Tablatures for stringed instruments and generating functions

Authors:
Davide Baccherini;Donatella Merlini;Renzo Sprugnoli
Affiliations:
Dipartimento di Sistemi e Informatica, Firenze, Italia;Dipartimento di Sistemi e Informatica, Firenze, Italia;Dipartimento di Sistemi e Informatica, Firenze, Italia
Venue:
FUN'07 Proceedings of the 4th international conference on Fun with algorithms
Year:
2007

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Abstract

We study some combinatorial properties related to the problem of tablature for stringed instruments. First, we describe the problem in a formal way and prove that it is equivalent to a finite state automaton. We define the concepts of distance between two chords and tablature complexity in order to study the problem of tablature in terms of music performance. By using the Schützenberger methodology we are then able to find the generating function counting the number of tablatures having a certain complexity and we can study the average complexity for the tablatures of a music score.