Symmetric Scale

For scale symmetry, see Symmetry#Scale symmetry and fractals.

In music, a symmetric scale is a music scale which equally divides the octave.[1] The concept and term appears to have been introduced by Joseph Schillinger[1] and further developed by Nicolas Slonimsky as part of his famous "Thesaurus of Scales and Melodic Patterns". In twelve-tone equal temperament, the octave can only be equally divided into two, three, four, six, or twelve parts, which consequently may be filled in by adding the same exact interval or sequence of intervals to each resulting note (called "interpolation of notes"[2]).

Examples include the octatonic scale (also known as the symmetric diminished scale; its mirror image is known as the inverse symmetric diminished scale) and the two-semitone tritone scale:

As explained above, both are composed of repeating sub-units within an octave. This property allows these scales to be transposed to other notes, yet retain exactly the same notes as the original scale (Translational symmetry).

This may be seen quite readily with the whole tone scale on C:

  • {C, D, E, F, G, A, C}

If transposed up a whole tone to D, contains exactly the same notes in a different permutation:

  • {D, E, F, G, A, C, D}

In the case of inversionally symmetrical scales, the inversion of the scale is identical.[3] Thus the intervals between scale degrees are symmetrical if read from the "top" (end) or "bottom" (beginning) of the scale (mirror symmetry). Examples include the Javanese slendro,[4] the chromatic scale, whole-tone scale, Dorian scale, the Mixolydian 13 scale (fifth mode of the melodic minor), and the double harmonic scale.

Asymmetric scales are "far more common" than symmetric scales and this may be accounted for by the inability of symmetric scales to possess the property of uniqueness (containing each interval class a unique number of times) which assists with determining the location of notes in relation to the first note of the scale.[4]

See also

Further reading

  • Yamaguchi, Masaya. 2006. The Complete Thesaurus of Musical Scales, revised edition. New York: Masaya Music Services. ISBN 0-9676353-0-6.
  • Yamaguchi, Masaya. 2006. Symmetrical Scales for Jazz Improvisation, revised edition. New York: Masaya Music Services. ISBN 0-9676353-2-2.
  • Yamaguchi, Masaya. 2012. Lexicon of Geometric Patterns for Jazz Improvisation. New York: Masaya Music Services. ISBN 0-9676353-3-0.


This article was sourced from Creative Commons Attribution-ShareAlike License; additional terms may apply. World Heritage Encyclopedia content is assembled from numerous content providers, Open Access Publishing, and in compliance with The Fair Access to Science and Technology Research Act (FASTR), Wikimedia Foundation, Inc., Public Library of Science, The Encyclopedia of Life, Open Book Publishers (OBP), PubMed, U.S. National Library of Medicine, National Center for Biotechnology Information, U.S. National Library of Medicine, National Institutes of Health (NIH), U.S. Department of Health & Human Services, and, which sources content from all federal, state, local, tribal, and territorial government publication portals (.gov, .mil, .edu). Funding for and content contributors is made possible from the U.S. Congress, E-Government Act of 2002.
Crowd sourced content that is contributed to World Heritage Encyclopedia is peer reviewed and edited by our editorial staff to ensure quality scholarly research articles.
By using this site, you agree to the Terms of Use and Privacy Policy. World Heritage Encyclopedia™ is a registered trademark of the World Public Library Association, a non-profit organization.