gilles Baroin è www.mathemusic.net
![Page 35: Strips, clocks and donughts: a journey through contemporary ...repmus.ircam.fr/_media/moreno/andreatta_padova_19-04...2018/04/19 · Strips, clocks and donughts: a journey through](https://reader033.vdocuments.net/reader033/viewer/2022051921/600e0418ba578c159c7736b4/html5/thumbnails/35.jpg)
Axe de tierces mineures
The Tonnetz, its symmetries and its topological structure P
R LMinorthird axis
?
transposition
L = Leading Tone
P as parallel
R as relative
![Page 36: Strips, clocks and donughts: a journey through contemporary ...repmus.ircam.fr/_media/moreno/andreatta_padova_19-04...2018/04/19 · Strips, clocks and donughts: a journey through](https://reader033.vdocuments.net/reader033/viewer/2022051921/600e0418ba578c159c7736b4/html5/thumbnails/36.jpg)
Axe de tierces mineures
PR L
L = Leading Tone
P as parallel
R as relative
transposition
è Source: Wikipedia
Minorthird axis
The Tonnetz, its symmetries and its topological structure
![Page 37: Strips, clocks and donughts: a journey through contemporary ...repmus.ircam.fr/_media/moreno/andreatta_padova_19-04...2018/04/19 · Strips, clocks and donughts: a journey through](https://reader033.vdocuments.net/reader033/viewer/2022051921/600e0418ba578c159c7736b4/html5/thumbnails/37.jpg)
• Assembling chords related by some equivalence relation– Transposition/inversion: Dihedral group action on P(Zn)
…C
E
G
B
B�F#
C#
AF
KTI[3,4,5]
The Tonnetz as a simplicial complexL. Bigo, Représentation symboliques musicales et calcul spatial, PhD, Ircam / LACL, 2013
Intervallic structure major/minor triads
![Page 38: Strips, clocks and donughts: a journey through contemporary ...repmus.ircam.fr/_media/moreno/andreatta_padova_19-04...2018/04/19 · Strips, clocks and donughts: a journey through](https://reader033.vdocuments.net/reader033/viewer/2022051921/600e0418ba578c159c7736b4/html5/thumbnails/38.jpg)
• Complexes enumeration in the chromatic system
Classifying Chord ComplexesL. Bigo, Représentation symboliques musicales et calcul spatial, PhD, Ircam / LACL, 2013
CE
G
B
B�F#
C#
AF
ß0=1ß1=2ß2=1
![Page 39: Strips, clocks and donughts: a journey through contemporary ...repmus.ircam.fr/_media/moreno/andreatta_padova_19-04...2018/04/19 · Strips, clocks and donughts: a journey through](https://reader033.vdocuments.net/reader033/viewer/2022051921/600e0418ba578c159c7736b4/html5/thumbnails/39.jpg)
• The search of the optimal space
Classifying Chord ComplexesL. Bigo, Représentation symboliques musicales et calcul spatial, PhD, Ircam / LACL, 2013
C
E
G
B
(2,3,7) (3,4,5)
C
E
G
B
432 3
![Page 40: Strips, clocks and donughts: a journey through contemporary ...repmus.ircam.fr/_media/moreno/andreatta_padova_19-04...2018/04/19 · Strips, clocks and donughts: a journey through](https://reader033.vdocuments.net/reader033/viewer/2022051921/600e0418ba578c159c7736b4/html5/thumbnails/40.jpg)
• The search of the optimal space
Classifying Chord ComplexesL. Bigo, Représentation symboliques musicales et calcul spatial, PhD, Ircam / LACL, 2013
C
E
G
B
C
E
G
B
(2,3,7) (3,4,5)
![Page 41: Strips, clocks and donughts: a journey through contemporary ...repmus.ircam.fr/_media/moreno/andreatta_padova_19-04...2018/04/19 · Strips, clocks and donughts: a journey through](https://reader033.vdocuments.net/reader033/viewer/2022051921/600e0418ba578c159c7736b4/html5/thumbnails/41.jpg)
The panoply of Tonnetze at the service of the analyst
(1,1,10)
11
2
10
11
10
(2,1,9)
21
3
9
219
![Page 42: Strips, clocks and donughts: a journey through contemporary ...repmus.ircam.fr/_media/moreno/andreatta_padova_19-04...2018/04/19 · Strips, clocks and donughts: a journey through](https://reader033.vdocuments.net/reader033/viewer/2022051921/600e0418ba578c159c7736b4/html5/thumbnails/42.jpg)
The geometric character of musical logicJohann Sebastian Bach - BWV 328
Johann Sebastian Bach - BWV 328 random chords
K[1,1,1
0]
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
]0
0,25
0,5
2-co
mpa
ctne
ss
Schönberg - Pierrot Lunaire - Parodie
Schönberg - Pierrot Lunaire - Parodie random chords
K[1,1,1
0]
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
]0
0,25
0,5
2-co
mpa
ctne
ss
Claude Debussy - Voiles
Claude Debussy - Voiles random chords
K[1,1,1
0]
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
]0
0,25
0,5
2-co
mpa
ctne
ss
C
E
G
B
T[2,3,7] T[3,4,5]
2 33 4
Bigo L., M. Andreatta, « Musical analysis with simplicial chord spaces », in D. Meredith (ed.), Computational Music Analysis, Springer, 2015
![Page 43: Strips, clocks and donughts: a journey through contemporary ...repmus.ircam.fr/_media/moreno/andreatta_padova_19-04...2018/04/19 · Strips, clocks and donughts: a journey through](https://reader033.vdocuments.net/reader033/viewer/2022051921/600e0418ba578c159c7736b4/html5/thumbnails/43.jpg)
The musical style...is the space!3 2
![Page 44: Strips, clocks and donughts: a journey through contemporary ...repmus.ircam.fr/_media/moreno/andreatta_padova_19-04...2018/04/19 · Strips, clocks and donughts: a journey through](https://reader033.vdocuments.net/reader033/viewer/2022051921/600e0418ba578c159c7736b4/html5/thumbnails/44.jpg)
!
