Related papers: Dynamical systems, celestial mechanics, and music:…
We show that, when music pieces are cast in the form of time series of pitch variations, the concepts and tools of dynamical systems theory can be applied to the analysis of {\it temporal dynamics} in music. (i) Phase space portraits are…
The complex planetary synchronization structure of the solar system, which since Pythagoras of Samos (ca. 570-495 BC) is known as the music of the spheres, is briefly reviewed from the Renaissance up to contemporary research. Copernicus'…
The collaboration of mathematics in the two musical systems of Pythagorean sounds and of equal sounds is evident and opportune for generating the elements and managing their relationships. The only essential notion for a rational…
To many people, music is a mystery. It is uniquely human, because no other species produces elaborate, well organized sound for no particular reason. It has been part of every known civilization on earth. It has become a very part of man's…
A new musical scale devised by the author, based on natural logarithms, is described. Most of the logarithmic pitches bear no correspondence to the twelve tones of the ancient tuning system attributed to Pythagoras, based on ratios of whole…
The concept of complexity as considered in terms of its algorithmic definition proposed by G.J. Chaitin and A.N. Kolmogorov is revisited for the dynamical complexity of music. When music pieces are cast in the form of time series of pitch…
Scientists often think of the world (or some part of it) as a dynamical system, a stochastic process, or a generalization of such a system. Prominent examples of systems are (i) the system of planets orbiting the sun or any other classical…
Two and a half millennia ago Pythagoras initiated the scientific study of the pitch of sounds; yet our understanding of the mechanisms of pitch perception remains incomplete. Physical models of pitch perception try to explain from…
The novel proposal to invoke the split of the Ricci scalar into bulk and boundary terms in the gravitational action, opens up a new avenue of investigation into stellar dynamics. The Lagrangian contains functional forms of the bulk term…
It has been shown that the great ancient Pythagorean ideas have found themselves in the latest researches in high energy elementary particles and nuclear physics. In this respect we concern and discuss the mathematical, physical and…
Dynamical systems are abstract models of interaction between space and time. They are often used in fields such as physics and engineering to understand complex processes, but due to their general nature, they have found applications for…
Cosmology is a well established research area in physics while dynamical systems are well established in mathematics. It turns out that dynamical system techniques are very well suited to study many aspects of cosmology. The aim of this…
Dynamic systems have found their use in sound synthesis as well as score synthesis. These levels can be integrated in monolithic autonomous systems in a novel approach to algorithmic composition that shares certain aesthetic motivations…
Dark energy is one of the deepest puzzles in modern cosmology, and mounting evidence suggests that it is not just a cosmological constant but a genuinely dynamical component. Although cosmology and dynamical systems theory emerged from…
The development of a mathematics for living systems is one of the most challenging prospects of this century. The search began with the pioneering contribution of Ilia Prigogine, who developed methods from statistical physics to describe…
We propose the use of specific dynamical processes and more in general of ideas from Physics to model the evolution in time of musical structures. We apply this approach to two \'Etudes by F. Chopin, namely op.10 n.3 and op.25 n.1,…
The synchronization between two dynamical systems is one of the most appealing phenomena occurring in Nature. Already observed by Huygens in the case of two pendula, it is a current area of research in the case of chaotic systems, with…
The Nobel Prize winning confirmation in 1998 of the accelerated expansion of our Universe put into sharp focus the need of a consistent theoretical model to explain the origin of this acceleration. As a result over the past two decades…
The concept of time series irreversibility -- the degree by which the statistics of signals are not invariant under time reversal -- naturally appears in non-equilibrium physics in stationary systems which operate away from equilibrium and…
Orbital systems are often self-organized and/or characterized by harmonic relations. Inspired by music theory, we rewrite the Geddes and King-Hele (QJRAS, 24, 10-13, 1983) equations for mirror symmetries among the distances of the planets…