New series of essays published

I have published a seven-part essay series titled Formal Functions in Menuets by Mozart. Part 7 is "Contemporaries and Successors, 1780-1828" and includes discussion of named menuets by Schubert.   Link to Part 7.


Here is the abstract.

This final essay in the Mozart series charts formal functions (after Caplin) in named menuets written by other composers during the last ten years of Mozart’s life, 1780-1791, and by three composers active in Vienna thereafter, through the death of Schubert (1828). The repertoire includes menuets by Carl and Anton Stamitz, Franz Joseph Haydn, Luigi Boccherini, Giovanni Viotti, and Adalbert Gyrowetz, and several others. The three later composers are Beethoven, Hummel, and Schubert. Concluding comments return to questions of musical form theory.

Here is a link to Part 1in the series: Formal Functions in Menuets by Mozart, Part 1: Orchestral Works and Independent Sets. And the abstract:

A study of formal functions (after Caplin) in named menuets by Mozart, the larger goal being to historicize more fully form-design practices in European music during the second half of the eighteenth century.

Finally, titles for Parts 2-6:

Part 2: Sonatas and Chamber Music.Part 3: A Comparison with Johann Christian Bach.Part 4: His Older Contemporaries, to 1770.Part 5: More to Theoretical Issues.Part 6: Contemporaries, 1771-1780.

A menuet by Mozart, age 9

IMSLP has a facsimile of Mozart's London notebook, digitized by the library of the Jagiellonian University, Cracow, Poland. The volume contains sketches, many of them complete, from 1764 and 1765. Three menuets are among the last pieces in the book. They are followed by a fourth but incomplete menuet and an incomplete fugue for strings (it breaks off just after the exposition finishes).

The three menuets are in F, Bb, and Eb, respectively. A facsimile of the third one is given below, followed by a digital engraving.

The design is 8 + 8, and a repeat sign should undoubtedly be placed in the middle. This little piece is another case of the sentence design showing up much earlier than it ought to do in the classical narrative (that is, Schoenberg's story, in which Beethoven invents the sentence design as better suited to the 19th century organic unity ideal).

Mozart gives the first idea of the continuation phrase the same inverted-arch shape as those in the presentation. The second idea is a formula cadence where the tonic scale degree (here, Bb) is approached from both below (A-natural) and above (C). The B section recasts the basic idea in form of an ascending sequence based on parallel tenths. The transposition of the continuation phrase (to make a "balanced binary" form of the whole) brings the melodic line up to Eb (over G3), then repeats the ascent in the final perfect authentic cadence.

The conflict of voice leading and line

In an early article, Kofi Agawu lists three guidelines for the analysis of closure in music:

1. Closure is a function of formal principles and/or generic signs.

2. Closure is not the same thing as an ending. . . . An ending refers to local elements in the musical structure, whereas closure denotes a global mechanism.

3. Closure is a function of both syntactic and semantic principles. (1987, 4)

In his explanation of the last of these, Agawu says that "The musical equivalent of poetic syntax is the set of rules that govern the succession of notes. For example, a ^2-^1 over V-I cadence offers the correct syntax for effecting a cadence." Or as below, from his most recent book, where Agawu says much the same: "a closed harmonic progression [that] constitutes the norm of coherent and meaningful tonal order" (109).

This progression, however, is hardly "syntactically correct" -- it shows the compromises necessary when melodic parsimony (move by step whenever you can, or not at all) conflicts with a strictly maintained four-voice texture (derived from continuo practice). The problem becomes obvious to the eye and ear if we put the alto or tenor at the top and move the soprano into the inner voices:

How to solve this without changing the number of parts? You can't. In the four solutions below, melodic parsimony is maintained but the final chord is incomplete (contrary to figured bass), as at (a) and (c). Or, Agawu's "syntax" is violated because ^2 retreats to ^3, as at (b) and (d).

What this suggests is that there will always be a conflict between the two-voice structure assumed by "^2-^1 over V-I" and the archetypal four-voice texture of figured bass. There is no reason to choose Agawu's "norm" with its damaged inner voices over (a) or (c) above with their incomplete final tonics. In fact, (b) and (d) would seem to be the best solutions, as they meet the requirements of both melodic parsimony and figured bass rules -- only the assertion of a very particular melodic requirement that arbitrarily applies parsimony and unidirectionality to just one voice can unseat them.

In the Attwood Studies, Mozart voices cadence chords differently than Agawu. Mozart calls the cadential six-four "accordo di quarta consonante" and the older-style dissonant vertical that would occupy the same accented position in a cadence the "accordo di quarta dissonante" (Heartz et al 1965, 21). See his voicings of the specific verticals involved in (a) and (b) below, respectively.

In a related document ascribed to him, Mozart also contrasts the older cadence with a 4-3 suspension over the dominant to the cadential six-four: the former is "contrapunctisch," the latter "modern (gallant [sic])," the obvious implication being that the latter replaced the former in practice) (Heartz and Mann 1969, 16-17). In those examples, too, the voicing differs from Agawu's "correct syntax."

