The Pitch Set as a Level of Description for Studying Musical Pitch Perception

  • Gerald J. Balzano


How shall we define the musical stimulus? Traditionally, music theorists interested in pitch phenomena have sought the definition in terms of ratios of whole numbers. Such ratios can provide a description of most, if not all, of the musical intervals in use today, and can be translated readily into ratios of physically realizable tone frequencies. Psychoacousticians, following the dictates of reductionism, have sought a finer grain of analysis than this, pointing out that the essential constituent of an interval is a tone, and that the study of music perception must ultimately refer to the perception of single tones and their frequency components. Accordingly, a great deal of scientific effort has gone into studying the perception of isolated tones.


Chromatic Scale Pitch Discrimination Scale Family Pitch Class Major Scale 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Attneave, F., and Olson, R.K., 1971, Pitch as a medium: A new approach to psychophysical scaling. Am. J. Psychol., 84:147–166.PubMedCrossRefGoogle Scholar
  2. Babbitt, M., 1972, The structure and function of musical theory, in “Perspectives on Contemporary Music Theory,” B. Boretz and E.T. Cone, eds., Norton, New York. (Reprinted from College Music Symposium, 1965(5).)Google Scholar
  3. Bachem, A., 1950, Tone height and tone chroma as two different pitch qualities. Acta Psychologica, 7:80–88.CrossRefGoogle Scholar
  4. Balzano, G.J., 1977a, “Chronometrie Studies of the Musical Interval Sense,” Doctoral diss., “Dissertation Abstracts International”, Stanford Universityxx, 38, 2898B (Univ. Microfilms, No. 77–25, 643).Google Scholar
  5. Balzano, G. J., 1977b, On the bases of similarity of musical intervals, J. Acoust. Soc. Am., 61-S51(Abs.)Google Scholar
  6. Balzano, G.J., 1978, The structural uniqueness of the diatonic order, in “Cognitive Structure of Musical Pitch,” R.N. Shepard (Chair), Symposium presented at the meeting of the Western Psychological Association, San Francisco, April 1978.Google Scholar
  7. Balzano, G.J., in press, The group-theoretfc description of twelve-fold and microtonal pitch systems. Comp. Mus. J. Google Scholar
  8. Bartlett, J.C., and Dowling, W.J., 1980, Recognition of transposed melodies: A key-distance effect in developmental perspective, J. Exp. Psychol./Human Perc. Perf. 6:501–515.CrossRefGoogle Scholar
  9. Benade, A.H., 1960, “Horns, Strings and Harmony,” Doubleday, New York.Google Scholar
  10. Boretz, B., 1970, The construction of musical syntax. I, Persp. New Mus., 9(l):23–42.CrossRefGoogle Scholar
  11. Boynton, R., 1975, The visual system: Environmental information, in “Handbook of Perception” Vol. 3, E.C. Carterette and M.P. Friedman, eds.. Academic Press, New York.Google Scholar
  12. Budden, F.J., 1972, “The Fascination of Groups,” Cambridge University Press, LondonGoogle Scholar
  13. Cassirer, E., The concept of group and the theory of perception, Philos. Phenonnenolog. Res., 5:1–36.Google Scholar
  14. Cavanaugh, J.P., 1972, Relation between the immediate memory span and the memory search rate, Psychol. Rev., 79:525–530.CrossRefGoogle Scholar
  15. Chalmers, J.H., Jr, 1975, Cyclic scales, Xenharmonikon Google Scholar
  16. Clifton, C., Jr, and Cruse, D., 1977, Time to recognize tones: Memory scanning or memory strength? Quart. J. Exp. Psychol., 29:709–726.CrossRefGoogle Scholar
  17. Cohen, A.J., 1975, “Perception of Tone Sequences from the Western-European Chromatic Scale: Tonality, Transposition and the Pitch Set,” Doct. diss. Queen’s University at Kingston (Canada), “Dissertation Abstracts International,” 1977, 37:4179B.Google Scholar
  18. Cohen, A.J., Cuddy, L.L., and Mewhort, D.J.K., 1977, Recognition of transposed tone sequences, J. Acoust. Soc. Am., 61:S87-S88 (Abs.)CrossRefGoogle Scholar
  19. Corso, J.F., 1954, Unison tuning of musical instruments, J. Acoust. Soc. 26:746–750.CrossRefGoogle Scholar
  20. Cuddy, L.L., Cohen, A.J., and Miller, J., 1979, Melody recognition: The experimental application of musical rules, Canad. J. Psychol., 33:148–157.PubMedCrossRefGoogle Scholar
  21. Dewar, K.M., 1977, Cues used in recognition memory for tones, J. Acoust. Soc. Am., 61: S49(Abs).CrossRefGoogle Scholar
  22. Dowling, W.J., 1978, Scale and contour: Two components of a theory of memory for melodies, Psychol. Rev., 85:341–354.CrossRefGoogle Scholar
  23. Forte, A., 1964, A theory of set-complexes for music, J. Mus. Theory, 8:136–183.CrossRefGoogle Scholar
  24. Frances, R., 1958, “La Perception de la Musique,” 3. Vrin, Paris.Google Scholar
  25. Fuller, R., 1975, A structuralist approach to the diatonic scale, J. Mus. Theory, 19:182–210.CrossRefGoogle Scholar
