Schenker's mysterious five

Nineteenth Century Music

Volumn 23, Issue 1, 1999, Pages 84-101

  Clark, Suzannah ^a  

^a NONE

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EID: 62449171259     PISSN: 01482076     EISSN: None     Source Type: Journal    
DOI: 10.1525/ncm.1999.23.1.02a00040     Document Type: Article

References (62)

1. Milton Babbitt, "Past and Present Concepts of the Nature and Limits of Music," in Perspectives on Contemporary Music Theory, ed. Benjamin Boretz and Edward T. Cone (New York, 1972), p. 5
2. Babbitt, "Past and Present," p. 5
3. It is interesting that although Babbitt rightly sees the futility of basing musical principles in scientific explanation, he partook in a different kind of scientific underpinning for music theory - and one which is only seemingly safer - namely, the adoption of scientific language and method (but not the specific scientific ideas) into theoretical discourse. On the effects of introducing the methods of science into music theory, see Marion A. Guck, "Rehabilitating the Incorrigible," in Theory, Analysis and Meaning in Music, ed. Anthony Pople (Cambridge, 1994), pp. 57-73
4. and Matthew Brown and Douglas J. Dempster, "The Scientific Image of Music Theory," Journal of Music Theory 33 (1989), 65-106
5. With regards to Schenker, there are many studies about the effect of "scientific" language in translations of his writings. Among them are: William Rothstein, "The Americanization of Schenker," in Schenker Studies, ed. Hedi Siegel (Cambridge, 1990), pp. 193-203
6. and Robert Snarrenberg, Schenker's Interpretive Practice (Cambridge, 1997)
7. The existence of the overtone series was brought to Rameau's attention by the physicist and Jesuit father Louis-Bertrand Castel in his review of Rameau's treatise, which appeared in the Journal de Trévoux (October-November 1722), reproduced in The Complete Theoretical Writings of Jean-Philippe Rameau (1683-1764), ed. Erwin R. Jacobi, vol. 1 (American Institute of Musicology, 1967), pp. xxviii-xlix
8. Rameau first responded to the news in Nouveau système de musique théoretique et pratique (1726)
9. but did not begin to explore the theoretical potential of the corps sonore until his Génération harmonique ou traité de musique théorique et pratique (1737)
10. The purpose of his next treatise, Démonstration du principe de l'harmonie servant de base à tout l'art musical théorique et pratique (1750), was, as the title suggests, to demonstrate scientifically how it serves as the founding principle of music, that is of all harmonic succession as well as of harmonic chords themselves
11. For a detailed reading of how Rameau's multiple treatises relate to development of scientific understanding of the corps sonore, see Thomas Christensen, Rameau and Musical Thought in the Enlightenment (Cambridge, 1993), esp. chap. 6
12. Rameau was also excited about the existence of the overtone series because it seemed to offer proof that the origin of music was harmonic and not melodic, as his rival Jean-Jacques Rousseau claimed in Essai sur l'origine des langues, où il est parlé de la mélodie, et de l'imitation musicale, Bibliothèque du Graphe (Paris, 1976)
13. Christensen, Rameau and Musical Thought, passim
14. The beginning of this can be traced in Schoenberg's writings. In his 1926 essay "Opinion or Insight?", he contemplated the degree to which tonal music is natural: "Tonality's origin is found - and rightly so - in the laws of sound" (Style and Idea [Berkeley and Los Angeles, 1975], p. 259)
15. Heinrich Schenker, Harmony, trans. Elisabeth Mann Borgese, ed. and ann. Oswald Jonas (Cambridge, Mass., 1973)
16. The first German edition was published anonymously "von einem Künstler" as Harmonielehre, vol. 1 of Neue musikalische Theorien und Phantasien (Vienna, 1906)
17. For the kind of tone Schenker adopted to distance himself from his predecessors and especially his contemporaries, see Leslie David Blasius, Schenker's Argument and the Claims of Music Theory (Cambridge, 1996), esp. chap. 1
18. Opinions on Schenker's use of nature are not always explicitly stated but are often easily inferred. Allen Forte ("Schenker's Conception of Musical Structure," in Readings in Schenker Analysis and Other Approaches, ed. Maury Yeston [New Haven, 1977], pp. 3-37) describes Schenker's system without any mention of its natural underpinning and sees Schenker's view of the history of triadic tonality as "desultory" (p. 36)
19. Edward Aldwell and Carl Schachter are skeptical about the overtone series' regulatory function for tonal music in Harmony and Voice Leading (New York, 1978), pp. 21-22
20. Nicholas Cook rightly argues for the need to know the details of this underpinning in order to understand the "otherwise arbitrary prejudices and restrictions in his analytical techniques" in A Guide to Musical Analysis (Oxford, 1987), p. 39
21. On the illogicality of simply taking the Ursatz as a formal and informal axiom, however, see Eugene Narmour, Beyond Schenkerism: The Need for Alternatives in Music Analysis (Chicago, 1977), pp. 12-30
22. Schenker, Harmony, p. 20
