A SAT Encoding to Compute Aperiodic Tiling Rhythmic Canons

Constructing and Formalizing Tiling Rhythmic Canons: a Historical Survey of a “mathemusical” Problem

Asymmetric Rhythms and Tiling Canons

A musical rhythm pattern is a sequence of note onsets. We consider repeating rhythm patterns, called rhythm cycles. Many typical rhythm cycles from Africa are asymmetric, meaning that they cannot be broken into two parts of equal duration. More precisely: if a rhythm cycle has a period of 2n beats, it is asymmetric if positions x and x + n do not both contain a note onset. We ask the questions ...

Rhythmic canons and Galois theory

The study of rhythmic canons by mathematicians with musical interest has given rise to unexpected connections to non trivial mathematical problems. The author tried a new approach based on a Galoisian interpretation of the novel results and concepts of Coven and Meyerowitz [4]. Extending this in a second part to finite fields, he concludes with unexpected results. 1 Rhythmic canons, tiling the ...

Why rhythmic canons are interesting

The subject of rhythmic canons has been revivified by new concepts, coming from the field of music composition. The present article is a survey of the mathematical knowledge in this field, from the 1950’s to state of the art results. 1 What is this all about ? Paving the way 1.1 Rhythmic canons and tiling I was introduced to the fascinating subject of rhythmic canons by people working at the Ir...

Modulus p Rhythmic Tiling Canons and some implementations in Open Music visual programming language

The concept of rhythmic canons, as it has been introduced by mathematician Dan Vuza in the 1990s, is the art of filling the time axis with some finite rhythmic patterns and their translations, without onsets superposition. The musical notion have been linked with some mathematical results, and since then, its mathematical study has always followed a will of picturing every new results in the vi...