Mental Reality

Guerino Mazzola, Maria Mannone, Yan Pang, Margaret O’Brien, Nathan T Torunsky

Research output: Chapter in Book/Report/Conference proceedingChapter


We have seen how music lives in the physical reality and in the mechanisms of human perception and emotion. In this chapter, we will discuss how music lives in the symbolic dimension of score notation, the tuning spaces, and their mathematical symmetries for harmony and counterpoint.

Original languageEnglish (US)
Title of host publicationComputational Music Science
PublisherSpringer Nature
Number of pages8
StatePublished - 2016

Publication series

NameComputational Music Science
ISSN (Print)1868-0305
ISSN (Electronic)1868-0313

Bibliographical note

Funding Information:
Although music was understood as a symbolic field since the Pythagorean tradition in ancient Greece, the French philosopher René Descartes (Figure 5.1) claimed that music needs a psychological foundation. In his compendium musicae (1618) [14], he explains eight fundamental rules for making and understanding music, such as “music must be simple to please the soul.” In recent times, the mental reality of music has been rediscovered, and has been supported by the work of mathematician Leonhard Euler. In this chapter, we will discuss the mental reality of music that complements (and sometimes contradicts) physical and psychological aspects.

Publisher Copyright:
© 2016, Springer International Publishing AG.


  • Chromatic Scale
  • Euler Space
  • Hide Symmetry
  • Musical Score
  • Symbolic Dimension


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