Contour Calculator


Contour Calculator is a calculator for the calculus of Contour Theory operations. The development of current web version has started in 2020 but it is a new generation of previous tools such as Goiaba, MusiContour and ContourMetrics.

This tool is a result of the research projects conducted by Marcos Sampaio in his Master's and Ph.D. projects, and his research about contour Similarity.

Music Contour Relations Theory

Contour Theory in current usage was started by Michael Friedmann, Robert Morris, and Elizabeth Marvin in 1980s. Plenty of authors have colaborated since them.

Concepts and operations

The calculator provides Theory's operations:

  1. Translation
  2. Equivalent class
  3. Adjacent series
  4. Inversion
  5. Retrogression
  6. Window reduction (3 and 5)
  7. Direction index
  8. Oscillation index
  9. Oscillation spectrum
  10. Oscillation similarity
  11. Global pattern similarity

Furthermore, the calculator provides auxiliary operations:

  1. Repetitions cleaning

The calculator lacks Morris', Schultz's and Sampaio's reduction algorithms.

See a brief description of these operations here.


  1. Bor, Mustafa. 2009. "Contour Reduction Algorithms: A Theory of Pitch and Duration Hierarchies for Post-Tonal Music." University of British Columbia.
  2. Friedmann, Michael L. 1985. "A Methodology for the Discussion of Contour: Its Application to Schoenberg's Music." Journal of Music Theory 29 (2): 223--48.
  3. Marvin, Elizabeth West. 1988. "A Generalized Theory of Musical Contour: Its Application to Melodic and Rhythmic Analysis of Non-Tonal Music and Its Perceptual and Pedagogical Implications." University of Rochester.
  4. Morris, Robert Daniel. 1987. Composition with Pitch-Classes: A Theory of Compositional Design. Yale University Press.
  5. Morris, Robert Daniel. 1993. "New Directions in the Theory and Analysis of Musical Contour." Music Theory Spectrum 15 (2): 205--28.
  6. Polansky, Larry and Bassein, Richard. 1992. "Possible and Impossible Melody: some Formal Aspects of Contour." Journal of Music Theory 36 (2): 259--84.
  7. Sampaio, Marcos da Silva. 2017. "A Teoria de Relações de Contornos No Brasil." In Teoria e Análise Musical Em Perspectiva Didática, 123--38. Salvador, BA: EDUFBA.
  8. Sampaio, Marcos da Silva. 2018. "Contour Similarity Algorithms." MusMat Brazilian Journal of Music and Mathematics 2 (2): 58--78.
  9. Sampaio, Marcos da Silva, and Pedro Kroger. 2016. "Contour Algorithms Review." MusMat - Brazilian Journal of Music and Mathematics 1 (1): 72--85.
  10. Sampaio, Marcos da Silva. 2012. "A Teoria de Relações de Contornos Musicais: Inconsistências, Soluções e Ferramentas." Universidade Federal da Bahia.
  11. Schmuckler, Mark A. 2010. "Melodic Contour Similarity Using Folk Melodies." Music Perception 28 (2): 169--194.
  12. Schultz, Rob D. 2016. "Normalizing Musical Contour Theory." Journal of Music Theory 60 (1): 23--50.