The Golden Mean and the Physics of Aesthetics

  • Subhash Kak


The golden mean, Φ, has been applied in diverse situations in art, architecture, and music, and although some have claimed that it represents a basic aesthetic proportion, others have argued that it is only one of a large number of such ratios. We review its early history, especially its relationship to Mount Meru of Piṅgala. We present multiplicative variants of Mount Meru that may explain why the octave of Indian music has 22 micronotes (śruti), a question that has perplexed musicologists for a long time. We also speculate on the neurophysiological basis behind the sense that the golden mean is a pleasing proportion. We conclude that perhaps aesthetic universals do not exist, and it is cultural authority and tradition that creates them, although they may be shaped by “universals” associated with our cognitive systems.


Fibonacci Number Golden Ratio Fibonacci Sequence Seventh Century Recurrence Sequence 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    Buenconsejo, José S. (ed.): A Search in Asia for a New Theory of Music. University of the Philippines, Centre for Ethnomusicology Publication, Quezon City (2003).Google Scholar
  2. 2.
    Burt, Warren: Developing and Composing with Scales Based on Recurrent Sequences. Proceedings ACMC (2002).
  3. 3.
    Cartwright, J. H., Gonzales, D. L., Pero, O. and Stanzial, D.: Aesthetics, Dynamics, and Musical Scales: A Golden Connection. Journal of New Music Research 31, 51–68 (2002).CrossRefGoogle Scholar
  4. 4.
    Clough, John, Douthett, Jack, Ramanathan, N., and Rowell, Lewis: Early Indian Heptatonic Scales Recent Diatonic Theory.Music Theory Spectrum 15, 36–58 (1993).CrossRefGoogle Scholar
  5. 5.
    Ingalls, Daniel, Masson, Jeffrey and Patwardhan, M. V. (tr.): The Dhvanyaloka of Anandavardhana with the Locana of Abhinavagupta. Harvard University Press, Cambridge (1990).Google Scholar
  6. 6.
    Kak, Subhash: Early Indian Music. In Buenconsejo (2003).
  7. 7.
    Kak, Subhash: Recursionism and Reality. Louisiana State University, Baton Rouge (2004).
  8. 8.
    Knuth, Donald E.: The Art of Computer Programming. Addison-Wesley, Reading, MA (2004).Google Scholar
  9. 9.
    Livio, Mario: The Golden Ratio: The Story of Phi. Broadway, New York (2002a).MATHGoogle Scholar
  10. 10.
    Livio, Mario: The Golden Ratio and Aesthetics. Plus Magazine, November (2002b).Google Scholar
  11. 11.
    Maceda, José: Introduction: A Search in Asia for a New Theory of Music. In Buenconsejo (2003).Google Scholar
  12. 12.
    McClain, Ernst: The Myth of Invariance. Nicolas Hayes, New York (1976).Google Scholar
  13. 13.
    Nooten, B. Van: Binary Numbers in Indian Antiquity. Journal of Indian Philosophy 21, 31–50 (1993).CrossRefGoogle Scholar
  14. 14.
    Singh, A. N.: On the Use of Series in Hindu Mathematics. Osiris, No. 1, 606–628 (1936).
  15. 15.
    Singh, Parmanand: The So-called Fibonacci Numbers in Ancient and Medieval India. Historia Mathematica 12, 229–244 (1985).MathSciNetMATHCrossRefGoogle Scholar
  16. 16.
    Weber, A.: Uber die Metrik de Inder. Harrwitz and Gofsmann, Berlin (1863).Google Scholar
  17. 17.
    Wilson, Ervin M.: The Scales of Mt. Meru. (1993).
  18. 18.
    Wilson, Ervin M.: Piṅgala’s Meru Prastara and the Sum of the Diagonals. (2001).
  19. 19.
    Zeising, Adolf: Neue Lehre von den Proportionen des menschlichen Korpers. (1854).Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  1. 1.Department of Computer scienceOklahoma State UniversityStillwaterUSA

Personalised recommendations