Abstract
The Tonal Game (Sect. 15.1) is a fallback strategy by which a transmitted score is processed as a major or minor key. The strategy consists of three main defaults, the order of which is motivated by the Economical Principle: a tonality (first major, then minor)—the only context-free default; a robust key; and finally, a key. Chopin’s Mazurka, Op. 24/2, offers highly instructive examples of the Tonal Game at work, including a contextually motivated overruling of the very first default, a major tonality. Finally, Sect. 15.2 studies a possible connection between the extraordinary tonal richness of Chopin’s Mazurka and the emergence early in the nineteenth century of “Tonality” as a notion of both synchronic and diachronic content, most notably in the work of François-Joseph Fétis.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
See Bent (1994), pp. 157–183, and Moreno (2004), pp. 128–159. In a similar vein, though not specifically in connection with key-judgment, Riemann (1914/15) refers to a “… Principle of the Greatest Possible Economy for the Musical Imagination [that] moves directly toward the rejection of more complicated structures, where other possible meanings suggest themselves that weigh less heavily on the powers of interpretation….” (Wason and Marvin 1992, p. 88, original emphasis). Weber’s “Principle of Simplicity” and Riemann’s “Principle of the Greatest Possible Economy for the Musical Imagination” may both be seen as versions of the Economical Principle. Saslaw (1991, footnote on p. 139) notes “a striking parallel” between Weber’s principle and one of the principles of gestalt theory.
- 2.
- 3.
“Lorsque celui-ci se fait entendre, il n’y a plus de doute sur le ton; tout le secret de la tonalité est révélé par le rapport du quatrième degré avec la dominante, et par le rapport attractif de ce quatrième degré avec la note sensible.” (Fétis 1853, p. 38)
- 4.
Note again that cue-cells are “context-free tonic-inducers.” In particular, they do not engage the expectation that scores contain the tonic, let alone begin with it.
- 5.
See also Brown (1988).
- 6.
See the discussion following Proposition 14.23. Although I-V in C is preferable to IV-I in G (as an interpreted signal), in the final analysis the Mazurka’s introductory measures remain tonally ambiguous to some extent. Indeed, Chopin seems to address the introduction’s latent ambiguity in the coda (mm. 105–120). Mm. 109–112, in particular, suggest both I-V in C (cf. mm. 1–4), and IV-I in G (cf. mm. 105–108).
- 7.
To save space, Chopin’s varied repetitions of eight-measure units are replaced in Fig. 15.3 with exact repetitions, indicated by repeat signs (sections b and B1). Moreover, Chopin’s twofold repetition of the four-measure group 73–76 (the second time with the left hand transposed an octave lower) is similarly abbreviated. In mm. 6 and 8 contextually implied tones are inserted parenthetically (cf. the parallel measures 10 and 12, respectively), applying the idea of “imaginary continuo” (see Sect. 7.1). Note that the four-measure coda of the A section (mm. 53–56) is placed next to the four-measure introduction, mm. 1–4, again to save space.
- 8.
Cf. Table 14.2. Chopin, who retains the empty signature throughout the A-section, nonetheless writes the B2 of m. 27 with a cautionary natural (similarly in m. 35). Thus, the existence of B
—“in the background” so to speak—is implied. - 9.
The avoidance of G
in the a1-section, at least harmonically, is amply compensated for in the a2-section that immediately follows. - 10.
Cf. the similarly local A
major tonality, mm. 62–64. - 11.
M. 57 may be heard momentarily as a “German” augmented-sixth chord, in which case the C-major key is robust (
, unlike 
, is first-order chromatic). However, the resolution to D in m. 58 rules out such a hearing in retrospect. - 12.
In real time one is hardly aware that an A-minor arrival is imminent until m. 88. However, given the four-measure groups and the emphasis on the “half-diminished sonority,” in retrospect one realizes that, if A minor is present in m. 88, it must have been present already in m. 85.
- 13.
Except for the “retransition” to the A-minor reprise the segments are all non-overlapping.
- 14.
I am indebted to William Rothstein for suggesting a Chopin-Liszt-Fétis connection in this context.
- 15.
- 16.
For more on Liszt’s (presumably) lost prelude, see Berry 2004, footnote on p. 257. See ibid., p. 258, for additional evidence corroborating Liszt’s presumed allegiance to Fétis’s ideas.
- 17.
P. 198. “On serait cependant dans l’erreur, dit-il, si l’on croyait que par la nécessité future de l’emploi fréquent de l’ordre omnitonique, on ne fera plus usage des autres ordres de tonalités: à Dieu ne plaise qu’il en soit ainsi! Chacun de ces ordres a ses avantages, ses qualités auxquels il faut bien se garder de renoncer, car ce serait appauvrir l’art d’un côté pendent qu’on l’enrichirait de l’autre. Le mélange des quatre ordres, chacun d’eux étant employé à propos, sera le dernier terme de la perfection tonale; cette perfection sera fondée à la fois sur la convenance et la variété.” Cited and translated in Berry 2004, pp. 256–257.
- 18.
Fétis’s theory of tonalité is indebted to Alexandre-Étienne Choron (1771−1834), who (apparently) coined the term tonalité in 1810. See Simms (1975).
