Fractal String Generation and Its Application in Music Composition

TL;DR

This paper explores generating fractal strings using logistic maps to model Indian classical ragas and applies correlation-based methods to compose music resembling specific ragas, emphasizing the fractal nature of musical sequences.

Contribution

It introduces a novel approach to generate and analyze musical sequences as fractal strings using logistic maps and correlation measures for raga-based music composition.

Findings

Generated discrete sequences with controlled amplitude levels.

Identified close relatives of ragas using correlation coefficients.

Demonstrated the fractal nature of musical strings through fractal dimension analysis.

Abstract

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 form discrete sequences, different frequencies present in the music corresponds to different amplitude levels (value) of the discrete sequence. Initially, a class of discrete sequences has been generated using logistic map. All these discrete sequences have at most n-different amplitude levels (value) (depending on the particular raga). Without loss of generality, we have chosen two discrete sequences of two types of Indian raga viz. Bhairabi and Bhupali having same number of amplitude levels to obtain/search close relatives from the class. The relative / closeness can be assured through correlation coefficient.The search is unbiased, random and non-adaptive. The obtained string is that which maximally resembles the given two sequences. The same can be thought of as a music composition of the given two strings. It is to be noted that all these string are fractal string which can be persuaded by fractal dimension.