On Harmony and Meter in Brahms's Op. 76, No. 8Author(s): David LewinSource: 19th-Century Music, Vol. 4, No. 3 (Spring, 1981), pp. 261-265Published by: University of California PressStable URL: http://www.jstor.org/stable/746699Accessed: 02/02/2010 20:28

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first composition of importance in which these sonorities are systematically related to the principal features of the design.

Such an argument begets another: Liszt's composition is advanced, too, in its formal im- plications. The fantasy and the fugue are here allied with a modified sonata form to produce a kind of polymorphous formal experiment, one which was not without deep impact on music after Liszt. The B-Minor Sonata of 1853 was the next major formal experiment, in which non- sonata elements were introduced into a sonata form, whereas mutatis mutandis in the Fan- tasy and Fugue a modified sonata form had been imposed upon a non-sonata formal divi- sion. Liszt's efforts did not wait long for imita- tions, particularly in the Organ Sonata on the 94th Psalm and Piano sonata in Bb Minor by Julius Reubke, composed in 1857,28 and the

28For a brief discussion, see Newman, pp. 406-08.

first composition of importance in which these sonorities are systematically related to the principal features of the design.

Such an argument begets another: Liszt's composition is advanced, too, in its formal im- plications. The fantasy and the fugue are here allied with a modified sonata form to produce a kind of polymorphous formal experiment, one which was not without deep impact on music after Liszt. The B-Minor Sonata of 1853 was the next major formal experiment, in which non- sonata elements were introduced into a sonata form, whereas mutatis mutandis in the Fan- tasy and Fugue a modified sonata form had been imposed upon a non-sonata formal divi- sion. Liszt's efforts did not wait long for imita- tions, particularly in the Organ Sonata on the 94th Psalm and Piano sonata in Bb Minor by Julius Reubke, composed in 1857,28 and the

28For a brief discussion, see Newman, pp. 406-08.

organ works of the Weimar composers Karl Miiller-Hartung and Johann Gottlob Topfer.29 Multiple formal development was inherited also by Schoenberg in such works as Verkldrte Nacht,30 the First String Quartet, and the First Chamber Symphony. And the list could be ex- tended to other composers.

In many respects, then, Liszt's Fantasy and Fugue was prophetic. It stands as a forceful re- newal of sonata form and the tonal system, a system not yet exhausted by Liszt in 1850, but one considerably transformed. Unlike Meyer- beer's Jean, who was manipulated, deceived, mistaken, and misled, Liszt turned out to be no false prophet. *a'

organ works of the Weimar composers Karl Miiller-Hartung and Johann Gottlob Topfer.29 Multiple formal development was inherited also by Schoenberg in such works as Verkldrte Nacht,30 the First String Quartet, and the First Chamber Symphony. And the list could be ex- tended to other composers.

In many respects, then, Liszt's Fantasy and Fugue was prophetic. It stands as a forceful re- newal of sonata form and the tonal system, a system not yet exhausted by Liszt in 1850, but one considerably transformed. Unlike Meyer- beer's Jean, who was manipulated, deceived, mistaken, and misled, Liszt turned out to be no false prophet. *a'

29Examined in Milton Sutter, "Liszt and the Weimar Organist-Composers," in Liszt Studien 1 (Graz, 1977), 203-14. 30An analysis of this work as a double sonata form is pro- vided by Richard Swift, "1/XII/99: Tonal Relations in Schoenberg's Verklirte Nacht," this journal 1 (1977), 3-14.

29Examined in Milton Sutter, "Liszt and the Weimar Organist-Composers," in Liszt Studien 1 (Graz, 1977), 203-14. 30An analysis of this work as a double sonata form is pro- vided by Richard Swift, "1/XII/99: Tonal Relations in Schoenberg's Verklirte Nacht," this journal 1 (1977), 3-14.

On Harmony and Meter in Brahms's Op. 76, No. 8

DAVID LEWIN

On Harmony and Meter in Brahms's Op. 76, No. 8

DAVID LEWIN

In 1853 Moritz Hauptmann introduced to Western music theory the idea that the philosophical principles underlying metric structure are the same as those underlying the harmonic structure of tonality.1 While the Hegelian cast of Hauptmann's discourse has dropped out of fashion during the twentieth century, the notion that harmony and meter are two manifestations of one formal organiz- ing principle has remained very much alive in new guises. Stockhausen, for instance, pro- claimed just such an idea anew in the recent

'Moritz Hauptmann, Die Natur der Harmonik und Metrik (Leipzig, 1853); trans. W. E. Heathcote (London, 1888).

