More on Forms with Refrains (3)

This is a follow-up to the post on the contredanse La Griel. I wrote there: "Contredanse folios published by the dancing master La Cuisse and reproduced on the Library of Congress American Memory site contain two remarkable fold-out graphics that collate music, text and graphic descriptions of figures, and drawings of the dancers."

La Griel, of course, is one: La Bionni is the other. Virtually everything said in the earlier post about La Griel applies equally to La Bionni, including the varying lengths of the figures and the grand rond or rond ordinaire danced to the first strain and its repetition. The music as performed (five strains with repeats, in an ABACA design) is reproduced below. (Click on the thumbnail for a larger image.)

From all this, three points may be made. First, it is hard to overemphasize the importance of the more or less formal (or ritualized) frame for the dance (in the rond ordinaire at the beginning and courtesies at the end). Second, it is equally hard to overemphasize the importance of the refrain. Third, although the musician is tempted to say that the refrain "structures" the music, that is only half the story, because a refrain in the music by no means signals a repetition of a figure in the dance.

More on Forms with Refrains (2)

Contredanse folios published by the dancing master La Cuisse and reproduced on the Library of Congress American Memory site contain two remarkable fold-out graphics that collate music, text and graphic descriptions of figures, and drawings of the dancers. For La Griel, I have reproduced the music below, labeled the strains and phrases, and then pulled out and labeled the music as it is shown in the large graphic. Note that the music is played as marked in the score, en rondeau, and dance figures vary in length from 2 bars to 8 (a gap in the music notation corresponds to a new figure in the dance). The greater complexity (compared to the long-dance style) is possible with a smaller group of dancers in the more formal quadrille square-dance structure, which was broadly speaking a compromise between the skilled, formal couple dancing of the menuet and the informal, highly social English long dance.

Music as distributed over the 8 figures of the dance:

La Cuisse published his contredanse folios in the mid-1760s, the French style became popular in Vienna in the early 1770s at the latest, and Bülow's manuscript compilation was made in the early 1780s -- therefore it is reasonable to assume that we are speaking about closely related practices. By Schubert's time, things had changed -- the menuet was often reduced to a comical Grossvater dance, and the formal quadrille had by and large been superseded by the decidedly less formal cotillon, or else adopted the latter's tendency to mix dancing with party games. More than ever, the design of a dance was in the hands of the caller or lead dancer (Vortanzer), and the music was shaped accordingly (and sometimes on the spot). As Schubert was playing for cotillons, then, he would take his cues from the Vortanzer (from the reminiscences, this was usually Josef von Spaun).

In this environment, the reprise was the principal device available for an aural structuring of the dance to complement the sequence of dance figures; the refrain, on the other hand, was a way of extending and enriching a particular sequence. The refrain and musical coda are obviously closely related -- the only real difference being that the coda usually consists of stereotypical cadence gestures mixed with material from the preceding sections , where the refrain is substantially new material. It's entirely possible that the refrain was not danced -- along the lines of the published waltzes of the 1830s and later, an instrumental introduction was likely (whether a prelude in the old manner, a vamp to establish rhythm, or a more elaborate piece) and -- if the Vortanzer directed it -- a final strain not danced was possible. One can, for example, easily imagine the dancers standing and clapping in rhythm to the yodeling refrain of D734n11.

The comments above can be regarded as an addendum to the post on performance designs.

More on Forms with Refrains

This is an addendum to last week's post on forms with refrains. Here are two contredanses from a manuscript collection preserved in the Royal Library, Copenhagen: the volume is simply labeled "Dances 1782-84" with the name Johan Bülow: a PDF file can be accessed through IMSLP.

Note that the first piece has two strains and four dance figures are described (that's one per strain with repetitions).

The second contredanse has three strains and six corresponding figures in the dance.

From the instructions (especially the mention of three couples), it seems clear that the music is intended for dancing in the English long-dance manner, not the square or round forms of the French quadrille. That means the music as given is probably only the barest outline of what actually happened when the music was played for dancing. (At the least, one would expect the strains to be played en rondeau, that is, with repetitions of the first strain following each successive strain.) On the other hand, the arrangements are clearly for keyboard (others in this and related collections are for violin; a few are marked "Flauto"): these could not be used in a hall but instead for private dancing occasions, including dance lessons for members of the Royal family or others in the Court. The simplicity of the given design would suit the needs of pedagogy.

On the Laendler in D734

Here is another passage from Litschauer and Deutsch (39; trans.):

Among Schubert's dances in triple meter are about 130 Ländler, composed between 1815 and 1826 and by and large preserved in manuscript sources. In contrast to the schottisches, german dances, and waltzes, however, the Ländler do not appear among Schubert's albumleaves or dedication compositions, and thus it is not suprising that these dances are rarely mentioned by the composer's friends and acquaintances. Furthermore, as two journal entries by Franz von Hartmann indicate, Ländler were commonly confused with German dances. (In both instances, the reference is to Schubert's "16 Ländler, opus 67" D734, which were published by Diabelli in December 1826 under the title "Hommage aux belles Viennoises: Wiener-Damen-Ländler.")

17 December 1826 (Sunday): By Spauns, where Gahy played brand-new Schubert German dances (with the title "homage to the belles of Vienna," which made Schubert quite angry).

6 January 1827: We went to Spauns, where we were invited, along with Gahy, to breakfast. . . . then Gahy played two superb sonatas by Schubert and the German dances that had enchanted us so at M on the 17th.

Hartmann probably should have known better, as few collections outside the first dozen or so numbers in D365 and D779 represent the Ländler style more consistently, but in his defense we should remember that Deutscher was not only the genre title for a particular group of dances and their musics, but also the family name for all "waltzing" dances.

Several points can be made about D734, many of them reminders of earlier posts:

(1) the boundary between Ländler and Deutscher was always fuzzy with respect to musical style in the urban dance cultures, being reduced by the 1820s to sweeter/quieter/slower (Ländler) versus formal/louder/faster (Deutscher).

(2) in dancing, the types were often intermingled to fit alternations between couple and group dancing. In D734, for instance, n2 comes as close as any Schubert dance to realizing the type of the rural Ländler in the late 18th century: D major, I and V only, violinistic melody with many third doublings. But n16 is clearly a Deutscher that would accompany the obligatory processional that ended an extended dance/cotillion.

(3) the "sweeter/quieter/slower" criterion is muddied by imitations of the Schnadahüpfl episodes in rural dancing. This alternation is clearly at work in D734n1: the first eight bars of Ländler are interrupted by the same music abruptly transformed into a loud, drone-accompanied Schnadahüpfl, then the Ländler returns. Remember that this is also what happens -- down to the direct mediant key shifts -- in D779n13 and D145n7.

