Graphical Abstract Figure
Graphical Abstract Figure
Close modal

Abstract

Music is a complex vibratory structure that evolves temporally and, while it has been studied for centuries, both quantitatively and qualitatively, it has seldom been studied under the lens of computer science and information theory. Further, while much research has been devoted to measuring and optimizing the acoustics of music venues, the computational ability of these spaces has never been explored. Using physical reservoir computing, this article presents an experimental verification that a music hall has computational ability. Two experimental setups are explored: one has a single speaker and information is sent sequentially and another has two speakers and information is sent simultaneously. Both of these exhibit qualitatively similar results. Thus, music might be, at least in part, a computational experience. The findings of this article could provide quantitative clues for the upper limit of tactus in music by considering the computational ability of the music hall. To the authors’ knowledge, this is the first time that a music hall has been utilized as a computational resource. Moreover, the computational ability of musical structures provides another tool to understand the complex relationship between music, vibrations, and human perception.

References

1.
London
,
J.
,
2004
,
Hearing in Time: Psychological Aspects of Musical Meter
,
Oxford University Press
,
New York
.
2.
Zatorre
,
R.
,
2005
, “
Music, the Food of Neuroscience?
,”
Nature
,
434
(
7031
), pp.
312
315
.
3.
Chan
,
A. S.
,
Ho
,
Y. -C.
, and
Cheung
,
M. -C.
,
1998
, “
Music Training Improves Verbal Memory
,”
Nature
,
396
(
6707
), pp.
128
128
.
4.
Zatorre
,
R. J.
,
Chen
,
J. L.
, and
Penhune
,
V. B.
,
2007
, “
When the Brain Plays Music: Auditory–Motor Interactions in Music Perception and Production
,”
Nat. Rev. Neurosci.
,
8
(
7
), pp.
547
558
.
5.
Koelsch
,
S.
,
Kasper
,
E.
,
Sammler
,
D.
,
Schulze
,
K.
,
Gunter
,
T.
, and
Friederici
,
A. D.
,
2004
, “
Music, Language and Meaning: Brain Signatures of Semantic Processing
,”
Nat. Neurosci.
,
7
(
3
), pp.
302
307
.
6.
Nakajima
,
K.
, and
Fischer
,
I.
,
2021
, “
Reservoir Computing
,” Springer, Singapore.
7.
Jaeger
,
H.
, and
Haas
,
H.
,
2004
, “
Harnessing Nonlinearity: Predicting Chaotic Systems and Saving Energy in Wireless Communication
,”
Science
,
304
(
5667
), pp.
78
80
.
8.
Lukoševičius
,
M.
, and
Jaeger
,
H.
,
2009
, “
Reservoir Computing Approaches to Recurrent Neural Network Training
,”
Comput. Sci. Rev.
,
3
(
3
), pp.
127
149
.
9.
Penkovsky
,
B.
,
Porte
,
X.
,
Jacquot
,
M.
,
Larger
,
L.
, and
Brunner
,
D.
,
2019
, “
Coupled Nonlinear Delay Systems as Deep Convolutional Neural Networks
,”
Phys. Rev. Lett.
,
123
(
5
), p.
054101
.
10.
Haynes
,
N. D.
,
Soriano
,
M. C.
,
Rosin
,
D. P.
,
Fischer
,
I.
, and
Gauthier
,
D. J.
,
2015
, “
Reservoir Computing With a Single Time-Delay Autonomous Boolean Node
,”
Phys. Rev. E
,
91
(
2
), p.
020801
.
11.
Appeltant
,
L.
,
Soriano
,
M. C.
,
Van der Sande
,
G.
,
Danckaert
,
J.
,
Massar
,
S.
,
Dambre
,
J.
,
Schrauwen
,
B.
,
Mirasso
,
C. R.
, and
Fischer
,
I.
,
2011
, “
Information Processing Using a Single Dynamical Node as Complex System
,”
Nat. Commun.
,
2
(
1
), pp.
1
6
.
12.
Shougat
,
M. R. E. U.
,
Li
,
X.
,
Mollik
,
T.
, and
Perkins
,
E.
