Mathematical Physics


Nonlinearity, Entropy and Chaos in Music

Authors: Sai Venkatesh Balasubramanian

This article explores the nonlinear aspects underlying music , particularly focusing on melody. By using the concept of scale as the basis, the article explores ways to formulate and study the features and 'feature richness' of a given melody or Raga, and to do this, the Raga scale is represented as a 1-Dimensional array. The Signature graph of a Raga plotted as Interval as a function of Note position, established a graphic visualization of the Raga. The progression and trend of intervals was computed using the Second Level Interval Array. This trend graph reveals the complexity in a Raga structure, through looping, crowded and intricate curves in the graph. Next, the concept of chaos in the context of melody is explored, fundamentally by performing a sensitivity test, which analyzes that given a Raga, and a particular evolution path, how starting at two nearby Swaras results in two entirely different ending Swaras, when sampled after a certain period in time. As a measure of the complexity in a Raga, the entropy, a measure of uncertainty is proposed, and computed using the interval arrays as bases for an occurrence array yielding empirical probabilities. The entropy is seen as a measure of richness, a measure of variety of inter-Swara intervals that a given Raga possesses. One notes that Ragas with high entropy, on account of their interval richness, usually fall under the category of pleasant, appealing and melodious Ragas. These are also the Ragas one finds being employed in film music, clearly owing to their pleasant feel.

Comments: 11 Pages.

Download: PDF

Submission history

[v1] 2017-05-22 05:15:16

Unique-IP document downloads: 42 times is a pre-print repository rather than a journal. Articles hosted may not yet have been verified by peer-review and should be treated as preliminary. In particular, anything that appears to include financial or legal advice or proposed medical treatments should be treated with due caution. will not be responsible for any consequences of actions that result from any form of use of any documents on this website.

Add your own feedback and questions here:
You are equally welcome to be positive or negative about any paper but please be polite. If you are being critical you must mention at least one specific error, otherwise your comment will be deleted as unhelpful.

comments powered by Disqus