Reference.

Litschauer, Walburga, and Walter Deutsch. Schubert und das Tanzvergnügen. Vienna: Holzhausen, 1997.

Litschauer and Deutsch on the Ländler

Here is a free and partial translation from the section on choreography of the Ländler (48-51):

About the dance performance of the Ländler during the Biedermeier period there remains considerable ambiguity. [Like the Deutscher,] the genre title Ländler represents a category encompassing both the so-called "almeric" (alpine) couple dances ("Steirische," "Wickler" "Schuhplattler") and the "ländlerisch" (rural) group dances. We can say with certainty only that the Ländler is a figure-dance for whose performance a moderate tempo is assumed.

Ernst Hamza has noted that the Ländler originally was a couple dance in which "the individual dance couples...had a large individual space at their disposal." The rich choreography of the almeric dances was (and still is) characterized by a number of figures with embracing movements, so that this Ländler type often appears as a lovers' dance. One can infer from dance illustrations in the Biedermeier period that similar arm figures were also typical of social dance, where in fact they were integrated into not the Ländler but [the urban dance most directly derived from it,] the "Straßburger." [the figures in this blog's logo are illustrations of this dance]

[The Ländler was apparently already being danced in Viennese society as early as 1790.] Around 1818 one can trace several variants of this dance in the repertoire of middle class house balls, where it was often danced in rural costumes. Because of the decorative character of the arm figures, the "Steierische" enjoyed great popularity at these festivities.

In the dance instruction manuals of the early 19th century the Ländler is usually called a "Länderer" and its figures are labeled "Ländern."

Reference.

Litschauer, Walburga, and Walter Deutsch. Schubert und das Tanzvergnügen. Vienna: Holzhausen, 1997.

more from Wilmot on dancing

Here are three more excerpts from Martha Wilmot's Letters concerning dancing. The first and second come from early in their time in Vienna.

The Spanish Ambassador's ball: The Empress did not arrive till late, that is, till half past nine. After sitting a few moments [she] rose, and followed by her Grande Maitresse and Grand Maitre, she went thro' the assembly room, talking to everybody. How those high people contrive to find something appropriate to say to so many is my astonishment, and She seems to be quite gifted in this way. When she had talked to almost everyone she proceeded to the ball room. Then begun the waltzes. There were not many dancers, except the Court, but if they were not glittering Waltzes never did I see any. . . . The Imperial party retired at eleven, and then begun the fun of the natives, who danced more freely with their equals. (46)

To her sister-in-law, January 1820:

I dare say you imagine us very frisky people, eternally gadding abroad, but you are mistaken if you do, for on an average I think we are 4 or five Evenings out of the seven quietly at home, but when we do go, tis something to make a figure in a letter, for example, the English and French Ambassadors balls, which we have attended, both of which were uncommonly brilliant, gay, and agreeable. One country dance is always danced, and then Waltzes and quadrilles only.

And, finally her account of Carneval season 1825:

All the balls that are given in the course of the year are given during the Carnival, which begins the 1st January and ends Ash Wednesday. This year the Archbishop would not allow it to begin so soon, and it lasted not quite 5 weeks. While it lasts the young people almost dance themselves to death, and then the last thing is a Ridout [Redoute], where the cram and mob is suffocating, the dancing and music maddening. Twelve O'Clock strikes! It announces the arrival of Ash Wednesday! The music makes a sudden stop, the sudden pause and quiet which follows is awful-it lasts a moment, when the buzz which succeeds is worse than the honest ball music and noise. . . .

I do not enter much into the gaietys of the Carnival. You must know that nothing would be easier than for us to go to a ball or two every night, but as our dancing days are over and our childrens dancing days are not come, the stupidity from want of interest is very great, and the expence of dressing very great likewise, added to which [my husband] William dislikes it, and in a wicked town like this I ought to be too happy that his home is his favorite ball room. . . . But my grand delight was the Opera. . . . I have been at 7 or 8 Operas this year and they are allowed to be the very best filled up opera's in Europe, as all the performers are excellent and 2 or three quite first rate. [Our daughter] Catharine begins to enjoy an Opera and a concert, so I take her to form her taste.

Reference.

Wilmot, Martha. Ed. by the Marchioness of Londonderry and H. M. Hyde. More letters from Martha Wilmot; impressions of Vienna, 1819-1829, relating her experiences in the brilliant cosmopolitan society of Vienna as the wife of the Rev. William Bradford, chaplain to the British embassy, during a period when Austria was the political and social centre of Europe, and including a journal of a tour in Italy and the Tyrol, and extracts from the diary of her elder daughter Catherine for 1829. London, Macmillan and co., limited, 1935.

Style topics in D145n7

In this entry, I wrote about the topical contrast in the first strain and contrasting middle of D145n7:

A simple diatonic mediant move (effecting the transformation R twice) is aligned with formal design in an early ternary waltz that also happens to contrast Ländler and deutscher traits (the former in the main theme, the latter in the contrasting middle) using sharp dynamic contrast to make the point unmistakably.

"Deutscher" here was a bit too confident -- I was relying on expressive and functional distinctions that often appear in and between Schubert's dances. First, recall that "deutscher" was a relatively broad category referring -- especially very early in the nineteenth century -- to all the waltzing dances. It was, in effect, the German "back-translation" of the French appellation from the 1760s, allemande (in contredanse allemande).

Second, "deutscher" was used more narrowly for music that had the processional (that is, somewhat formal) character of the menuet; by 1810, it was often impossible to tell the two apart -- to a composer, the deutscher was often just a menuet with few of that genre's long-since-clichéd gestures. It was the contrast between the processional "waltz" (deutscher) and the romantic couple dance of the Ländler that was clearly meaningful to Schubert and that I was relying on.

But, third, the foot-stamping segments of a folk dance could also be represented along with the drone instrument (bagpipe, Dudelsack, etc.) that accompanied folk (rural) dancing well into the nineteenth century (Petermayr, 83-84).

In other words, here Schubert is offering us two very different sides of his tune: as sweet Ländler in the first strain, but probably as accompaniment to rural stampfen thereafter, not to a more refined urban processional dance.