Lab Reb Sib Mib Si Mi Reb Fa# Re Sol Mi La Re Lab Reb Do Mib
Symmetries in Paolo Conte’s Madeleine
Almost total covering of the major-chords space
![Page 45: Strips, clocks and donughts: a journey through contemporary ...repmus.ircam.fr/_media/moreno/andreatta_padova_19-04...2018/04/19 · Strips, clocks and donughts: a journey through](https://reader033.vdocuments.net/reader033/viewer/2022051921/600e0418ba578c159c7736b4/html5/thumbnails/45.jpg)
Gilles Baroin è www.mathemusic.net
![Page 46: Strips, clocks and donughts: a journey through contemporary ...repmus.ircam.fr/_media/moreno/andreatta_padova_19-04...2018/04/19 · Strips, clocks and donughts: a journey through](https://reader033.vdocuments.net/reader033/viewer/2022051921/600e0418ba578c159c7736b4/html5/thumbnails/46.jpg)
Harmonic progressions as spatial trajectories
RL
è Source : https://upload.wikimedia.org/wikipedia/commons/6/67/TonnetzTorus.gif
![Page 47: Strips, clocks and donughts: a journey through contemporary ...repmus.ircam.fr/_media/moreno/andreatta_padova_19-04...2018/04/19 · Strips, clocks and donughts: a journey through](https://reader033.vdocuments.net/reader033/viewer/2022051921/600e0418ba578c159c7736b4/html5/thumbnails/47.jpg)
Gilles Baroin è www.mathemusic.net
![Page 48: Strips, clocks and donughts: a journey through contemporary ...repmus.ircam.fr/_media/moreno/andreatta_padova_19-04...2018/04/19 · Strips, clocks and donughts: a journey through](https://reader033.vdocuments.net/reader033/viewer/2022051921/600e0418ba578c159c7736b4/html5/thumbnails/48.jpg)
Reading Beethoven backwards
time
![Page 49: Strips, clocks and donughts: a journey through contemporary ...repmus.ircam.fr/_media/moreno/andreatta_padova_19-04...2018/04/19 · Strips, clocks and donughts: a journey through](https://reader033.vdocuments.net/reader033/viewer/2022051921/600e0418ba578c159c7736b4/html5/thumbnails/49.jpg)
The collection of 124 Hamiltonian Cycles
!
G. Albini & S. Antonini, University of Pavia, 2008
![Page 50: Strips, clocks and donughts: a journey through contemporary ...repmus.ircam.fr/_media/moreno/andreatta_padova_19-04...2018/04/19 · Strips, clocks and donughts: a journey through](https://reader033.vdocuments.net/reader033/viewer/2022051921/600e0418ba578c159c7736b4/html5/thumbnails/50.jpg)
Hamiltonian cycles with inner periodicityL 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 ...
RL
P
La sera non è più la tua canzone (Mario Luzi, 1945, in Poesie sparse)
La sera non è più la tua canzone,è questa roccia d’ombra traforatadai lumi e dalle voci senza fine,la quiete d’una cosa già pensata.
Ah questa luce viva e chiara vienesolo da te, sei tu così vicinaal vero d’una cosa conosciuta,per nome hai una parola ch’è passatanell’intimo del cuore e s’è perduta.
Caduto è più che un segno della vita,riposi, dal viaggio sei tornatadentro di te, sei scesa in questa purasostanza così tua, così romitanel silenzio dell’essere, (compiuta).
