In the notation of vertical sonorities, it is well-known that composers space chordal tones using wider interval sizes in the bass region. A classic study by Plomp and Levelt (1965) argued that the organization of vertical sonorities in music is related to the phenomenon of critical bands. A replication of Plomp and Levelt's work shows that their demonstration was confounded by an unfortunate artifact and that their results did not support the conclusions drawn. Using a different method, a comparison of actual music with a control sample of "random" music shows that musical practice is consistent with the compositional pursuit of a greater uniformity of spelling with respect to critical bands. Although these results are consistent with conclusions given in Plomp and Levelt, the methods used here avoid the difficulties evident in the earlier study.

[Footnotes]

[Footnotes]
1
Parncutt, 1989).
3
(Moore & Glasberg, 1983).

References

References
Christ, W., DeLone, R., Kliewer, V., Rowell, L. &c Thomson, W. Materials and structure of music, 3rd ed. Englewood Cliffs, NT: Prentice-Hall, 1980.
Huron, D. Error categories, detection and reduction in a musical database. Computers and the Humanities, 1988, 22(4):253-264.
Moore, B. C. J., & Glasberg, B. R. Suggested formulae for calculating auditory-filter band- widths and excitation patterns. Journal of the Acoustical Society of America, 1983, 74(3):750-753.
Parncutt, R. Harmony: A psychoacoustical approach. Berlin: Springer- Verlag, 1989.
Piston, W. Harmony, 3rd ed. New York: W.W. Norton, 1941/1962.
Plomp, R., & Levelt, W. J. M. Tonal consonance and critical bandwidth. Journal of the Acoustical Society of America, 1965, 38, 548-560.
Siegel, S. Nonparametric statistics for the behavioral sciences. New York: McGraw-Hill, 1956.
Vos, J., & van Vianen, B. G. The effect of fundamental frequency on the discriminability between pure and tempered fifths and major thirds. Perception & Psychophysics, 1985, 37, 507-514.
Yost, W. & Nielsen, D. W. Fundamentals of hearing: An introduction. New York: Holt, Rinehart and Winston, 1977.
Zwicker, E., Flottorp, G., & Stevens, S. S. Critical band width in loudness summation. Journal of the Acoustical Society of America, 1957, 29(5), 548-557.

Works Analyzed

Works Analyzed
Bach, Johann Sebastian (1685-1750) "Trio Sonata No. 2" BWV 526; third movement, for organ from Trio Sonatas [for organ] Book IV, London: Novello Edition, 1953; (ed. by J. D. Bower & W. Emery).
Bach, Johann Sebastian (1685-1750) Fugue 14 (in f# minor); WTC Book II, BWV 883b, for clavier.
Bartók, Béla (1881-1945) "Children's Song" No. 106 from Mikrokosmos, Vol. IV, (1926-37) for piano.
Brahms, Johannes (1833-1897) "Intermezzo" Opus 118 No. 2 (1893) for piano.
Frescobaldi, Girolamo (1583-1643) "Canzona" from The Fugue Vol. 1, edited by Adam Adrio; Cologne: Arno Volk Verlag 1961 pp. 45-49.
Gabrieli, Andrea (1510-1586) "Ricercar" from The Fugue Vol. 1, edited by Adam Adrio; Cologne: Arno Volk Verlag, 1961, pp. 21-23.
Handel, Georg Friedrich "Fuga VI" for keyboard (1735) from Hallische Händel-Ausgabe Bärenreiter Kassel (Basel) 1970; Serie IV, Band 6, pp. 21-23 HHA iv/6,21 New Grove No. 83; for four voices.
Haydn, Joseph (1732-1809) String Quartet Opus 50, No. 3, fourth movement, "Finale. Presto" (1787).
Haydn, Joseph (1732-1809) String Quartet Opus 64, No. 5, second movement, "Adagio cantabile" (1790?).
Haydn, Joseph (1732-1809) Sonata in D minor, second movement, "Adagio/Larghetto" Hoboken XVI/24, for piano.
Hindemith, Paul (1895-1963) "Fuga Septima" in A minor from Ludus Tonalis (1943) for piano.
Ives, Charles (1874-1954) The Unanswered Question, Opus 23, No. 1 (1906) for wind and string ensemble.
Mendelssohn Bartholdy, Felix (1809-1847) "Fuge D-Dur".
Pachelbel, Johann (1653-1706) "Fuga" in Early German Keyboard Music (including Austria & Netherlands); An Anthology, Howard Ferguson (ed.), Vol. 2, London: Ox- ford University Press, 1970; pp. 28-31 Source: British Museum, Add. MS 31221, f. 59v.
Satie, Erik (1866-1925) "Air de l'Ordre" Sonneries de la Rose + Croix for piano.
Schoenberg, Arnold (1874-1951) "String Quartet in D major" (1897), first movement.
Schubert, Franz (1797-1828) "Fuge e-Moll" Opus 152 (1828) for organ.
Schumann, Robert (1810-1856) "Fuge d-Moll" from Vier Fugen Opus 72 (1845).
Shostakovich, Dmitri (1906-1975) "Fuge e-Moll" from the 24 Preludes and fugues, Opus 87 (1951).
Telemann, Georg Philipp (1681-1761) "Fuga No. 1" from Kleine Fugen, Hamburg (1731), for keyboard instrument.
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