In the course of this, he might even have been duplicating the contrasting segments of rural or lower-class group dancing. Petermayr quotes a description of such dancing from later in the century (NB: the segments are marked by numbers in square brackets):

The string players have tuned their instruments and begun to play dance music in three-quarter time with their characteristically piercing tones, while they stamp their feet in duple time. [1] The dancers don't hold back: pair on pair they step into the line of dance and go some steps forward, following the beat, man and woman side by side (specifically, with the woman on the outside). [2] Then they grasp hands and make several turns [or figures [the word is Schwenkungen]], so that the woman appears briefly on the inside then again on the outside of the line. Then both raise their arms high above their heads and the woman turns herself once under the man's arm. [3] Then both settle back [to side-by-side position] and execute several figures, as before. [4] Again the arms go up and the woman turns quickly twice, so that her skirts swirl upward and out. [5] Each couple then embraces [that is, takes a clasping hold] and turns waltzing in a circle. [6] Again the couples settle back, but now the dancers move forward stomping on the floor so vigorously that the windows shake and the dust rises. While doing this they clap hands in time, call out, and sing in chorus the powerful, not easily forgotten "Schnadahüpfl" [also known as "Vierzeiler" -- commonly known bits of verse, sometimes nonsense]. [When all this is done,] the couples change, as each woman moves forward up the line to the next man, and the whole sequence begins again. This is repeated as often as there are dancing couples, so that at the end each man has his original partner. (94-95; trans.)

Reference.

Petermayr, Claus. "Nieder- und oberösterreiche Quellen zum Volkstanz im Biedermeier." In Harrandt, Andrea, and Erich Wolfgang Partsch. Tanzkultur im Biedermeier: wissenschaftliche Tagung 1. bis 2. Oktober 2004, Ruprechtshofen, N. Ö, 75-96. Series: Publikationen des Instituts für Österreichische Musikdokumentation, vol. 31. Tutzing: Hans Schneider, 2006.

The Sound of Dancing: update

The answer to the question posed in the previous post (Did Schubert's friends change shoes for dancing?) appears to be: No. Lightweight shoes, often without heels, were the fashion. (Whether they were always of cloth, or could be of leather, is unclear.) Sturdy covering boots and shoes were worn when going outdoors. Buxman: "fashion [in shoes] changed -- throughout the first half of the nineteenth century one used flat footwear, shoes with cross straps, cloth shoes or boots" (185; translated).

Here are two details from Viennese drawings, the first from 1816, and other from 1827.

We can assume a consistent style of dress in Vienna through the period of Schubert's adulthood, as Parisian fashions were dropped in 1815 (Congress of Vienna; end of the Napoleonic Wars) and then almost as quickly adopted again in 1830 (July Revolution).

Writing about Carneval 1826, Martha Wilmot (Mrs. William Bradford) describes in great detail a rather unusual costume ball that consisted of 12 very elaborate walking tableaux (she does not mention dancing but as she labels some of the tableaux "quadrilles" it is likely they danced as well as marched). In the paragraph about her own dress, she mentions "white satin shoes and broad flat pink saddle bows" (239). After the final tableau, however, general dancing started, and all characters, classes, and ages intermingled, in the most informal manner of the contredanse. At 2:00am a supper was served. The party was given by the British ambassador; Wilmot was the spouse of the embassy chaplain. (She reports that by request of the Emperor the entire series of tableaux was repeated in the palace the following evening and "the quadrilles for want of dancing Masters as Heralds to guide them, got into . . . glorious confusion" (240); also that "after the Imperial family had seen the quadrilles there was a little dancing in the Crown Prince's Apartment" (241).

Wilmot also mentions dancing in the context of a typical day for the children and their governess. (Wilmot, Blanche, and Catharine are the Bradfords' three children. ) Note particularly the promenade (the polonaise) that offers the characteristic formal close to a session of dancing (equivalent to the procession of couples waltzing about the room to a deutscher Tanz).

The governess "makes both Wilmot and Blanche say lessons twice a day, in french, then she can practice them in dancing, teach work, and superintend . . . their [dancing and] other Masters. She dresses them for dessert, and comes in with them. After sitting about half an hour, I get up and announce a ball; [the governess] then waltzes with Catharine while I play some excellent waltzes that I have got. Then she waltzes with Blanche, (in fun) who will be an exquisite dancer, the little manner of her in setting about it is so admirable. The Squire has his turn [and] when this is ended [he] leads out one in a polonaise, the others follow, and so they proceed to the nursery--after which they sup, tell stories, and the two youngest go to bed. (83)

Alas, this report is from September 1820, before Schubert's D365 was published, but as the Bradfords remained in Vienna till 1829, it is entirely possible that she "got" music of his and played it at some later time -- she reports that the family always had a (rented) pianoforte in the house.

[note added 5-19-10: the longevity of the polonaise as a formal or processional dance is attested by Barbara Boisit's reproduction of the sequence of dances (Tanzordnung) for the first ball of the Gesellschaft der Musikfreunde (1830): the evening was divided into two halves with an hour's rest inbetween -- the first was polonaise, waltz, waltz, cotillon and galop, waltz; the second shuffled the dances but kept the formal dance at the head: polonaise, waltz, cotillon and galop, waltz, cotillon and galop (158, illustration). The same organization's ball for 1847 was considerably more complex, but still placed the polonaise at the beginning of the first part: polonaise, waltz, waltz, quadrille, waltz, quadrille, waltz, quadrille, mazurka, quadrille, waltz. The second part consisted of waltz and polka, quadrille, waltz, quadrille, waltz, menuet (!), quadrille, waltz and polka (Legler and Kubik, 94 illustration).]

References.

Wilmot, Martha. Ed. by the Marchioness of Londonderry and H. M. Hyde. More letters from Martha Wilmot; impressions of Vienna, 1819-1829, relating her experiences in the brilliant cosmopolitan society of Vienna as the wife of the Rev. William Bradford, chaplain to the British embassy, during a period when Austria was the political and social centre of Europe, and including a journal of a tour in Italy and the Tyrol, and extracts from the diary of her elder daughter Catherine for 1829. London, Macmillan and co., limited, 1935.

Buxbaum, Gerda. Mode aus Wien, 1815-1938. Salzburg: Residenz Verlag, for the Hochschule für Angewandte Kunst in Wien, c1986.

Boisits, Barbara. "Der erste Ball der Gesellschaft der Musikfreunde in Wien im Jahre 1830." In Boisits, Barbara, and Klaus Hubmann. Tanz im Biedermeier: Ausdruck des Lebensgefühls einer Epoche, 151-166. Proceedings from the Symposium Musizierpraxis im Biedermeier: Tanzmusik im ländlichen und städtischen Bereich, Graz, Austria, 26.-27. März 2004. Series: Neue Beiträge zur Aufführungspraxis, vol. 6. Vienna : Mille Tre Verlag Robert Schächter, 2006.