0148-2076/81/010261 +05$00.50 ? 1981 by The Regents of the University of California.

In 1853 Moritz Hauptmann introduced to Western music theory the idea that the philosophical principles underlying metric structure are the same as those underlying the harmonic structure of tonality.1 While the Hegelian cast of Hauptmann's discourse has dropped out of fashion during the twentieth century, the notion that harmony and meter are two manifestations of one formal organiz- ing principle has remained very much alive in new guises. Stockhausen, for instance, pro- claimed just such an idea anew in the recent

'Moritz Hauptmann, Die Natur der Harmonik und Metrik (Leipzig, 1853); trans. W. E. Heathcote (London, 1888).

0148-2076/81/010261 +05$00.50 ? 1981 by The Regents of the University of California.

past.2 I propose to discuss in this connection measures 1 through 15 of Johannes Brahms's Capriccio in C, op. 76, no. 8. The score is re- produced as plate 1 (p. 265).

Example 1 illustrates some salient features of harmony and meter in the passage, using the bass line as a guide. To fit the middleground metric structure of the music into familiar no- tational templates, I give Brahms's rhythmic notation in reduction or diminution. A mea- sure of the piece, comprising three half notes or two dotted halves, becomes three quarter notes or two dotted quarters in the example. And a group of measures in the piece becomes a hypermeasure. The first hypermeasure, for

2Karkheinz Stockhausen, ". .. how time passes ...", trans. C. Cardew, Die Reihe 3 (1959), 10-40.

past.2 I propose to discuss in this connection measures 1 through 15 of Johannes Brahms's Capriccio in C, op. 76, no. 8. The score is re- produced as plate 1 (p. 265).

Example 1 illustrates some salient features of harmony and meter in the passage, using the bass line as a guide. To fit the middleground metric structure of the music into familiar no- tational templates, I give Brahms's rhythmic notation in reduction or diminution. A mea- sure of the piece, comprising three half notes or two dotted halves, becomes three quarter notes or two dotted quarters in the example. And a group of measures in the piece becomes a hypermeasure. The first hypermeasure, for

2Karkheinz Stockhausen, ". .. how time passes ...", trans. C. Cardew, Die Reihe 3 (1959), 10-40.

261 261

REHEARINGS REHEARINGS

1 m. of piece= . of example 2 3 4

m"U ,I^ 1 j J j Ij ,

(repeat)

L-4 4 i 4 i : i I Jl _ J. I J. J . J-4 4 ij ^ ibetc - t. ':. "- t- REHEARINGS

Example 2

structural ambivalence involving the melodic functions of those tones in the bass line. Example 2, reducing example 1 to yet another metric level, focuses the issue. Does the F at the first barline of example 2 resolve as a Phry- gian second degree to the e at the second bar- line? Or is that e rather a neighboring leading tone to the F, moving back to F at the third bar- line of the figure, across the repeat?

The Fs and es at the barlines of example 2 of course function in tandem with the governing force of F and e harmonies, already discussed, over the antecedent and consequent sections of the passage. Now all these ambivalent rela- tions serve one larger function: to present ex- pository material for a composition in C major. The C triad is notably absent; even the tonality of C is only suggested in the foreground. Nevertheless, C tonicity is implicit as a Ver- mittlung between the contending F and e events. Melodically, both e-to-F and F-to-e can function idiomatically in C. And harmonically, the F and e chords balance each other around the C on the circle of fifths: F is one step on the flat side of C, e is one step on its sharp side. When one listens to the passage as a whole in C, it is clear that e is a dominant substitute. The approach to the e harmony through its dominant in m. 8 parallels the approach to the G harmony through its dominant in m. 4 (though the G root-position chord has fewer beats of preparation).