23. All but the concept of obligatory register appear in Harmony. Obligatory register is treated in Schenker, Free Composition (Der freie Satz): Volume III of New Musical Theories and Fantasies, trans. and ed. Ernst Oster, 2 vols. (New York, 1979), secs. 268-70
24. On the ear, see sec. 11 and the voice, sec. 13 in Harmony. Schenker also mentions the limitations of the eye with regard to perceiving light spectra. Interestingly, he also comments on the limit of the eye in relation to the five-line staff in sec. 11
25. The first few times Schenker observes the presence of the number five, he does not associate it with the mysterious (see Harmonielehre, pp. 37-38)
26. Schenker made a similar claim concerning his discovery of the fundamental line in Das Meisterwerk in der Musik: Ein Jahrbuch, vol. II (Munich, 1926), p. 41, where he claimed "Ich habe die Urlinie erschaut, nicht errechnet!"
27. Snarrenberg, Schenker's Interpretive Practice, p. 10, n. 3
28. Matthew Brown, "The Diatonic and the Chromatic in Schenker's Theory of Harmonic Relations," Journal of Music Theory 30 (1986), 10
29. Schenker, Harmony, pp. 26, n. 17 and 30, n. 19 respectively
30. Schenker, Free Composition, p. 145 (emphasis added)
31. Schenker, "On Organicism in Sonata Form," The Masterwork in Music: A Yearbook, v.2 (1926), ed. William Drabkin (Cambridge, 1996), p. 23
32. Given his notion of the genius figure, however, he could equally be aligning himself with the genius, not in order to claim intellectual prowess but rather to suggest that he is a vehicle, specifically nature's vehicle, exposing the Truth about tonality. For a discussion of Schenker's notion of genius, see Nicholas Cook, "Schenker's Theory of Music as Ethics," Journal of Musicology 7 (1989), 415-39
33. Robert Snarrenberg also discusses Schenker's references to genius and his comparisons with the sleepwalker, but he concludes, however, that Schenker's use of the "as if" clause suggests he was unconvinced by his speculation that nature had a mysterious power (Schenker's Interpretive Practice, pp. 84-86)
34. Why did Schenker's sample of the overtone series end at the sixteenth partial? Although he indicates the series is infinite, this selection suggests a closed system (the sixteenth partial is the note C)
35. Ultimately only the pattern and not the tuning of the first five notes interested Schenker, who simply saw equal temperament as a practical adaptation of nature. He spent no time justifying it, instead dismissing any objections with the advice that "more detailed information about this phenomenon can be found in any dictionary of music" (Harmony, p. 83)
36. Schenker never really justified his choice of the fifth, probably not feeling he had to. Rameau long before him had given theoretical roles to intervals from the overtone series: the octave represented the "proof" for the principle of inversion, and the fifth represented the "proof" for motion in music. This was as much as was needed to theorize about music: one interval explained the vertical aspect, the other the horizontal. While the third completes the major triad, it otherwise plays no theoretical role. Schenker's discussion of the prevalence of the fifth as an interval and relationship appears in Harmony, pp. 26 and 29 respectively. While it may appear unseemly to put Rameau and Schenker together, given Schenker's view of Rameau in "Rameau or Beethoven? Creeping paralysis or spiritual potency in music?", the fact remains that many of Rameau's assumptions, which gained force through consistent theoretical use in the eighteenth and nineteenth centuries, are also prevalent in Schenker's thinking. Not least, the cadential prototype that, according to Rameau, is responsible for motion in music becomes the interval (in reverse order I-V, followed by closure to I) that Schenker will eventually rank in Free Composition as empowered by nature with momentum enough to drive an entire structure
37. Schenker's essay on Rameau appears in The Masterwork in Music: A Yearbook v.3 (1930), ed. William Drabkin (Cambridge, 1997), pp. 1-9
38. Jonas footnoted this remark and in his annotation in Harmony (p. 41, n. 24) disagreed with Schenker, adding that "the lower fifth cannot be considered as a representative of another, more remote system."
39. His position on this is elaborated in his Introduction to the Theory of Heinrich Schenker (Einführung in die Lehre Heinrich Schenkers): The Nature of the Musical Work of Art, trans. and ed. John Rothgeb (New York, 1982), pp. 21-23
40. This idea will also underscore the bass arpeggiation in Free Composition. Having achieved the dominant by following the upward trajectory prescribed by nature, the bass must return to its tonic, which entails inversion. (I will return to this point shortly.)
41. It is interesting in this connection to note that, contrary to Schenker's advice, Jonas did set up a system of six rising fifths in his Introduction to the Theory of Heinrich Schenker, p. 21. Although one might assume that Jonas was introducing and explaining Schenker's ideas to the Schenkerian student, he in fact altered two crucial components of Schenker's argument on the derivation of the scale: most fundamentally, he disagreed with Schenker's notion of the Mysterious Five (as discussed above), and secondly, he did not place the subdominant harmony below the tonic