Legler, Margit, and Reinhold Kubik, "Anmutige Verschlingungen. Tänze des Vormärz: Quellen – Notation – Ausführung." In Boisits, Barbara, and Klaus Hubmann, 89-131.

The Sound of Dancing

In an earlier post on the geography of dancing (that is, the physical spaces in which Schubert improvised/played dance music) I wrote the following:

The distinct timbres of the three main registers on contemporary pianofortes would be audible nearby, less so on the dance floor, where the swishing of clothes and muffled swish-slide of light cloth dancing shoes would mingle with the music.

Since writing that sentence, I have been wondering about those shoes. I wrote "light cloth dancing shoes" (that is to say, shoes of a fabric, shape, and weight similar to modern ballet slippers) because those are recognized as the standard from historical sources (dance instruction manuals and iconography). Here is a close-up from the rightmost couple in my logo graphic. This comes from 1808 and so can reasonably be regarded as typical at least into the early 1820s, and the dancers are dressed in a way that corresponds to the social class of Schubert and his friends.

A dance party (house ball) was not like a Clara Schumann recital -- strictly ordered, staid, and quiet. And since one of the few predictable elements would have been the alternation between dancing and eating/drinking, one has to ask whether the participants changed their shoes from one to the other. Given the protocols for dress, it would seem uncouth (or else youthfully rebellious) to wear dancing slippers while eating and talking. If Schubert's friends took the time to change their shoes, that action would would have affected the timing and process of the dancing and therefore also of Schubert's playing: it would necessarily articulate or "formalize" the dancing -- setting a particular dance segment off, as when a modern dance band takes a break. For Schubert, the inclination to group his waltzes by some (any) sort of connecting logic would have increased at least as much as with the "endless cotillions." In fact, perhaps more so, as he would have had more opportunity to organize distinct, small sets in the dance-trio(s) mould.

D924 and dancing

The last two blog entries, which contrasted traditional Urlinie readings with those based on an Ursatz manqué, made an assumption that is typical of these modes of analysis but is questionable, especially for waltzes (or other small-scale pieces, such as songs). Far from being the staid forms that tie the chaos of the foreground to the eternal, these backgrounds are highly contingent -- fragile and easily disrupted. We've met some of the devices before: the stability of its tonal "reference point" -- whether upper voice or bass -- is quickly undermined if it is played as trio to another dance, or enhanced if it is given a trio and a subsequent da capo.

In the double-tonic numbers of D924 there is even another possibility -- that the strains themselves were detached from their companions and played in differing combinations. This is of course speculative -- an extension "backwards" to Schubert's improvisation practice -- but one does find such "floating strains" in Schumann's Papillons, for example, and the topically uniform character of most of D924 makes its both easier and more plausible as well.

I have assembled below a dance-sequence that uses the first strain of n3 as the refrain. More repetition or extension would probably be necessary, but even in this form up to three minutes of dancing would be available. The sequence is n3, a, b, a -- n2, all -- n3, a -- n5, all -- n3, a -- n4, all. The key sequence is c#, E, c# - E - c# - A - c# - A.

The geography of dance music

I am using "geography" here to denote the immediate physical environment of Schubert's playing -- the piano, Schubert on a chair, anyone not dancing standing near him, the dancers coming by relatively close, the sound of the room, the shifting groupings and activities of the participants.

Given that Schubertiades took place with audiences anywhere from a few to a hundred, we have to assume that the physical spaces for dancing varied greatly, too. In a small space -- a drawing room of one of his friends' apartments -- the piano would probably be small, too, square. Chair with a back, not a modern-style piano bench. The piano positioned either along a side wall or, if there is space, angled out into the room (as in Kupelwieser's watercolor). The amount of resonance in the room would vary greatly, depending on wall coverings and the number of people, but would probably be fairly high since the floors would not be carpeted (or any carpets would be drawn back for the dancing).

Schubert playing, looking occasionally to the side at the dancers, especially the Vortänzer (the lead couple), and listening in case the Vortänzer call for a different figure, dance, or a pause (common in longer dance sessions), during which Schubert might continue to play or might stop, too. Persons not dancing, male or female, sitting or standing close by, occasionally talking to one another or even making brief comments to Schubert on his improvisations or requests to hear familiar dances. The distinct timbres of the three main registers on contemporary pianofortes would be audible nearby, less so on the dance floor, where the swishing of clothes and muffled swish-slide of light cloth dancing shoes would mingle with the music. The shapes of the dancing would have varied, from couples dancing freely within the dance space, couples moving in a "round dance" format (around the room along a line of dance) to chain dances or even something like the "parlor game" formats of the quadrille. Windows closed, perhaps shuttered against the night.

In breaks, food and perhaps the light, young Austrian white wines of which Schubert was said to be particularly fond. He was a "lively" drunk, and it would probably have been difficult to get him to return to the piano late in the evening if he had had too much. These, among others, were the occasions when his duet-partner, Josef von Gahy, would take over to play for any dancing done in the late night hours.

In larger spaces, Schubert would probably have had a correspondingly louder wing-shaped pianoforte to play, and the temptation to move back and forth between music for dancing and dance-music performances would have been that much greater, as well.

Note: In Kupelwieser's watercolor, the pianoforte appears to be a small spinet -- thus, neither the square piano one might expect in that space nor the larger instrument one sees in the Schubertiade drawings and other graphics.

Two readings after Cohn and Dempster, no. 1

Richard Cohn and Douglas Dempster criticize the treatment of motivic patterning in Schenkerian analysis as internally inconsistent: "In principle, motivic relationships must emerge as a by-product of voiceleading reduction; but in practice, voice-leading reductions are molded in part to optimize motivic relations" (171). In part as a way of respecting the directionality implied by this observation, they rethink the relationship of hierarchical levels in an ingeniously plural conception of a top-down hierarchy, according to which a given musical "surface"--a text (however construed)--"'holds together' underlying diversity by providing a compositional solution to multiple and disparate demands of harmonic, contrapuntal, motivic, and rhythmic operations" (177). As Robert Fink puts it, Cohn and Dempster “make a convincing case that viewing the musical surface solely as the product of a single generative hierarchy is too limiting; they prefer to consider it as the product of multiple interlocking hierarchies. Their revisionism does not, [however,] encompass the [more] radical step of detaching the surface from hierarchy altogether” (105).

