Corpus ID: 16114176

# THE MATHEMATICS OF PER NØRGÅRD ’ S RHYTHMIC INFINITY SYSTEM

```@inproceedings{Shallit2002THEMO,
title={THE MATHEMATICS OF PER N{\O}RG{\AA}RD ’ S RHYTHMIC INFINITY SYSTEM},
author={Jeffrey Shallit},
year={2002}
}```
The Danish composer Per Nørg̊ard (1932–) invented a procedure for generating rhythms which was described by Erling Kullberg . Reworded in mathematical notation, this procedure is as follows: Let the Fibonacci numbers (Fn)n≥0 be defined as usual by F0 = 0, F1 = 1, and Fn = Fn−1 + Fn−2. Starting with the pair (c0, c1) = (F2n, F2n+1), perform the following operation n− 2 times: • If a number Fi appears in an even-indexed position, replace it with (Fi−2, Fi−1) • If a number Fi appears in an odd… Expand
5 Citations
THE FIBONACCI QUARTERLY
By Zeckendorf’s theorem, an equivalent definition of the Fibonacci sequence (appropriately normalized) is that it is the unique sequence of increasing integers such that every positive number can beExpand
Volume Index
ALLADI, KRISHNASWAMI. "A Farey Sequence of Fibonacci Numbers," Vol. 13, No. 1, pp. 1-10. "A Rapid Method to Form Farey Fibonacci Fractions," Vol. 13, No. 1,p. 31. "Generalized Fibonacci Tiling," Vol.Expand
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