42. For a lively discussion of the philosophy of nature and "what kind of nature" is assumed in environmental ethics, see Kate Soper, What is Nature?: Culture, Politics and the Non-Human (Oxford, 1995). This volume provides a helpful background for discussions of nature and art
43. One could, of course, put this the other way around and say that, in the major diatonic system, the location of the diminished fifth determines the limit of the series of perfect fifths, thereby establishing the Mysterious Five. In that case, when it comes to the minor mode, Schenker presumably would not allow the diminished fifth to be a determining factor, but instead would give more weight to the Mysterious Five. Another student of Schenker, Felix-Eberhard von Cube, did use the diminished fifth as determiner and built the layout of ascending and descending fifths of all modes according to it. Von Cube, The Book of the Musical Artwork: An Interpretation of the Musical Theories of Heinrich Schenker, trans. David Neumeyer, George R. Boyd, and Scott Harris (Lewiston, N.Y., 1988), table III, pp. 94-95; for the corresponding descriptions of each the seven systems, see pp. 93-111. Von Cube also made no mention of the Mysterious Five in his book on Schenker's theory but is nevertheless clearly interested in numbers. His numbers are 7 and 12 because of the seven-tone system of tonality and the church modes and the twelve-note system of atonality. He connected the systems with an arithmetic joke (that he himself meant in that spirit): "What is half of 12?" The answer is 7
44. This view is maintained (but without reference to the naturalness or artificiality of keys) in Charles Rosen, Sonata Forms (rpt. New York, 1988), pp. 354-55
45. Tovey, for example, sees the second theme for its contrast to the first and not for its underlying stability. As he put it, these modulations offset a movement that thus far has experienced a "severe monotony of key." Tovey, Essays in Musical Analysis, vol. 3 Concertos (London, 1936), p. 85
46. I shall not address here the equally interesting question of the contents of the Urlinie. It will be clear, however, that my examination of the bass has implications in this regard. On the development of Schenker's Urlinie, see William Pastille, "The Development of the Ursatz in Schenker's Published Writings," in Trends in Schenkerian Research, ed. Allen Cadwallader (New York, 1987), pp. 71-85
47. On the idea that the Urlinie need not necessarily exclusively descend, see Charles J. Smith, "Musical Form and Fundamental Structure: An Investigation of Schenker's Formenlehre," Music Analysis 15 (1996), 273 and his graphs passim
48. This clearly has implications for the notion of closure, a subject beyond the immediate scope of this article
49. Schenker, Der Tonwille, vol. 4 (Vienna, 1923; rpt. Hildesheim, 1990), p. 19 and the graph is on p. 2 of the foldout for vol. 4
50. The other analysis is in Free Composition, vol. 2, fig. 47, 1
51. See James Webster's discussion of the "double return" in "Sonata Form" in The New Grove Dictionary of Music and Musicians, ed. Stanley Sadie (London, 1980), vol. 17, pp. 497-503
52. By contrast, Schoenberg believed that: "A motive is something that gives rise to a motion. . . . one can compare the motive with a driving force." Schoenberg, Coherence, Counterpoint, Instrumentation, Instruction in Form, trans. and ed. Séverine Neff and Charlotte M. Cross (Lincoln, Neb., 1994), p. 27
53. John L. Snyder, "Schenker and the First Movement of Mozart's Sonata, K. 545: An Uninterrupted Sonata-Form Movement?" Theory and Practice 16 (1991), 66
54. Snyder, "Schenker and Mozart's Sonata, K. 545," p. 62
55. Schenker, Der Tonwille, p. 19
56. Snyder, "Schenker and Mozart's Sonata, K. 545," pp. 64 and 61
57. David Beach, "Schubert's Experiments with Sonata Form: Formal-Tonal Design versus Underlying Structure," Music Theory Spectrum 15 (1993), 9-13
58. Beach gives a brief summary of various opinions on what constitutes design and structure. His own use of the terms posits that: underlying structure refers to the "underlying voice leading and harmonic organization of a given work or passage," and tonal design refers to the "layout of keys in the course of a composition, which is an entirely different matter than tonal structure." "Schubert's Experiments," p. 3
59. Smith, "Schenker's Formenlehre," p. 270
60. Smith writes that Snyder and Beach "both grapple fairly successfully with forms of this sort" ("Schenker's Formenlehre," p. 292, n. 114)
61. The three types are interrupted structures. Type 1 presents the first descent as subordinate to the second, Type 2 presents the second descent as subordinate to the first, and Type 3 presents both descents as equal. Charles J. Smith, "Schenker's Formenlehre," p. 268
62. For a similar discussion, see Peter H. Smith, "Brahms and Schenker: A Mutual Response to Sonata Form," Music Theory Spectrum 16 (1994), 77-103