Instead of conceiving analysis in terms of a top-down or chain-of-being hierarchy (after Zbikowski), they advance "a view of musical structure as a network resulting from a set of generative operations that are intertwined yet independent of one another" (172). Specifically, they suggest the use of product networks for "modeling music [in a way that is] simultaneously generative (in the sense of precisely specifying each event) and nonhierarchical" (174). They offer four examples. The first is drawn from David Lewin (204-6; Cohn and Dempster, 172-4) and allows for simultaneous generation in melodic and harmonic (intervallic) dimensions for organum. The other three examples set Schenkerian voice leading analysis against a "more loosely defined scheme of motivic generation" (174); a voice leading frame against a plan of figuration (in Bach, Well-Tempered Clavier, vol. 1, Preludes in C Major and C Minor); and "voice-leading designs [against] metric/figurational schemes" (175).

The last of these is of particular interest here because the authors point to topical conventions, which often "subsume conventions of meter, tempo, duration, and figuration into a higher-level construct" (175). If, following Cohn and Dempster, we want to locate D779n13 "at the intersection of voice-leading paradigms and topical conventions, [through a] product network [that] values the unifying potential of movement along either of the two axes" (175), we might exploit our narrative-topical conception of the piece as a portrait of a dancing couple (earlier post to this: link; also see "dancing" in the Labels sidebar). The topic is single (the waltz itself); the narrative consists of the formation of the couple, the dance figures (multiples of two-measure groups), and the separation of the couple as the dance concludes. For the voice leading generator, we could use any linear reading.

I have made an attempt at representing such an analysis in the graphic below. The upper line shows the initial courtesies (M = Man, W = Woman) and formation of the couple (F), the figures of the dance (D) and their multiples against each section of the music, and finally the separation at the end (F-1). The second line is a "primitive urlinie" ^3-^2-^3 (which, of course, could be easily renotated as a simple elaboration of the proto-background ^3-^3): here the graph shows all repetitions and thus a correct representation of the music in the time-line of the dance.

There is some virtue in writing out the repetitions -- as a reminder of the unifying power for (any) music of that simple process, but D and its multiples leave out two important features of the dance: the detail that each figure consists of a step by the man in one measure mirrored by the woman in the next, and the larger, contingent factor of the environment: how many figures one dances along any side of the room and how many figures may be accomplished in a complete circuit depends on the size of the room. Since Schubert's waltzes were played at house balls and parties, the spaces involved would most often have been relatively small.

By way of experiment, my partner and I managed 8-9 compact figures in circuits of a rectangular floor at 12 x 16 feet, and thus a couple could be expected to go around the room at least three times while dancing to D779n13. The surface represented in the graphic, then, is not a reading of the text of D779n13: it is the contingent circumstance of a dance to that music. In Cohn and Dempster's terms, we conceive this "complex . . . surface [not] as unified by an underlying structural simplicity [but] as a solution to the compositional problem of mutually satisfying the demands of several sets of independent formal operations" (176; their emphasis); that is to say, the dancers dancing and the music playing produce the dance. Note that the operations are in fact independent: unlike the extended figures of a quadrille, the figures of the waltz are coordinated with the music only up to the two-bar hypermetric level.

References:

Cohn, Richard, and Douglas Dempster. "Hierarchical Unity, Plural Unities: Toward a Reconciliation." In Bergeron, Katherine and Phillip V. Bohlman, eds. Disciplining Music: Musicology and its Canons, 156-81. Chicago: University of Chicago Press, 1992.

Fink, Robert, “Going Flat: Post-Hierarchical Music Theory and the Musical Surface.” In Cook, Nicholas, and Mark Everist, eds. Rethinking Music, 102-37. 2d ed. New York: Oxford University Press, 2001.

Lewin, David. Generalized Music Intervals and Transformations. New Haven: Yale University Press, 1987.

Schenkerian hermeneutics, part 2

Yesterday I wrote the introduction for a reading in the mode of Schenkerian hermeneutics, using as a model an article by Frank Samarotto. Here is the final paragraph again:

The parallel to D779n13 should be unmistakable: we just replace ^#4 with ^#5 (that is, E#) and the same process of chromatic progression and "rethinking" or "sublimation" takes place in the second strain as E5 becomes E#5 but then is pulled back to E-natural5 for the reprise. I will explore the details of a reading based on this idea in tomorrow's post.

I will use the proto-background ^3-^5 as the framework. Any of the four readings with ^5 would be workable, but, among all the proto-backgrounds, ^3-^5 is the one I prefer here, in part because (as I wrote in the comparison post) the strongly teleological readings seem out of sync with a waltz whose sections move unpredictably, and the analyses that isolate either ^3 or ^5 (or ignore them, as in the unison ^1 and octave) are much harder to hear than the one that combines ^3 and ^5 (soprano and alto, male and female dancers).

The inflection of ^5 is deeply embedded in the design, as if, in thematic terms, the rising motion is what this waltz is about, an increasing exhilaration in the dancing couple as the waltzing turns continue. Even if he wasn't a dancer, Schubert would have known from the experience and comments of his friends that, because of a basic difference in center of gravity, women in general find it much more pleasurable to turn and spin than do men -- in this portrait of dancing, then, the upper voice expresses the exhilaration, not the lower. The action is shown in the small, as well, in the later-level N

and in the immediate, as, at the beginning, E5 barely sounds before it pushes upward to F#5 and then to A5:

After all these hints (or preliminary attempts), it is hardly a surprise when the soprano pushes (completes the middleground turn?) up to A5 in the cadence.

There is thus a definite kinship -- a shared impulse -- between the E# of the background, the rising cadential gesture of the middleground, and the neighbor note of the foreground.

It is a curiosity that ^#4 or D# never appears in D779n13 as an inflection of ^4 -- instead, D# is ^2 in C# minor/major. The role of distinctive chromatic note is thus all the more clearly thrown onto ^#5 in the second strain -- but that note has a decided inner conflict: in the immediate, it is stable and F#5 is the neighbor, the dominant seventh that must resolve to it, but in the background, E# would move further upward, to that same F# as tonic to E#'s leading tone. The moment of sublimation comes in the transition, where the E#-G# pair that are the C#-major equivalents of C#-E begin to move, not up, but down in a chain of parallel tenths (see graphic below), thus imitating the determined descent of the suspension chain in the first strain. This motion would seem quickly to cancel out E#, but the E-natural belongs to a very unstable chord. Eventually the tenths arrive at C#-E as the reprise comes into focus. But in the meantime the soprano has gone out of the voice leading altogether as the ascending fourths pile up and F#6 is reached; the soprano even reaches again for a high A -- see the text at the top of the graphic. Here is that same transcendent voice, reaching up and out of the harmony, that Lewin describes.