,
2021
, “
A Hopf Physical Reservoir Computer
,”
Sci. Rep.
,
11
(
1
), pp.
1
13
.
13.
Shougat
,
M. R. E. U.
,
Li
,
X.
, and
Perkins
,
E.
,
2022
, “
Dynamic Effects on Reservoir Computing With a Hopf Oscillator
,”
Phys. Rev. E
,
105
(
4
), p.
044212
.
14.
Shougat
,
M. R. E. U.
,
Li
,
X.
,
Shao
,
S.
,
McGarvey
,
K.
, and
Perkins
,
E.
,
2023
, “
Hopf Physical Reservoir Computer for Reconfigurable Sound Recognition
,”
Sci. Rep.
,
13
(
1
), p.
8719
.
15.
Shougat
,
M. R. E. U.
,
Li
,
X.
,
Mollik
,
T.
, and
Perkins
,
E.
,
2021
, “
An Information Theoretic Study of a Duffing Oscillator Array Reservoir Computer
,”
ASME J. Comput. Nonlinear Dyn.
,
16
(
8
), p.
081004
.
16.
Nokkala
,
J.
,
Martínez-Peña
,
R.
,
Zambrini
,
R.
, and
Soriano
,
M. C.
,
2021
, “
High-Performance Reservoir Computing With Fluctuations in Linear Networks
,”
IEEE Trans. Neural Netw. Learn. Syst.
,
33
(
6
), pp.
2664
2675
.
17.
Shougat
,
M. R. E. U.
, and
Perkins
,
E.
,
2023
, “
The Van Der Pol Physical Reservoir Computer
,”
Neuromorphic Comput. Eng.
,
3
(
2
), p.
024004
.
18.
Moon
,
J.
,
Ma
,
W.
,
Shin
,
J. H.
,
Cai
,
F.
,
Du
,
C.
,
Lee
,
S. H.
, and
Lu
,
W. D.
,
2019
, “
Temporal Data Classification and Forecasting Using a Memristor-Based Reservoir Computing System
,”
Nat. Electron.
,
2
(
10
), pp.
480
487
.
19.
Ghosh
,
S.
,
Opala
,
A.
,
Matuszewski
,
M.
,
Paterek
,
T.
, and
Liew
,
T. C.
,
2020
, “
Reconstructing Quantum States With Quantum Reservoir Networks
,”
IEEE Trans. Neural Netw. Learn. Syst.
,
32
(
7
), pp.
3148
3155
.
20.
Mizrahi
,
A.
,
Hirtzlin
,
T.
,
Fukushima
,
A.
,
Kubota
,
H.
,
Yuasa
,
S.
,
Grollier
,
J.
, and
Querlioz
,
D.
,
2018
, “
Neural-Like Computing With Populations of Superparamagnetic Basis Functions
,”
Nat. Commun.
,
9
(
1
), pp.
1
11
.
21.
Grollier
,
J.
,
Querlioz
,
D.
,
Camsari
,
K.
,
Everschor-Sitte
,
K.
,
Fukami
,
S.
, and
Stiles
,
M. D.
,
2020
, “
Neuromorphic Spintronics
,”
Nat. Electron.
,
3
(
7
), pp.
360
370
.
22.
Larger
,
L.
,
Baylón-Fuentes
,
A.
,
Martinenghi
,
R.
,
Udaltsov
,
V. S.
,
Chembo
,
Y. K.
, and
Jacquot
,
M.
,
2017
, “
High-Speed Photonic Reservoir Computing Using a Time-Delay-Based Architecture: Million Words per Second Classification
,”
Phys. Rev. X
,
7
(
1
), p.
011015
.
23.
Barazani
,
B.
,
Dion
,
G.
,
Morissette
,
J.-F.
,
Beaudoin
,
L.
, and
Sylvestre
,
J.
,
2020
, “
Microfabricated Neuroaccelerometer: Integrating Sensing and Reservoir Computing in MEMS
,”
J. Microelectromech. Syst.
,
29
(
3
), pp.
338
347
.
24.
Shougat
,
M. R. E. U.
,
Kennedy
,
S.
, and
Perkins
,
E.
