Generalized Fibonacci Numbers and Music


  • Anthony G Shannon Emeritus Professor, University of Technology Sydney, NSW 2007
  • Irina Klamka
  • Robert van Gend



Fibonacci numbers, golden ratio, Simson's identity, Binet formula


Mathematics and music have well documented historical connections. Just as the ordinary Fibonacci numbers have links with the golden ratio, this paper considers generalized Fibonacci numbers developed from generalizations of the golden ratio. It is well known that the Fibonacci sequence of numbers underlie certain musical intervals and compositions but to what extent are these connections accidental or structural, coincidental or natural and do generalized Fibonacci numbers share any of these connections?


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How to Cite

Shannon, A. G., Klamka, I., & Gend, R. van. (2018). Generalized Fibonacci Numbers and Music. JOURNAL OF ADVANCES IN MATHEMATICS, 14(1), 7564–7579.