The sublimation, then, is a complicated process here. In the background, exhilaration/ecstasy gives way in the end to the form of the dance. In the immediate, however, the soprano holds to that feeling (or its memory) and floats free of the voice leading for a moment. And in the middleground, Schubert has accomplished something that would take a whole generation of French opera composers after him to manage by force of sheer repetition: make the rising gesture in the waltz's final cadence seem quite conventional, the most natural thing in the world.

References:

Frank Samarotto. "Sublimating Sharp ^4: An Exercise in Schenkerian Energetics." Music Theory Online 10/3 (September 2004): link.

Lewin, David. "Women's Voices and the Fundamental Bass." In Studies in Music with Text, 267-281. New York: Oxford University Press, 2006.

Waltz-song recomposition

This is a continuation of yesterday's post on embodied shapes and schemata. If, as I wrote there, the persistent counterpoint of soprano and alto in this zärtliche Walzer is an astonishing evocation of the physicality of the standard waltz step, then we should feel comfortable representing this "sweet dancing" by means of text, as well.

Schubert as painter and poet of love is the effect that I have put into a song version of the A-major waltz (see graphic at the end of this post; first phrase only). Waltz-songs, especially for chorus, were common by mid-century (Brahms's two sets of Liebeslieder Walzer are obvious examples; but the Blue Danube is prominent among concert waltzes to which texts were also set and publicly performed). Schubert may be said to have anticipated that practice with a waltz perfectly suited to song.

Oddly enough, all this suggests a step away from the physicality of the dance – a portrait or a remembrance of the dance, not the dance. This distancing comes about because of the A-major waltz's metric peculiarities; now it seems like a pause in the dance, isolated yet again from the dances that surround it in D779.

More on music-literal and schemata, after Guck, Saslaw

This entry provides more information about Marion Guck's "music-literal" analysis mode, along with Janna Saslaw's comments connecting Guck's arch shape with image schemata. The post is an extended postscript to the earlier one that matches notions of movement in dancing to shapes in listening: Low/high pairs.

Much has been written over the past two decades about metaphor, cognition, and language. As Marion Guck has shown, controlling metaphors and metaphorical language play a role even in apparently objective descriptive accounts of music ("Analytical Fictions"); in another place, she uses metaphor as a way to build such analytical accounts ("Two Types"). For Chopin's Prelude in B Minor, op. 28 no. 6, she compiled student reactions to hearing the piece, with and without score. These "eventually suggested to me a detailed analysis," summarized as follows: "I imagine the prelude as two-measure arching melodies nested within phrase-length arches in turn nested within a single prelude-long arch. The relatively literal spatial notion of melodic arch leads me on to the movements of arching gestures and then, beyond those, to the rise and fall of mood and to a narrative curve" (204).

Thus, the analysis assumes a loosely hierarchical model: the direct, aurally palpable two-measure arches of melody are "music-literal," the phrase-length arches are figurative (they "do not form a continuous line but rather generalize a directional emphasis" [206] and therefore "the conversion [from arch image to increase and decrease of tension] superimposes a metaphorical reinterpretation on the music-literal, and the resulting description is more deeply metaphoric" [207]), and the "single prelude-long arch" ties both "literal" and figurative to movement and mood, "incorporating all in a depiction of human (inter-)actions: the piece's arch is a narrative curve" (207; her emphasis).

How exactly we move from spatial metaphors to "human (inter-)actions"–and just what its "narrative" might be–is not clear, but that uncertainty is no obstacle to our application of a theme/thesis analysis in Guck's article: the theme may be stated as "direct aural experience [the "music-literal"] can be tied to abstract levels of apprehending music by means of layered (nested) metaphors"; the thesis is directly stated at the end of the article, as if in form of a moral: analysis by metaphor "facilitate[s] an endlessly closer, more profound hearing of each musical work" (212).

Guck begins her discussion by saying that spatial images are "so pervasively and deeply embedded in the language of musical discourse . . . [that] we must speak in spatial terms" (201). Commenting on this work, Janna Saslaw says that Guck "gets very close to the idea of embodiment when she discusses body sensations associated with [the] arch metaphor" in the Chopin Prelude ("Forces" 238n9), as when she compares an "arch's line" (it "ascends, focuses, and curves") to the movement of "the arm that threw the ball" (an image already familiar from Cone (26-28)):

To hear arching movement, one most likely recalls, subliminally, memories that incorporate the fine, continuous adjustments in muscle tensions needed to produce the smooth gesture: the initial impetus that increasingly opposes gravity as the arm rises, stretching to the point of fullest extension, then decreasing tension as the arm yields to gravity. In the [arch] gesture, rise and fall are also converted into increase and decrease of effort and tension. . . . The conversion superimposes a metaphorical reinterpretation on the music-literal, and the resulting description is more deeply metaphoric. ("Forces" 206-207)

Here the metaphoric seems to be equated with the abstract. For Saslaw, following Lakoff and Johnson, body metaphors underly the image schemas that permeate all language, including conceptual language: "image schemas are based on direct experience of a kinesthetic nature," and they "operate at a very basic level of cognitive organization, a level that Johnson has called 'preconceptual'" ("Forces" 218). Saslaw sorts a list of these

kinesthetic image schemas. . . . into two types. First are those that deal with our bodies themselves, including the container, center-periphery, front-back, and part-whole schemas. The container schema, for example, derives from our sense that one's body is a container with an inside and outside. The second group of image schemas . . . consists of those that deal with our orientation in, and relationship to, the world, including link, force, path, source-path-goal, and near-far (218).

These image schemas originate in our physical experience, but, "in order to structure domains that are not experienced directly, we map the kinesthetic image schemas . . . onto these more abstract domains. The mappings take the form of metaphors" (220). Guck's throwing arm–and the arch that might be said to derive from it–is a special case, then, of a general kinesthetic schema of trajectory that involves not only origination-to-goal but force or effort. For Saslaw, "if composers and listeners conceive of tones as objects that move in space, then these conceptual objects can have the attributes of real-world objects: weight, speed, force, direction of motion, etc." (235)

As I claimed in the early post, the persistent counterpoint of soprano and alto in this zärtliche Walzer is an astonishing evocation of the physicality of the standard waltz step. The music-literal allows us a way to think about the "blank" opening bars that permit hearing the waltz as counterpoint not between soprano and alto, but between right hand and left, between the complex of melodic upper voices and the bass. Whether or not these bars are actually danced, one can see/hear the male dancer in bar 1 followed in bar 2 by the musical mimicry of the woman's twirl in the eighth-note figure. The "foundational" (harmonic) leader–perhaps the Vortanzer–courteously makes no distinctive (musical) gesture before the "ornamental" (melodic) partner enters with an individual display of the essential motif of the waltz, the turn or twirl. After this, the couple together performs a larger-scale set of turns through the series of two-bar hypermeasures that make up the waltz. (Note that the harmony, too, is unwavering in its two-bar groups.)