Modern use of the term "cadence galant" comes from Charles Cudworth (1949), who ascribed its invention to the early 18th century Neapolitan opera composers and in particular to Leonardo Vinci. It seems likely, however, that the change was generational, as Daniel Heartz and Bruce Alan Brown point out ([2009]) -- and, according to Lucinde Braun (2007), it can in fact be found in French claveçin composers, among others, around the same time. It was this clichéd formula that Schenker eventually took for granted as a possible component of Urlinien: the cadential dominant figure appears without comment in Free Composition, Fig. 16 (the table of bass motions under the Urlinie from ^5).

Agawu asserts that his "closed harmonic progression" "is characterized by a sense of departure . . . and return, [or] motion from one (relatively) stable point to another (more stable point)" (2009, 109). Echoing Lerdahl and Jackendoff, Meyer, and others, he explains that "departure generates tension and arouses expectations, while return provides resolution and fulfillment of expectations." A century earlier, August Halm had said much the same, although, following the Ramellian tradition, he tends to attribute the essential qualities of tension/relaxation to the dominant chord itself ("Urkeim [der Kadenz] ist die Dominante mit ihrer inneren Bewegung zur Tonika" (5) [rough translation: "the core of the cadence is the dominant with its inner motion toward the tonic"]). His example (below) is described as "die primitivste Musik" but "zweifellos Musik! Es ist das erste Geschehnis, Leben der Töne, Bewegungsanstoß and -Abschluß! . . . . Die Kadenz ist, richtig verstanden, Grundlage und Urbild des Musizierens überhaupt!" (14-15) [rough translation: "the most primitive music, but unquestionably music! It is the first event, the life of tones, the incitement to movement and the end of movement. The cadence, understood correctly, is the foundation and the basic construct of music making itself!"]

Note, however, that Halm did not require a soprano note above or away from ^1 for his first chord. And we cannot appeal to "pure melodic principles," either -- every one of the cantus firmi that Fux uses for his species counterpoint exercises begins and ends on the finalis (modal tonic).

Clearly, Agawu's archetype is not archetypical -- it is a progression strongly interpreted according to a specific bias, which, whether accidentally or deliberately, erases the significance of the leading tone (^7). In an upcoming post, I will discuss the problem of the "two leading tones" and how that impinges on the question of the rising Urlinie.

References:

Agawu, Kofi. "Concepts of Closure and Chopin's Opus 28." Music Theory Spectrum 9 (1987): 1-17.

Agawu, Kofi. Music as Discourse: Semiotic Adventures in Romantic Music. New York: Oxford University Press, 2009.

Braun, Lucinde. "Das galante Fluidum – von der Tenorklausel zur "cadence galante'." Conference paper read at the 18th Congress of the International Musicological Society, Zurich, 12 July, 2007.

Cudworth, Charles. "Cadence galante: the Story of a Cliché." Monthly Musical Record 79 (1949): 176–8.

Heartz, Daniel, and Bruce Alan Brown. [2009]. "Galant." Grove Music Online. Ed. L. Macy (Accessed 1 December 2009). .

Heartz, Daniel, Erich Hertzmann, Alfred Mann, and Cecil Bernard Oldman. 1965. Thomas Attwoods Theorie- und Kompositionsstudien bei Mozart. Neue Mozart Ausgabe NMA X/30/1. Kassel: Bärenreiter.

Heartz, Daniel, and Alfred Mann. 1969. Neue Mozart Ausgabe X/30/1: Thomas Attwoods Theorie- und Kompositionsstudien bei Mozart, Kritischer Bericht. Kassel: Bärenreiter.

Schenker, Heinrich. [1935, rev. 1956] 1979. Free Composition. Trans. and ed. Ernst Oster. New York: Longman.

Halm, August. Harmonielehre. Berlin & Leipzig: Vereinigung Wissenschaftlicher Verleger, 1920. (Reprint of the 1905 edition.)

Ländler and deutscher, part II

The deutscher Tanz, or just Deutscher, is harder than the Ländler to pin down. It was probably a generic term for German dancing styles in the later 18th century -- Mozart's sets of deutsche Tänze, K. 509, 600, 602, 605, and 606, for example, include music that sounds in some cases like simplified (or metrically unsubtle) menuets, in others like Ländler, and in still others like 3/4-meter versions of contredanses. By Schubert's time, there was very little difference between menuet and deutscher. It was only after Schubert's death that the familiar, stereotyped form of the waltz arose, mostly thanks to the efforts of Lanner and Strauss, sr., in the 1830s and 1840s. It was also during that period that the title deutscher disappeared in favor of Walzer.

From the vantage point of the late 1820s, the "Strauss waltz" is essentially a sped-up Ländler -- very probably it would be most familiar to someone at that time as the "waltz" that typically closed a dance (Litschauer, XI). Before 1830, however, the deutscher was danced in much the same way as the Ländler: a promenade onto and around the room, a series of dance figures for couples, and a concluding "waltz" around the room along a line of dance (Litschauer, X). The only real difference was tempo.

If there is anything like a "typical" deutscher around 1820, D365n31 fits it. Note the rhythmic variety in melodic gestures and accents, the occasional but by no means obligatory use of the oom-pah left hand figure, and the processional "tutti" passages. Also consider how easy it would be to recast this as a menuet in the style of Haydn or Mozart.

