Skip to main content

A model of the perceptual root(s) of a chord accounting for voicing and prevailing tonality

II. From Pitch to Harmony

Part of the Lecture Notes in Computer Science book series (LNAI,volume 1317)

Abstract

A theory of harmony is presented that predicts the perceptual root of any simultaneity within the chromatic scale, embedded in the context of any chord progression. The theory takes into account the pitch classes (pcs) of the chord, its voicing, the prevailing tonality, and local voice-leading. Pcs: the perceptual root of an isolated, octave-generalized chord is determined by the root-support intervals P1, P5, M3, m7 and M2. Voicing: other things being equal, the bass note is more likely to function as the root than the other notes. Tonality: the harmonic profile of a chord in a tonal context is given by the sum of the chord's profile in isolation and the pc-stability profile of the prevailing tonality. Voice leading: parallel movement of parts increases the likelihood that the roots of two sonorities will be heard to move in parallel with the voices. Predictions of the theory for the perceptual roots of diatonic triads and 7ths and of common chromatic chords in major and minor keys are intuitively reasonable, but will need to be tested against the results of perceptual-cognitive experiments and systematic studies of scores and improvised performances.

Keywords

  • Chromatic Scale
  • Music Theory
  • Root Position
  • Pitch Class
  • Tonal Context

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.

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • DOI: 10.1007/BFb0034114
  • Chapter length: 19 pages
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
eBook
USD   109.00
Price excludes VAT (USA)
  • ISBN: 978-3-540-69591-2
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book
USD   149.00
Price excludes VAT (USA)

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • Agmon, E. (1993). Towards a theory of diatonic intonation. Interface-Journal of New Music Research, 22, 151–163.

    Google Scholar 

  • Bregman, A. (1990). Auditory scene analysis: The perceptual organization of sound. Cambridge, MA: The MIT Press.

    Google Scholar 

  • Ferrar, W. (1941). Algebra: A text-book of determinants, matrices, and algebraic forms. Oxford: Oxford University Press.

    Google Scholar 

  • Forte, A. (1974). Tonal harmony in concept and practice (2nd ed.). New York, NY: Holt, Rinehart and Winston.

    Google Scholar 

  • Fyk, J. (1995). Melodic intonation, psychoacoustics, and the violin. Zielona Gora: Organon Press.

    Google Scholar 

  • Huron, D. (1994). The Humdrum toolkit reference manual. Menlo Park, CA: Centre for Computer Assisted Research in the Humanities.

    Google Scholar 

  • Huron, D., & Parncutt, R. (1993). An improved model of tonality perception incorporating pitch salience and echoic memory. Psychomusicology, 12, 152–169.

    Google Scholar 

  • Järvinen. (1995). Tonal hierarchies in jazz improvisation. Music Perception, 12, 415–437.

    Google Scholar 

  • Krumhansl, C., & Kessler, E. (1982). Tracing the dynamic changes in perceived tonal organization in a spatial representation of musical keys. Psychological Review, 89, 334–368.

    Google Scholar 

  • McHose, A. (1947). The contrapuntal harmonic technique of the 18th century. Englewood Cliffs, NJ: Prentice-Hall.

    Google Scholar 

  • Parncutt, R. (1988). Revision of Terhardt's psychoacoustical model of the roots of a musical chord. Music Perception, 6, 65–94.

    Google Scholar 

  • Parncutt, R. (1993). Pitch properties of chords of octave-spaced tones. Contemporary Music Review, 9, 35–50.

    Google Scholar 

  • Parncutt, R. (1994). Template-matching models of musical pitch and rhythm perception. Journal of New Music Research, 23, 145–168.

    Google Scholar 

  • Parncutt, R., & Stuckey, R. (1992). Towards a standard alternative notation and terminology based on the chromatic scale. Musikometrika, 4, 117–143.

    Google Scholar 

  • Pritschet, H. (1992). Wahrnehmung des Grundtons von Dreikldngen: Eine experimentelle Untersuchung. Regensburg: S. Roderer.

    Google Scholar 

  • Terhardt, E. (1982). Die psychoakustischen Grundlagen der musikalischen Akkordgrundtöne und deren algorithmischen Bestimmung. In C. Dahlhaus & M. Krause (Eds.), Tiefenstruktur der Musik. Berlin: Technical University of Berlin.

    Google Scholar 

  • Terhardt, E., Stoll, G., & Seewann, M. (1982). Algorithm for extraction of pitch and pitch salience from complex tonal signals. The Journal of the Acoustical Society of America, 71, 679–688.

    Google Scholar 

  • Thomson, W. (1993). The harmonic root: A fragile marriage of concept and percept. Music Perception, 10, 385–416.

    Google Scholar 

  • von Oettingen, A. (1866). Harmoniesystem in dualer Entwicklung: Studien zur Theorie der Musik. Dorpat, Leipzig: W. Gläser.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 1997 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Parncutt, R. (1997). A model of the perceptual root(s) of a chord accounting for voicing and prevailing tonality. In: Leman, M. (eds) Music, Gestalt, and Computing. JIC 1996. Lecture Notes in Computer Science, vol 1317. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0034114

Download citation

  • DOI: https://doi.org/10.1007/BFb0034114

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-63526-0

  • Online ISBN: 978-3-540-69591-2

  • eBook Packages: Springer Book Archive