[note (12-20-09): Michael Spitzer writes a critique of music/body-analogies, including Guck's, arguing that the "commitment to somatic immediacy" that she and others, including Robert Hatten, David Lidov, and Alexandra Pierce, stress cannot bridge a gap between the "concrete immediacy [of] performed gestures [and] the deeper principle that enables bodily thought, [or] schematism." (See his Music and Metaphor, 88-91).]

References:

Cone. Edward T. Musical form and musical performance. New York: W.W. Norton, 1968.

Guck, Marion. "Analytical Fictions." In Adam Krims, ed. Music/Ideology: Resisting the Aesthetic, 157-77. Amsterdam: G + B Arts International, 1998. Originally published in Music Theory Spectrum 16/2 (1994): 217-230.

Guck, Marion. 1992. "Two Types of Metaphoric Transference." In Katherine Bergeron and Phillip V. Bohlman, eds. Disciplining Music: Musicology and its Canons, 201-212. Chicago: University of Chicago Press, 1992.

Saslaw, Janna. "Forces, Containers, and Paths: The Role of Body-Derived Image Schemas in the Conceptualization of Music." Journal of Music Theory 40/2 (1996): 217-43.

Spitzer, Michael. Metaphor and Musical Thought. Chicago: University of Chicago Press, 2004. Spitzer criticizes Guck and several other writers for perpetuating a body/structure dualism. He says that they "identify the bodily experience of a performer with an immediacy that is distanced from musical structure. [The latter], with its abstract and articulated systems of internal relations, can still echo . . . or be echoed by . . . structures of bodily motion, [but] a commitment to somatic immediacy-the continuous, particular, and analog character of musical gesture-stands in the way of discriminating and categorizing the various types of bodily experience" (90).

Low/high pairs as "music-literal," after Marion Guck

In an earlier post I discussed D779n13 as a miniature portrait of a dancing couple. The graphic from that post is reproduced here with a slightly different explanation focused on the music's hemiola patterns; this discussion leads to another that makes a more abstract tie between the dance and "shapes" in the music.

The graphic matches the figures of the valse à trois temps and a rhythmically dissonant hemiola pattern. The first iteration of this hemiola (mm. 3-4) may be taken as a courtesy to the woman, whose figure runs in four steps followed by a two-beat pivot turn that does not shift weight, or a rhythm q-q-q-|q-h, which aligns nicely with the hemiola, while the man's mirroring figure initially fights against it: q-h-|q-q-q. (btw, I am using the gender labels appropriate to the period. Although other combinations and roles were certainly possible in couple dancing, I am focusing on the mode for public dancing, which is also what Schubert's friends report in their reminiscences of house balls and parties.)

Whether portrait (rhythmic depiction of the dance) or not, this figure of the dance can also be taken as the basis of a reading following Marion Guck's metaphor-based method. What she calls the "music-literal"--and uses to guide analysis--might be taken as "shapes in space" or "qualities of movement." I have not carried out student surveys of the kind that support Guck's claims about the arch figure as a controlling metaphor in the Chopin Prelude in B Minor, but the experience of playing D779n13 and working out other analyses suggests strongly that the "music-literal" here is a sense of pairing (generally, lower against higher). Apparent immediately in the separation of voices on the downbeat of m. 3, this idea works itself out through the hemiola patterns.

The eighth-note figures (circled) are paired, moving from lower voice to upper voice. This latter pair is also the basis of the entire C#-major section, after which the eighth-note pairs resume (mm. 30, 32) and we eventually hear one last iteration of eighth-notes to rising quarters (mm. 34, 36). A rising gesture, or a pattern of low-->high, thus obtains consistently throughout the waltz, and I would take that as equivalent in function to the arch that Guck finds in the Chopin Prelude.

The suspensions work in a larger time-frame to express the same gesture. As the brackets and connecting line show, the suspensions remain in the lower voice (and emphasize not only "low" but "descending") through all of the first phrase except the close, where a suspension-like effect is achieved with the 6-5 over I. The same pattern of staying-low-then-ascending-at-the-end follows in the second phrase, the F#-E now forming a 9-8 suspension-like effect in m. 15 in combination with a true suspension in the alto. In the second strain, the suspensions remain firmly in the lower voice (mm. 21- 25, 31, 33) until the repetition of m. 15 as m. 35.

The abstract echoes of these patterns resound in registral motions across the first strain (F#5 and E5 till the cadence that rises to G#5 and A5). At the level of the entire waltz, the figure is not "perfect" (the waltz does not end in the highest register), and I am tempted to link the final retreat from the sixth octave to the suspensions (the suspension being a classic instance of a recessive gesture). If so, one might argue for the final integration of the two spatial metaphors, a single metrical group in which the long, asymmetrical low-to-high pair is motion toward an accent and the recessive gesture falls (literally) after the downbeat at m. 31.

Reference:

Guck, Marion. "Analytical Fictions." In Adam Krims, ed. Music/Ideology: Resisting the Aesthetic, 157-77. Amsterdam: G + B Arts International, 1998. Originally published in Music Theory Spectrum 16/2 (1994): 217-230.

D779n13 and dancing

In Schubert's major published collections of dances, the only piece to bear an affect label--apart from the occasional dolce in early sets--is D. 779 no. 13 (zart), but because there is no extant holograph, we cannot be sure the label is actually his.

I have noted several times already that this waltz has a distinctive design. All the numbers of D. 779 are in small two-reprise forms of either sixteen or twenty four bars; the A Major Waltz is thirty eight bars (18 + 20). The first reprise would be eight bars if it had a repeat sign, but the repetition of the first reprise is written out to simplify the overlap of the ending and return of the opening phrase; the introduction adds two additional bars. The second reprise would be sixteen bars, but Schubert's abrupt harmonic shifts oblige him to smooth things over with analogues to the introduction, adding two bars to each eight-bar phrase.