In the graphic below, I have rewritten D779n13 as a deutscher. The tempo is marked as faster than the Ländler version in yesterday's post; if an entire dance was to be done in the circular turns we now associate with the waltz, the music would most likely be a deutscher.

Note that the actual D779n13 is neither typical Ländler nor typical deutscher. Perhaps one of the reasons for its distinctive charm--and motivation for either Schubert or the publisher to include it in D 779--is exactly that exquisite balance of types that would still have been familiar to an audience in the early 1820s.

The history sketched in these two posts is sufficient to the purpose here. It should be understood, however, that any history combining music and dance will be complicated, in this case all the more so because social dance fashions changed by the decade throughout the period in question, or roughly 1760-1840. Beyond this caveat, the one point I would like to emphasize is that histories of dance musics can never be written adequately -- or, in my view, with even minimal plausibility -- in isolation from the dance.

Reference:

Litschauer, Walburga, ed. Franz Schubert. Neue Ausgabe sämtlicher Werke, Series 7, part 2: Werke für Klavier zu zwei Händen, Band 6: Tänze I. Kassel: Bärenreiter, 1989.

Metrical reading (after London)

Today and tomorrow’s readings are based on theories with sharply opposed views of temporality in music. In Justin London's theory meter and rhythm are distinct. Meter is portrayed as cyclical, based on entrainment and other cognitive constraints. Meter is "time-continuous," patterned cyclically: once the listener is entrained through subjective rhythmization (14-5) by a minimal number of phenomenal events (an event at a beat level within perceptible range plus one set of subdivisions), meter recycles itself and thus continues "in mind" independently of phenomenal events unless undermined or contradicted by them. The issue for analysis is how well a meter is defined, how "thick" or "thin" it is ("one may characterize meters in terms of their hierarchic depth–that is, whether a meter involves a rich hierarchy of expectation on many levels at once, or only a limited set of expectations as to when things are going to occur" (25)).

I will work through an example, using not D779n13 but the well-known theme of Mozart's K. 331, I. We start with the establishment of meter through entrainment. To simplify discussion, I assume a tempo where a dotted quarter equals 60–tempo is crucial to London's theory because it determines the possible meters and the range of their rela-tionships. The first chord (a in the graphic) cannot establish meter in itself, nor can the sixteenth that follows–the latter is a subdivision perhaps, but of an unexpressed beat in a meter not yet established (b). The second chord repeats the first, and that in one respect is a weakness–the meter is still not established because the second chord is just as likely to be the second beat of a duple meter as the third eighth of a 6/8 measure (c). Only with the quarter note chord is the meter unequivocally set (as triple or compound duple, that is): we have now heard well-defined events on two beats and at least one of the triplet eighth subdivisions (itself supported by a still smaller value as a "pickup") (d).

The meter is now set, and Mozart continues to define it effectively through the quarter-eighth rhythm. Given the ubiquity of this figure across the entire theme, and the fact that Mozart even turns to continuous eighth notes in the second section, I would describe the meter in this theme as "thick," as heavily and continuously reinforced by phenomenal events. With the measure moving at 30 bpm (or 2000 ms), the upper threshold for perception of a (hyper)metric unit (6000 ms) would be reached by the end of measure 3. Thus, it is quite easy to maintain a palpable or immediate sense of hypermeter at the two-bar level, a perception that Mozart patently encourages. Beyond that, a regular hypermeter and the symmetrical proportions that can derive from it are abstractions, constructs in memory. Beyond this distinction between the immediate and the abstract, however, there is no need to separate meter from hypermeter; as London puts it, "the number of metric levels both above and below the beat can and does fluctuate, [and thus] there is no substantive distinction between meters and so-called hypermeters" (25); elsewhere he says that "having several levels of metric structure present above the perceived beat is no more extraordinary than having several levels of subdivisions below it" (19).

I find London's cyclical conception of meter appealing, in part because it respects distinctions between rhythm and meter (or between patterns of phenomenal events and processes of metric entrainment), in part because it is intuitively more satisfying than Lerdahl and Jackendoff's hierarchical model. London's cyclical conception of meter allows one, by contrast, to see that the heads of the longest time spans, "structural down-beats," "structural accents," and similar terms as Lerdahl and Jackendoff and others deploy them, are rhythmic/metric themes for hierarchy-based readings whose central task is to sort out the roles of the various temporal units that can be distinguished in hearing a musical performance.

The results obtained for K331, I, apply equally well to D779n13: meter is "thick," heavily and continuously reinforced by phenomenal events. The entrainment of meter happens in the introduction (as the dancers would require), and once the right hand part enters the metric levels of beat (quarter beats), subdivision (groups of eighths), measure, and two-bar hypermeter are maintained consistently throughout (even the right-hand hemiolas are consistent and readily subsumed in the ongoing meter). Only at the four-bar level is hypermeter inconsistent, but by now we know that trait of D779n13 well.

Reference:
Justin London. Hearing in Time: Psychological Aspects of Musical Meter. New York: Oxford University Press, 2004.