Combinatorics of words and morphisms in some pieces of Tom Johnson

Abstract

We survey several occurrences of combinatorics of words and morphisms in the pieces of Tom Johnson, showing in particular that some of the sequences of notes that he used intuitively can be interpreted or constructed through combinatorial objects such as morphisms. Furthermore some of these sequences have an independent interest in number theory and theoretical computer science.

Keywords:

• combinatorics on words
• morphisms
• creative process
• composition
• sequence (structural)
• form
• rhythm and meter

2010 Mathematics Subject Classification:

• 11B85
• 68R1

Acknowledgments

We would like to thank the referees for their suggestions which helped to improve this article. The first named author thanks É. Allouche for her remarks.

Disclosure statement

No potential conflict of interest was reported by the authors.