L’aria tace ed il tempo dietro a tesi leva come un’arida montagnadove vaga il tuo spirito e si perde,un vento raro scivola e ristagna.
http://www.mathemusic.netmin. 1’02’’
Music: M. AndreattaArrangement and mix: M. Bergomi & S. Geravini(Perfect Music Production)Mastering: A. Cutolo (Massive Arts Studio, Milan)
![Page 51: Strips, clocks and donughts: a journey through contemporary ...repmus.ircam.fr/_media/moreno/andreatta_padova_19-04...2018/04/19 · Strips, clocks and donughts: a journey through](https://reader033.vdocuments.net/reader033/viewer/2022051921/600e0418ba578c159c7736b4/html5/thumbnails/51.jpg)
Gilles Baroin è www.mathemusic.net
![Page 52: Strips, clocks and donughts: a journey through contemporary ...repmus.ircam.fr/_media/moreno/andreatta_padova_19-04...2018/04/19 · Strips, clocks and donughts: a journey through](https://reader033.vdocuments.net/reader033/viewer/2022051921/600e0418ba578c159c7736b4/html5/thumbnails/52.jpg)
The use of constraints in arts
Raymond QueneauIl castello dei destiniincrociati, 1969
Cent mille milliards de poèmes, 1961
Italo Calvino
La vie mode d’emploi,
Georges Perrec
OuLiPo (Ouvroir de Littérature Potentielle)
![Page 53: Strips, clocks and donughts: a journey through contemporary ...repmus.ircam.fr/_media/moreno/andreatta_padova_19-04...2018/04/19 · Strips, clocks and donughts: a journey through](https://reader033.vdocuments.net/reader033/viewer/2022051921/600e0418ba578c159c7736b4/html5/thumbnails/53.jpg)
Valentin Villenave Mike SolomonJean-François Piette
Martin Granger
Joseph Boisseau Moreno Andreatta Tom Johnson
http://oumupo.org/
From the OuLiPo to the OuMuPo (ouvroir de musique potentielle)
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
![Page 54: Strips, clocks and donughts: a journey through contemporary ...repmus.ircam.fr/_media/moreno/andreatta_padova_19-04...2018/04/19 · Strips, clocks and donughts: a journey through](https://reader033.vdocuments.net/reader033/viewer/2022051921/600e0418ba578c159c7736b4/html5/thumbnails/54.jpg)
èhttp://www.lacl.fr/~lbigo/hexachord
Keeping the space...but changing the trajectory!
![Page 55: Strips, clocks and donughts: a journey through contemporary ...repmus.ircam.fr/_media/moreno/andreatta_padova_19-04...2018/04/19 · Strips, clocks and donughts: a journey through](https://reader033.vdocuments.net/reader033/viewer/2022051921/600e0418ba578c159c7736b4/html5/thumbnails/55.jpg)
Rotation(autour du do)
Keeping the space...but changing the trajectory!
Beatles, Hey Jude (orig. version) Beatles, Hey Jude (transformed version)
![Page 56: Strips, clocks and donughts: a journey through contemporary ...repmus.ircam.fr/_media/moreno/andreatta_padova_19-04...2018/04/19 · Strips, clocks and donughts: a journey through](https://reader033.vdocuments.net/reader033/viewer/2022051921/600e0418ba578c159c7736b4/html5/thumbnails/56.jpg)
The SMIR Project: Structural Music Information Research
Structural Symbolic Music Information Researchhttp://repmus.ircam.fr/moreno/smir
Mathematicalmodels
Algebraicmodels
Topologicalmodels
Computational modelsCognitive models
Signal-basedMusic
InformationRetrieval
Oleg Berg
![Page 57: Strips, clocks and donughts: a journey through contemporary ...repmus.ircam.fr/_media/moreno/andreatta_padova_19-04...2018/04/19 · Strips, clocks and donughts: a journey through](https://reader033.vdocuments.net/reader033/viewer/2022051921/600e0418ba578c159c7736b4/html5/thumbnails/57.jpg)
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)
![Page 58: Strips, clocks and donughts: a journey through contemporary ...repmus.ircam.fr/_media/moreno/andreatta_padova_19-04...2018/04/19 · Strips, clocks and donughts: a journey through](https://reader033.vdocuments.net/reader033/viewer/2022051921/600e0418ba578c159c7736b4/html5/thumbnails/58.jpg)
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. 303-314
� �
![Page 59: Strips, clocks and donughts: a journey through contemporary ...repmus.ircam.fr/_media/moreno/andreatta_padova_19-04...2018/04/19 · Strips, clocks and donughts: a journey through](https://reader033.vdocuments.net/reader033/viewer/2022051921/600e0418ba578c159c7736b4/html5/thumbnails/59.jpg)
Some cognitive implications of mathemusical research
« La théorie des catégories est une théorie desconstructions mathématiques, qui est macroscopique, etprocède d’étage en étage. Elle est un bel exempled’abstraction réfléchissante, cette dernière reprenant elle-même un principe constructeur présent dès le stade sensori-moteur. Le style catégoriel qui est ainsi à l’image d’unaspect important de la genèse des facultés cognitives, est unstyle adéquat à la description de cette genèse »
J. Piaget
Jean Piaget, Gil Henriques et Edgar Ascher, Morphismes et Catégories. Comparer et transformer, 1990
![Page 60: Strips, clocks and donughts: a journey through contemporary ...repmus.ircam.fr/_media/moreno/andreatta_padova_19-04...2018/04/19 · Strips, clocks and donughts: a journey through](https://reader033.vdocuments.net/reader033/viewer/2022051921/600e0418ba578c159c7736b4/html5/thumbnails/60.jpg)
THANK YOU FOR YOUR ATTENTION