相关论文: Fractal String Generation and Its Application in M…

We study a periodic vibrating string composed of a finite sequence of string segments connected periodically, with each segment characterized by a constant linear mass density. The main purpose is to provide a configuration that can mimic…

We present an algebraic construction of music notes and show how to associate them inseveral ways to construct music ranges. Then a family of ranges emerge with a fixed number of notes: two, three, five, seven, twelve, seventeen, etc. A…

In this work we perform a fractal analysis of 160 pieces of music belonging to six different genres. We show that the majority of the pieces reveal characteristics that allow us to classify them as physical processes called the 1/f (pink)…

Spurred by the potential of deep learning, computational music generation has gained renewed academic interest. A crucial issue in music generation is that of user control, especially in scenarios where the music generation process is…

Often, I hear a piece of music and wonder what the name of the piece is. Indeed, there are applications such as Shazam app that provides music matching. However, the limitations of those apps are that the same piece performed by the same…

For a Borel measure on the unit interval and a sequence of scales that tend to zero, we define a one-parameter family of zeta functions called multifractal zeta functions. These functions are a first attempt to associate a zeta function to…

Musical frequencies in Just Intonation are comprised of rational numbers. The structure of rational numbers is determined by prime factorisations. Just Intonation frequencies can be split into two components. The larger component uses only…

The works of Rabindranath Tagore have been sung by various artistes over generations spanning over almost 100 years. there are few songs which were popular in the early years and have been able to retain their popularity over the years…

The term fractal refers to the fractional dimensions that have recursive nature and exhibit better array factor properties. In this article, we present a new class of sparse array where the recursive nature of a fractal can be used in…

This paper focuses on the modeling of musical melodies as networks. Notes of a melody can be treated as nodes of a network. Connections are created whenever notes are played in sequence. We analyze some main tracks coming from different…

The mathematics of musical intervals and scales has been extensively studied. Vastly simplified, our ears seem to prefer intervals whose frequency ratios have small numerator and denominator, such as 2:1 (octave), 3:2 (perfect fifth), 4:3…

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…

This paper presents an attempt to study the aesthetics of North Indian Khayal music with reference to the flexibility exercised by artists in performing popular compositions. We study expressive timing and pitch variations of the given…

A combination of three or more tones played together is called a chord. In the chromatic scale, chords which are consonant are of particular interest and can be divided into several groups, two main ones being the major and minor chords.…

A recitation is a way of combining the words together so that they have a sense of rhythm and thus an emotional content is imbibed within. In this study we envisaged to answer these questions in a scientific manner taking into consideration…

Correlations in music that exist within its waveform are studied. Monophonic wave files of random music are generated and the probability distribution function of time interval between large signal values is analyzed. A power law behavior…

Raga identification is an important problem within the domain of Indian Art music, as Ragas are fundamental to its composition and performance, playing a crucial role in music retrieval, preservation, and education. Few studies that have…

This paper reports a preliminary study on quantitative frequency domain rhythm cues for classifying five Indian languages: Bengali, Kannada, Malayalam, Marathi, and Tamil. We employ rhythm formant (R-formants) analysis, a technique…

The statistical precision of a chord method for estimating fractal dimension from a correlation integral is derived. The optimal chord length is determined, and a comparison is made to other estimators. These calculations use the…

Symbolic music generation has attracted increasing attention, while most methods focus on generating short piece (mostly less than 8 bars, and up to 32 bars). Generating long music calls for effective expression of the coherent music…