The Harmonic Aspect

Guerino Mazzola, Joomi Park, Florian Thalmann

Research output: Chapter in Book/Report/Conference proceedingChapter


Harmony is a magic word in music theory and practice. It is not only a technical term but also refers to more transcendental layers of existence. In ancient Greece, harmony was the ultimate ground of the universe. In Pythagorean philosophy, the ultimate formula of the universe was their tetractys, a triangular arrangement of ten points starting at the base with 4, then 3, then 2, then 1 on top. You have already seen in the previous chapter on intervals that the successive ratios of these triangular numbers—2/1, 3/2, 4/3—are the intervals of an octave, perfect fifth, and perfect fourth. So the tetractys was the universal law behind both music and the universe. This formula was an expression of harmony since these intervals were considered to be particularly agreeable, or “consonant,” as music theorist call them. In opposition to consonant intervals, they speak of “dissonant” intervals; for example, the minor second or the tritone are dissonant and sound less agreeable to many persons—but not all. We come back to these interval qualities in tutorial 11 about counterpoint.

Original languageEnglish (US)
Title of host publicationComputational Music Science
PublisherSpringer Nature
Number of pages10
StatePublished - 2011

Publication series

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

Bibliographical note

Publisher Copyright:
© 2011, Springer-Verlag Berlin Heidelberg.


  • Harmonic Function
  • Magic Word
  • Music Theory
  • Musical Object
  • Traditional Music


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