On Mathematical Functions for Theoretical and Experimental Distributions for Shrutis (Micro Tonal Intervals) and Their Application in Hindustani Music

TL;DR

This paper develops exact and generalized mathematical functions for modeling Shruti distributions in Hindustani music, demonstrating high conformity with experimental data and enhancing understanding of micro tonal intervals.

Contribution

It introduces a generalized mathematical function for Shrutis that closely matches experimental distributions, improving upon existing theoretical models.

Findings

Generalized function shows higher conformity with experimental data.

Exact functions formulated for three key theoretical Shruti distributions.

Enhanced modeling of micro tonal intervals in Hindustani music.

Abstract

In this work, exact mathematical functions have been formulated for three important theoretical Shruti (micro tonal interval) distributions, i.e. for Western Compilation, Deval, and Nagoji Row in Hindustani music. A generalized mathematical function for Shrutis has also been formulated. This generalized function shows a very high order of conformity with the experimentally derived Shruti distribution, than those of the theoretical Shruti distributions.