,
2023
, “
A Self-Sensing Shape Memory Alloy Actuator Physical Reservoir Computer
,”
IEEE Sens. Lett.
,
7
(
5
), pp.
1
4
.
25.
Kan
,
S.
,
Nakajima
,
K.
,
Takeshima
,
Y.
,
Asai
,
T.
,
Kuwahara
,
Y.
, and
Akai-Kasaya
,
M.
,
2021
, “
Simple Reservoir Computing Capitalizing on the Nonlinear Response of Materials: Theory and Physical Implementations
,”
Phys. Rev. Appl.
,
15
(
2
), p.
024030
.
26.
Ma
,
S.
,
Antonsen
,
T. M.
,
Anlage
,
S. M.
, and
Ott
,
E.
,
2022
, “
Short-Wavelength Reverberant Wave Systems for Physical Realization of Reservoir Computing
,”
Phys. Rev. Res.
,
4
(
2
), p.
023167
.
27.
Fernando
,
C.
, and
Sojakka
,
S.
,
2003
, “
Pattern Recognition in a Bucket
,”
European Conference on Artificial Life
,
Dortmund, Germany
,
Sept. 14–17
,
Springer
, pp.
588
597
.
28.
Shougat
,
M. R. E. U.
,
Li
,
X.
, and
Perkins
,
E.
,
2024
, “
Multiplex-Free Physical Reservoir Computing With an Adaptive Oscillator
,”
Phys. Rev. E
,
109
(
2
), p.
024203
.
29.
Shougat
,
M. R. E. U.
,
Li
,
X.
, and
Perkins
,
E.
,
2024
, “
Self-Learning Physical Reservoir Computer
,”
Phys. Rev. E
,
109
(
6
), p.
064205
.
30.
Lee
,
R. H.
,
Mulder
,
E. A.
, and
Hopkins
,
J. B.
,
2022
, “
Mechanical Neural Networks: Architected Materials That Learn Behaviors
,”
Sci. Robot.
,
7
(
71
), p.
eabq7278
.
31.
Weng
,
J.
,
Ding
,
Y.
,
Hu
,
C.
,
Zhu
,
X.-F.
,
Liang
,
B.
,
Yang
,
J.
, and
Cheng
,
J.
,
2020
, “
Meta-Neural-Network for Real-Time and Passive Deep-Learning-Based Object Recognition
,”
Nat. Commun.
,
11
(
1
), p.
6309
.
32.
Moghaddaszadeh
,
M.
,
Mousa
,
M.
,
Aref
,
A.
, and
Nouh
,
M.
,
2024
, “
Mechanical Intelligence via Fully Reconfigurable Elastic Neuromorphic Metasurfaces
,”
APL Mater.
,
12
(
5
), pp.
051117
051121
.
33.
Garrett
,
S. L.
,
2020
,
Understanding Acoustics: An Experimentalist’s View of Sound and Vibration
,
Springer Nature
,
Cham, Switzerland
.
34.
Crighton
,
D. G.
,
1979
, “
Model Equations of Nonlinear Acoustics
,”
Annu. Rev. Fluid Mech.
,
11
, pp.
11
33
.
35.
Long
,
M.
,
2005
,
Architectural Acoustics
,
Elsevier
,
Burlington, MA
.
36.
Cucchi
,
M.
,
Abreu
,
S.
,
Ciccone
,
G.
,
Brunner
,
D.
, and
Kleemann
,
H.
,
2022
, “
Hands-On Reservoir Computing: A Tutorial for Practical Implementation
,”
Neuromorphic Comput. Eng.
,
2
(
3
), p.
032002
.
37.
Shannon
,
C. E.
,
1948
, “
A Mathematical Theory of Communication
,”
Bell Syst. Tech. J.
,
27
(
3
), pp.
379
423
.
38.
DeFord
,
R. I.
,
2015
,
Tactus, Mensuration and Rhythm in Renaissance Music
,
Cambridge University Press
,
Cornwall, UK
.
39.
Normann
,
T. F.
,
1953
, “
Rhythm and Tempo: A Study in Music History
,”
J. Res. Music Educ.
,
1
(
2
), pp.
143
145
.
You do not currently have access to this content.