  26. Gamer, C., 1967, Some combinational resources of equal-tempered systems, J. Mus. Theory, 11:32–59.CrossRefGoogle Scholar
  27. Goodman, N., 1966, “The Structure of Appearance,” (2nd ed.), Bobbs-Merill, Indianapolis.Google Scholar
  28. Helmholtz, H. von, 1885, “On the Sensations of Tone as as Physiological Basis for the Theory of Music, “A.J. Ellis, ed. and trans., 1954, Dover, New York.Google Scholar
  29. Holland, J. 1972, “Studies in Structure,” Macmillan, London.Google Scholar
  30. Killam, R.N., Lorton, P.V., and Schubert, E.D., 1975, Interval recognition: Identification of harmonic and melodic intervals, J. Mus. Theory, 19:212–233.CrossRefGoogle Scholar
  31. Kohier, W., 1938, Physical Gestalten, in “A Source Book of Gestalt Psychology,” W.D. Ellis, ed., Routiëdgeóc Kegan Paul, London.Google Scholar
  32. Krumhansl, C.L., 1979, The psychological representation of musical pitch in a tonal context, Cog. Psych., 11:346–374.CrossRefGoogle Scholar
  33. Krumhansl, C.L., and Shepard, R.N., 1979, Quantification of the hierarchy of tonal functions within a diatonic context, J Exp. PsychoL/Human Perc. Perf., 5:579–594.CrossRefGoogle Scholar
  34. Kruskal, J.B., 1964a, Multidimensional scaling by optimizing goodness of fit to a nonmetric hypothesis, Psychometrika, 29:1–27.CrossRefGoogle Scholar
  35. Kruskal, J.B., 1964b, Nonmetric multidimensional scaling: A numerical method, Psychometrika, 29:115–129.CrossRefGoogle Scholar
  36. Lakner, Y., 1960, A new method of representing tonal relations, J. Mus. Theory Google Scholar
  37. Lewin, D., 1959, Intervallic relations between two collections of notes, J. Mus. Theory, 3:298–301.CrossRefGoogle Scholar
  38. Lewin, D., 1960, The intervallic content of a collection of notes, J. Mus. Theory, 4:98–101.CrossRefGoogle Scholar
  39. Lewin, D., 1977, Forte’s interval vector, my interval function, and Regener’s common-note function, J. Mus. Theory 21:194–237.CrossRefGoogle Scholar
  40. Lundin, R.W., 1953, “An Objective Psychology of Music,” Ronald Press, New York.Google Scholar
  41. O’Connell, W., 1962, Tone spaces, Die Reihe, 8:34–67.Google Scholar
  42. Plomp, R., 1964, The ear as a frequency analyzer, J. Acoust. Soc. Am., 36:1628–1636.CrossRefGoogle Scholar
  43. Plomp, R., 1976, “Aspects of Tone Sensation,” Academic Press, New York.Google Scholar
  44. Plomp, R., Wagenaar, W.A., and Mimpen, A.M., 1973, Musical interval recognition with simultaneous tones, Acustica, 29:101–109.Google Scholar
  45. Regener, E., 1973, “Pitch Notation and Equal Temperament: A Formal Study,” University of California Press, Berkeley.Google Scholar
  46. Revesz, G., 1954, “Introduction to the Psychology of Music,” University of Oklahoma Press, Norman, Oklahoma.Google Scholar
  47. Rothenberg, D., 1978a, A model for pattern perception with musical applications. I, Pitch structures as order-preserving maps. Math. Systems Theory, 11:199–234.CrossRefGoogle Scholar
  48. Rothenberg, D., 1978b, A model for pattern perception with musical applications. II, The information content of pitch structures. Math. Systems Theory, 11:353–372.CrossRefGoogle Scholar
  49. Schenker, H., 1906, “Harmony”, republ. 1973, O. Jonas, ed., E.M. Borgese, trans., MIT Press, Cambridge.Google Scholar
  50. Shepard, R.N., 1962a, The analysis of proximities: Multidimensional scaling with an unknown distance function, I, Psychometrika, 27:125–139.CrossRefGoogle Scholar
  51. Shepard, R.N., 1962b, The analysis of proximities: multidimensional scaling with an unknown distance function, II, Psychometrika, 27:219–246.CrossRefGoogle Scholar
  52. Shepard, R.N., 1964, Circularity in judgements of relative pitch, J. Acoust. Soc. Am., 36:2346–2353.CrossRefGoogle Scholar
  53. Shepard, R.N., in press. Structural representations of musical pitch, in “Psychology of Music,” D. Deutsch, ed.. Academic Press, New York.Google Scholar
  54. Sternberg, S., 1967, Two operations in character recognition: Some evidence from reaction-time measurements, Perc. & Psychophys., 2:45–53.CrossRefGoogle Scholar
  55. Trotter, J.R. 1967, I he psychophysics of melodic interval: Definitions, techniques, theory and problems, Aust. J. Psychol., 19:13–25.CrossRefGoogle Scholar
  56. Zuckerkandl, V., 1956, “Sound and Symbol,” Princeton University Press, Princeton.Google Scholar
  57. Zuckerkandl, V., 1971, “The Sense of Music,” Princeton University Press, Princeton, rev. ed.Google Scholar

Copyright information

© Springer Science+Business Media New York 1982

Authors and Affiliations

  • Gerald J. Balzano
    • 1
  1. 1.Department of MusicUniversity of California at San DiegoLa JollaUSA

Personalised recommendations