- 19.
As Berry (2004, p. 256) notes, on May 12th 1832, just days before starting his lecture series, Fétis published a review of Gottfried Weber ’s Versuch. His ordre pluritonique, and particularly, the omnitonique, seem to resonate with Weber’s Mehrdeutigkeit (“multiple meaning”). On Weber and multiple meaning, see Saslaw (1990–1991).
—“in the background” so to speak—is implied.
in the a1-section, at least harmonically, is amply compensated for in the a2-section that immediately follows.
, unlike 
, is first-order chromatic). However, the resolution to DReferences
Aldwell, E., & Schachter, C. (2003). Harmony and voice leading (3rd ed.). Belmont: Wadsworth Group.
Bent, I. (Ed.). (1994). Music analysis in the nineteenth century (Vol. I). Cambridge: Cambridge University Press.
Berry, D. (2004). The meaning(s) of ‘without’: An exploration of Liszt’s Bagatelle ohne Tonart. 19th-Century Music, 27(3), 230–262.
Bloom, P. (2006). Fétis’s review of the Transcendental Etudes. In H. Gibbs & D. Gooley (Eds.), Franz Liszt and his world (pp. 427–440). Princeton: Princeton University Press.
Brown, H. (1988). The interplay of set content and temporal context in a functional theory of tonality perception. Music Perception, 5(3), 219–250.
Brown, H., & Butler, D. (1981). Diatonic trichords as minimal tonal cue-cells. In Theory Only, 5(6–7), 39–55.
Browne, R. (1981). Tonal implications of the diatonic set. In Theory Only, 5(6–7), 3–21.
Christensen, T. (1996). Fétis and emerging tonal consciousness. In I. Bent (Ed.), Music theory in the age of romanticism (pp. 37–56). Cambridge: Cambridge University Press.
Eigeldinger, J.-J. (1986). Chopin, pianist and teacher, as seen by his pupils (N. Shohet, K. Osostowicz & R. Howat, Trans. & R. Howat, Ed.). Cambridge: Cambridge University Press.
Fétis, F.-J. (1853). Traité complet de la théorie et de la pratique de l'harmonie (5th ed.). Paris: Brandus. Electronic ed. in Traités français sur la musique, G. Di Bacco (Director). http://www.chmtl.indiana.edu/tfm. Accessed 10 Jan 2012.
Fétis, F.-J. (2008). Complete treatise on the theory and practice of harmony (P. Landey, Trans.). New York: Pendragon.
Gjerdingen, R. (1988). A classic turn of phrase: Music and the psychology of convention. Philadelphia: University of Pennsylvania Press.
Kirkendale, W. (1979). Fugue and fugato in Rococo and Classical chamber music (M. Bent, Trans. & Author). Durham: Duke University Press.
Lewin, D. (1984). Amfortas’s prayer to Titurel and the role of D in Parsifal: The tonal spaces of the drama and the enharmonic C
/B. 19th-Century Music, 7(3), 336–349.Moreno, J. (2004). Musical representations, subjects, and objects. Bloomington: Indiana University Press.
Ratner, L. (1980). Classic music: Expression, form, style. New York: Schirmer.
Riemann, H. (1914/15). Ideen zu einer ‘Lehre von den Tonvorstellungen.’ Jahrbuch der Musikbibliothek Peters 21/22, 1–26. Reprint 1965.
Saslaw, J. (1990–1991). Gottfried Weber and multiple meaning. Theoria 5, 74–103.
Saslaw, J. (1991). Gottfried Weber’s cognitive theory of harmonic progression. Studies in Music from the University of Western Ontario, 13, 121–144.
Schachter, C. (1999). Analysis by key: Another look at modulation. In J. Straus (Ed.), Unfoldings: Essays in Schenkerian theory and analysis (pp. 134–160). New York: Oxford University Press. Reprinted from Music Analysis 6(3), 1987.
Simms, B. (1975). Choron, Fétis, and the theory of tonality. Journal of Music Theory, 19(1), 112–139.
Sydow, B. (Ed.). (1962). Selected correspondence of Fryderyk Chopin (A. Hedley, Trans.). London: Heinemann.
Vos, P. (2000). Tonality induction: Theoretical problems and dilemmas. Music Perception, 17(4), 403–416.
Walker, A. (1970). Liszt and the twentieth century. In A. Walker (Ed.), Franz Liszt: The man and his music (pp. 350–364). New York: Taplinger.
Wason, R., & Marvin, W. E. (1992). Riemann’s Ideen zu einer ‘Lehre von den Tonvorstellungen’: An annotated translation. Journal of Music Theory, 36(1), 69–117.
Weber, G. (1830–1832). Versuch einer geordneten Theorie der Tonsetzkunst (3rd Rev. ed.). Mainz: Schott.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Agmon, E. (2013). The Tonal Game. In: The Languages of Western Tonality. Computational Music Science. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-39587-1_15
Download citation
DOI: https://doi.org/10.1007/978-3-642-39587-1_15
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-39586-4
Online ISBN: 978-3-642-39587-1
eBook Packages: Computer ScienceComputer Science (R0)