Thus, there is tension between this waltz as music for dancing and as a small-scale piece for listening. Like the peculiar scherzo-like pieces in the posthumous Letzte Walzer (D. 146)--most of which were composed not as waltzes but rather as minuets or scherzi with trios--the A Major Waltz threatens to burst the boundaries of its genre on the scale of the individual waltz, just as Weber's Invitation to the Dance and the concert waltzes of Chopin and others broke the boundaries of the functional dance environment and moved the waltz to the salon recital and, eventually, the concert hall.

Eric McKee argues that it is problematic to use this shift as an excuse to cut off these dances from their social origins and treat them merely as autonomous artworks (155) -- that is to say, he disagrees with Margaret Notley (see the score post). Although Chopin began to introduce non-dance elements into his waltzes after 1830 (when he left Warsaw), still "many of [his] Viennese and Parisian waltzes are eminently danceable, and the distinction between functional and stylized was largely a matter of how they were used in their social context" (121).

The A Major Waltz does remain invested in the social culture of dancing (despite its hypermetric peculiarities); to go even farther, more than any other waltz of the early 1820s, it is easily heard as a miniature portrait of a couple dancing. (This again follows McKee, who argues that Chopin's waltzes are "musical visions of the dancers on the ballroom dance floor" (122) and that the composer tends to focus his musical gaze, as it were, on the woman (141).)

Schubert did not have Chopin's ability, gained from his own experience, "to translate [dancers'] bodily motions into an artistic musical vision" (McKee, 121), but from everything we know about Schubert's extensive activities as an improviser for social dancing, we can assume a similar skill from him even if he did not dance himself.

The bass figures provide the necessary metric contexts, and the two "empty" bars (1-2) depict the dancers setting themselves and internalizing meter and tempo. The two upper voices are continuously paired, soprano and alto, leader and follower, mirroring each other's figures in the two-bar pattern of the waltz step (in the graphic below, "W" is "woman," "M" is "man," "L" and "R" are left and right foot, respectively, and "p" is the pivot made without a new step). What we hear once these voice leading parts acquire voices, as it were--once they become agents or personae--is what we might see in the valse à trois temps, a common waltz figure known before the turn of the century and common through the 1830s (Aldrich 1991, 19-20; Aldrich 1997, 134; McKee, 123-4.): not simply alternation of figures, but, in the eighth-note gestures, the waltz's trademark circling or whirling.

And what we sense is not so much desire as it is the piquant charm of sublimated desire (flirting, in a word): two persons in a social setting accept one another as partners and dance. One would normally dance with a number of partners through an evening in, say, a house ball, but it is clear from statements in contemporary sources that a couple's sexuality was always a potential diversion of the dance from its social purpose. (For additional context and description, see my discussion of D779n13 and dancing in Neumeyer 2006, 217-220.)

The A Major Waltz, under those terms, might even be taken as a portrait of a couple in love and of the power relations that obtained in their intimacy during the era at hand. The effect would be very like the one David Gramit describes as arising near the end of Schubert's song "Seligkeit" (D. 433), whose Ländler rhythms and strict four-bar phrase design at first seem "allegorical-a symbol of worldly pleasure standing in for heavenly ones." In the final strophe, however, the poem's narrator reveals his willingness to abandon heaven for the favors of his earthly lover; thus, "what we initially hear like a dance turns out to be dance itself; the hoped-for pleasure is not spiritual but embodied" (222; his emphasis). (A similar use was cited by Hoorickx in "Hänflis Liebeswerbung," D. 552, but in this case a deutscher (D. 972 no. 3) is quoted intact as the introduction. Hoorickx also notes that in the same year (1817) Schubert quoted all of the Cotillon, D. 976, as the second theme in the finale of the Violin Sonata, D. 574.)

References:

Aldrich, Elizabeth. "Social Dancing in Schubert's World." In Raymond Erickson, ed. Schubert's Vienna, 119-40. New Haven: Yale University Press, 1997.

Aldrich, Elizabeth. From the Ballroom to Hell: Grace and Folly in Nineteenth-Century Dance. Evanston: Northwestern University Press, 1991.

Gramit, David. "Between Täuschung and Seligkeit: Situating Schubert's Dances." Musical Quarterly 84/2 (2000): 221-37.

Hoorickx, Reinhard van. "Schubert's Reminiscences of His Own Works." The Musical Quarterly 60/3 (1974): 373-88.

McKee, Eric. "Dance and the Music of Chopin: The Waltz." In Halina Goldberg, ed. The Age of Chopin: Interdisciplinary Inquiries, 106-61. Bloomington: Indiana University Press, 2004.

Neumeyer, David. "Description and Interpretation: Fred Lerdahl's Tonal Pitch Space and Linear Analysis," review-article, Music Analysis 25/1-2 (2006): 201-30.

D779n13 in Music Analysis article (2006)

In my review-article on Fred Lerdahl's Tonal Pitch Space, I introduce a number of analyses of D779n13. This post lists them.

1.-3. I reproduce Figure 10.1 from Lerdahl and Jackendoff, their time-span reduction or analysis of the metrical structure of D779n13. To that I add a prolongational reduction or reading of the harmonic-voiceleading structure following their rules. Finally, I interpret the prolongational reduction in terms of Lerdahl's function rule (from TPS) (Neumeyer 2006, 209-214).

4.-7. Then I introduce what I call "four contexts" into which to place the A major Waltz: (1) "functional patterns in waltzes of the 1820s as they would be known by one accustomed to playing or improvising dance music; (2) D. 779 as a collection; (3) the waltz as danced; and (4) other modes of structural hearing as represented in alternative analyses." (Neumeyer 2006, 214-221; quote edited from 214). To no. 4: I create a reading based on a germinal motive that is a registral pattern, not the usual melodic figure. This is worked out hierarchically, including a registral foreground (Neumeyer 2006, 224-226).

8. Carl Schachter's rhythmic-metric reduction is translated into standard Schenkerian notation in Ex. 7 (Neumeyer 2006, 221).

References:

Lerdahl, Fred. Tonal Pitch Space. New York: Oxford University Press, 2001.

Lerdahl, Fred, and Ray Jackendoff. A Generative Theory of Tonal Music. Cambridge, MA: MIT Press, 1983.

Neumeyer, David. "Description and Interpretation: Fred Lerdahl's Tonal Pitch Space and Linear Analysis," review-article,Music Analysis 25/1-2 (2006): 201-30.

Schachter, Carl. "Rhythm and Linear Analysis: Durational Reduction." Music Forum 5 (1980): 197-232. Reprinted as "Durational Reduction" in Schachter 1999a, 54-78. (Schachter, Carl. Joseph Straus, ed. Unfoldings: Essays in Schenkerian Theory and Analysis. New York/London: Oxford University Press, 1999).