The indirectness by which the tonic key of this piece is defined corresponds to an even greater indirectness, that by which its "tonic meter" is defined. Examining the rhythmic foreground of the music (see plate 1) we note that, though the piece has a 6 time signature, 6 foreground meter is projected clearly only at the consequent, e-minor passage in mm. 9-12. The thematic process would lead one to think of this material as "secondary" rather than tonic-an idea supported by the harmonic turn to the sharp side on the circle of fifths. If we examine the "primary" thematic idea, we note

a clear grouping of motivic contours in mm. 1-2 and 5-6 that would lead us to write 2, rather than 6, as a time signature. (The sycopa- tions in the right hand do suggest metric insta- bility, and specifically the possibility of accent- ing the fourth quarter-beat of the measure. Still, the right hand presents internal groupings of 3 x 2 quarter notes, just like the left.)

The metric situation is further complicated by the hemiola in mm. 3-4. The harmonic rhythm clearly outlines 3 x 2 half notes here, rather than 2 x 3 halves. This metric event is triggered precisely by the arrival of the impor- tant bass F at the barline of m. 3. (The hemiola is foreshadowed by the anticipatory C in the bass two-thirds of the way through m. 1.)

At other points in the music, meter be- comes ambiguous and modulatory. Mm. 7-8, for example, start to recreate the hemiola of mm. 3-4; but the pattern changes during m. 8, preparing the 6 metric feeling which m. 9 is about to project strongly. Note that the metric modulation here, from hemiola to , coincides with the tonal "modulation," from the F har- mony of m. 7 to the e harmony of m. 9.

In order to get a sharper focus on all these metric complexities, as they interact with tonal events, it will be helpful to inspect ex- ample 1 once more. This figure diminutes the rhythmic notation of the piece, and repre- sents the measure groups of the piece as hypermeasures. So mm. 1-2 of the piece, a group of two 2 measures, are notated as one hypermeasure of 2 x 3, that is, as one 6 hypermeasure. Similarly, the group of mm. 9-10, two 6 measures of the piece, reduces in the example to 2 x 6, or one 12 hypermeasure. And the hemiola group of mm. 3-4, compris- ing three whole notes, is notated as one 3 hypermeasure.

As I hear the piece, a "tonic" quality adheres to the 6 hypermeter of hypermeasures 1 and 3. These hypermeasures present the in- cipits of the principal thematic idea; they also contain the Cs in the bass-line, along with the

263

. -. 1

. -'I

b. 6 4

3 2

Figure 1

bs that inflect them. As one metric contrast to these tonic 6 hypermeasures, we have hypermeasure 2, with its 3 hypermeter. This span is triggered by the strongest subdominant tonal event of the passage, the bass-and-root F. A different metric contrast to the 6 hypermeter is provided by the 12 hypermeasures. These spans are triggered by and prolong the big dom- inant tonal event, bass-and-root e. Hypermea- sures 4 and 7 modulate respectively from 6 (3?) to 2 hypermeter, and back. In sum: considering the 6 hypermeter as psychologically "tonic" in this passage, we can fancifully think of the 3 hypermeter as "subdominant" because of its association with the big F bass-root beat; we can likewise think of the 12 hypermeter as "dominant" because of its association with the big e bass-root beat.

What makes this interpretation more than simply fanciful are two striking formal aspects of the arrangement. First, both the metric rela- tion of 6 to 3 and that of 6 to 12 involve the play of the ratios 2:3 and 3:2. And these are the same ratios involved in pitch relationships of a fifth, the dominant and subdominant relations to a tonic pitch. Second, the relation of 6 to 12 inverts, in a certain sense, the relation of 6 to 3. And this feature of the rhythmic situation is numerically analogous to the inversion of tonic-dominant and tonic-subdominant pitch relations. Figures la and lb will help clarify these matters.

In figure la, an abstract measure, as a span of time, is divided by abstract 6 meter into two subspans, and by 2 meter into three subspans. That is, 6 articulates duply what 3 articulates 4 2 triply. Figure lb displays another abstract mea- sure, at twice the scale of figure la. Each half of this measure is articulated triply by 6 and duply by 1, producing twin inverted forms of the structure pictured in la. The two figures, in 264

sum, show how the metric relations are both "rhythmic fifth relations," involving propor- tions 2:3 and 3:2. They also show how the sec- ond relation is essentially the inversion of the first, if we allow for the "rhythmic octave" that produces a double image in figure lb.

