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 ...

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...

Abstract In this paper it is shown that interpretive canons are either constitutionally invalid because of the principles interpretation establishes, or a theory can be made to inconsistent: where says do p, then new canon say not-p. This called Canon Dilemma. Whichever horn dilemma taken as acceptable (accept invalidity possible inconsistency), shows cause more problems for theorising about th...

The relationship between music and geometry goes back thousands of years to the Greek quadrivium. Fractal structures have been explored in music and sound since at least 1978 (Gardner) and this work has recently been extended to specifically explore fractal structures in melodies (Mason and Saffle, 1994; Chesnut, 1996) and in musical forms and phrase structures (Solomon, 1998). Among the fracta...

Measurements of the human face as part of the body have been performed since the Greek era, and many aspects of ancient measurements can be found in modern clinical anthropometry. A historical appraisal of the use of facial measurements is presented. The influence on modern facial anthropometry of Greek proportion sciences, the golden proportion, canons of important Renaissance artists, physica...

This paper presents two fundamental arguments. Firstly, it is proposed that most of the currently-available systems development methodologies are founded on concepts which emerged in the period from about 1967 to 1977. This argument is presented through the use of literature references. The second argument is that the profile of the development environment now faced in organisations is very dif...