Sturmian Canons
نویسنده
چکیده
Sturmian words are balanced, almost periodic, self-similar and hierarchical infinite sequences that have been studied in music theory in connection with diatonic scale theory and related subjects.[3][5] Carey and Camplitt 1996 give a brief but suggestive rhythmic example in which these properties are made manifest in a particularly visceral manner. The present paper expands upon this example, considering the properties of canons based on Sturmian words, or Sturmian canons. In particular, a Sturmian word of irrational slope a with a hierarchical periodicity of p gives rise to p-tuple canons, the voices and relations of which are determined by the terms of the continued fraction expansion of a.
منابع مشابه
Are Neoclassical Canons Valid for Southern Chinese Faces?
BACKGROUND Proportions derived from neoclassical canons, initially described by Renaissance sculptors and painters, are still being employed as aesthetic guidelines during the clinical assessment of the facial morphology. OBJECTIVE 1. to determine the applicability of neoclassical canons for Southern Chinese faces and 2. to explore gender differences in relation to the applicability of the ne...
متن کاملModulus 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...
متن کاملA Characterization of Bispecial Sturmian Words
A finite Sturmian word w over the alphabet {a, b} is left special (resp. right special) if aw and bw (resp. wa and wb) are both Sturmian words. A bispecial Sturmian word is a Sturmian word that is both left and right special. We show as a main result that bispecial Sturmian words are exactly the maximal internal factors of Christoffel words, that are words coding the digital approximations of s...
متن کاملJ.S. Mill’s Canons of Induction: from True Causes to Provisional Ones
In this essay, my aim is twofold: to clarify how the late Mill conceived of the certainty of inductive generalizations and to offer a systematic clarification of the limited domain of application of the Mill’s Canons of Induction. I shall argue that Mill’s views on the certainty of knowledge changed overtime and that this change was accompanied by a new view on the certainty of the inductive re...
متن کاملA First Investigation of Sturmian Trees
We consider Sturmian trees as a natural generalization of Sturmian words. A Sturmian tree is a tree having n+1 distinct subtrees of height n for each n. As for the case of words, Sturmian trees are irrational trees of minimal complexity. We give various examples of Sturmian trees, and we characterize one family of Sturmian trees by means of a structural property of their automata.
متن کامل