We must not try to push too far the tonal analogy for these figures. For instance, if we were to regard the 6 spans of the pictures as modeling "tonic" modes of vibration for strings, the model would suggest a "dominant" function for the 3 spans of figure la, and a "subdominant" function for the 18 spans of lb. We have seen, however, that Brahms presents the 3 hypermeter as co-extensive with sub- dominant (F) music, and the 12 as co-extensive with dominant (e) music, thus reversing the as- sociations suggested by the model. One might argue that the reversal could be justified by in- verting ratios of string lengths, to become in- verse ratios of frequency numbers; one could also argue that the reversal is plausible in itself, considering that the piece already exploits in- verted relationships of various sorts in various ways. But I should not like to pursue such ar- guments with fervor, amusing as they may be. I do not feel, that is, an urge to argue exact for- mal isomorphism in the metric and tonal structures of the passage. Rather at issue, I should say, is the point I made in my opening reference to Hauptmann, attributing to him the idea that the philosophical principles un- derlying metric structures are the same as those underlying the harmonic structure of to- nality. It seems to me that the passage under discussion strongly exemplifies just this idea.

We have seen, namely, that pitch centricity over the passage is manifested as a Vermittlung between the extremes of F on the one hand (m. 3) and e on the other (m. 9), respectively one step to the flat side and one to the sharp side of

19TH CENTURY

MUSIC

a.

REHEARINGS 8.

Capriccio.

Plate 1: First page of Brahms's Capriccio in C major, op. 76, no. 8. Reproduced from the first edition, published by Simrock in 1879. Courtesy of the McCorkle Brahms Cataloguing Project at the Department of Music, University of British Columbia.

the tonal center. Those steps involve explicit or implicit motions of a structural fundamen- tal bass by fifths, displaying complementary ratios of 2:3 and 3:2 in the tonal domain. The same complementary ratios, when interpreted rhythmically, are evident in the relations of 4 hypermeter to 3 and 12. And the tonicity of 6 hypermeter for this passage is manifest not only in its association with primary thematic material, but also in its function as a Ver- mittlung between the complementary ex- tremes of 3 and 12. At one rhythmic extreme, the 3 hypermeasure begins with the prominent bass F at m. 3, also a tonal extreme. At the op- posite rhythmic extreme, the 1 hypermeasures begin with the big bass e of m. 9, the opposite tonal extreme.

Though my analysis has asserted the 6 hypermeter as "tonic" for the passage, one should bear in mind that the 6 hypermeasure symbolizes a group of two 3 measures of actual music. So the 6 hypermeter, despite its local tonicity, does not reflect the notated time- signature. The latter is reflected rather by groups of "real" 6 measures, which are sym- bolized as the 1hypermeasures. And those, so far, are associated with secondary thematic material in a dominant(-substitute) key. The complexities to which this state of affairs gives rise, as the piece continues, are worth explor- ing. The curious reader is referred particularly to m. 61 (seven measures from the end) as a point of departure for such exploration. .

265

' ii;~'~ CLLCtLL~,r#rjJS i ty. ~~~~~~~~~~~~~~~~~~~~~~~~~~

~'JI L r' r I / /

14

Article Contentsp. 261p. 262p. 263p. 264p. 265

Issue Table of Contents19th-Century Music, Vol. 4, No. 3 (Spring, 1981), pp. 191-284Volume Information [p. 284]Front MatterThe Mirror of Tonality: Transitional Features of Nineteenth-Century Harmony [pp. 191 - 208]Liszt's Saint-Simonian Adventure [pp. 209 - 227]Liszt's "Lyon": Music and the Social Conscience [pp. 228 - 243]RehearingsChopin, Prelude in A Minor, Op. 28, No. 2 [pp. 245 - 250]Liszt, Fantasy and Fugue for Organ on "Ad nos, ad salutarem undam" [pp. 250 - 261]On Harmony and Meter in Brahms's Op. 76, No. 8 [pp. 261 - 265]

Reviewsuntitled [pp. 266 - 270]untitled [pp. 270 - 273]untitled [pp. 273 - 276]untitled [pp. 276 - 280]

Comment & Chronicle [pp. 281 - 283]Back Matter