相关论文: Fractals in Africanist Music

Choreographer Reggie Wilson and mathematician Jesse Wolfson describe interactions of math and dance emerging from their 12+ year engagement with Black movement and music traditions as part of Wilson's…

If our aesthetic preferences are affected by fractal geometry of nature, scaling regularities would be expected to appear in all art forms, including music. While a variety of statistical tools have been proposed to analyze time series in…

In this paper we have defined one function that has been used to construct different fractals having fractal dimensions between 1.58 and 2. Also, we tried to calculate the amount of increment of fractal dimension in accordance with the base…

Music is a string of some of the notes out of 12 notes (Sa, Komal_re, Re, Komal_ga, Ga, Ma, Kari_ma, Pa, Komal_dha, Dha, Komal_ni, Ni) and their harmonics. Each note corresponds to a particular frequency. When such strings are encoded to…

Our main goal in this long survey article is to provide an overview of the theory of complex fractal dimensions and of the associated geometric or fractal zeta functions, first in the case of fractal strings (one-dimensional drums with…

We analyze the fractal dimension of melodic contours and pitch time series of classical music and folk music tunes. The fractal dimensions obtained from box counting and detrended fluctuation analysis show significant differences. They are…

The relationship between musical material and physical phenomena has become a topic in the musicological literature over the last several decades, particularly concerning elements of the musical system itself, and constructions found in the…

We present an overview of a theory of complex dimensions of self-similar fractal strings, and compare this theory to the theory of varieties over a finite field from the geometric and the dynamical point of view. Then we combine the several…

This is a brief introduction to fractals, multifractals and wavelets in an accessible way, in order that the founding ideas of those strange and intriguing newcomers to science as fractals may be communicated to a wider public. Fractals are…

This work is an analytical and numerical study of the composition of several fractals into one and of the relation between the composite dimension and the dimensions of the component fractals. In the case of composition of standard IFS with…

This paper is devoted to the mechanics of fractal materials. A continuum framework accounting for the topological and metric properties of fractal domains in heterogeneous media is developed. The kinematics of deformations is elucidated and…

The abstraction of musical structures (notes, melodies, chords, harmonic or rhythmic progressions, etc.) as mathematical objects in a geometrical space is one of the great accomplishments of contemporary music theory. Building on this…

Urbanization is a phenomenon of concern for planning and public health: projections are difficult because of policy changes and natural events, and indicators are multiple. There are previous studies of development that used fractals, but…

Multifractal analysis techniques are applied to patterns in several abstract expressionist artworks, paintined by various artists. The analysis is carried out on two distinct types of structures: the physical patterns formed by a specific…

Structure is one of the most essential aspects of music, and music structure is commonly indicated through repetition. However, the nature of repetition and structure in music is still not well understood, especially in the context of music…

We consider fractures in a stratified composite material with solid layers separated by thin slices of extremely soft matter. Viscoelastic effects associated with the soft layers are taken into account via the simplest model for weakly…

The propagation of elastic waves in a fractured rock is investigated, both theoretically and numerically. Outside the fractures, the propagation of compressional waves is described in the simple framework of one-dimensional linear…

In this paper, first musical compositions are presented, which are created using the mathematical counterpoint theory of Guerino Mazzola and his collaborators. These compositions also use the RUBATO(R) software's components for counterpoint…

Real-space singularities underpin diverse wave phenomena yet remain largely unexplored in elastic wave systems. We report the observation of real-space topological singularities in structured flexural waves on finite-sized solids. These…

In this paper we consider extensions of the gradient elasticity models proposed earlier by the second author to describe materials with fractional non-locality and fractality using the techniques developed recently by the first author. We…