The repertory of proto-backgrounds within the octave is 9: three unisons, three intervals above ^1, two intervals above ^3, and one interval above ^5. The repertory of first-order transformations is not fixed, but I assume it includes at least LINE, N(eighbor), and their inverses. The article also introduces two registral (rather than linear) transformations: DIV(ision) and ADDINV. For the notational style most closely matching that of the article, see the Fifth and Sixth Readings below.
Given that the hierarchical character of linear analysis is unavoidable in practice (if by no means immune to criticism), there is value in increasing the number of available top-level constructs in order to promote flexibility and range in analytic practice.
This essay is a case study in application of the proto-backgrounds and readings based on informal transformations. After cataloguing six of the nine available readings, I evaluate them, mainly according to plausibility but ultimately in terms of my own personal preferences, following the lead of David Lewin (as discussed in the MTS article and particularly in reference to Lewin's essay "R. Schumann's Anfangs wollt' ich : A Study in Phrygian and Modern Minor," in his Studies in Music with Text, 53-108. New York: Oxford University Press, 2006).
M. Landrin's "Blac Danse"
The work at hand is a melody for dancing: the first tune in a set of contredanses anglaises published in Paris sometime between 1760 and 1785 (in my view, most likely before 1770). M. Landrin may be the author of the tune, but it could just as likely be the work of someone else or simply a tune well known at the time. It is a typical 2/4 contredanse (though with an eighth rather than quarter note pickup) and has nothing "English" about it -- "anglaise" refers to the style of dancing (in a column rather than circle or square), not to the style of music (on the English long dance, see Contredanse and Classical Finales, Illustrations 1 & 2 and explanatory text). In performance, "Blac Danse" would most likely be played by a single violinist -- probably the caller/dance-master himself (Landrin was known as a dance teacher and leader). Alternatives common at the time would be two violins, with the second part possibly improvised, or two violins and bass. (Examples of the former may be seen here: Clarchies; examples of the latter here: Neue Mozart Ausgabe -- look under Serie IV, vol. 13, Abt. 1/1: menuets). Full string band performances would only happen in the large dance spaces afforded by aristocratic or public balls.
To approximate the performance modes mentioned above, I have constructed scores for two violins (below) and for two violins and bass (see Blac Danse arrangement.)
I should also note that, in an actual dance setting, the melody would be played multiple times in order to accommodate all the dancers -- this was especially true of the English long dance, which did not dictate a specific number of dancers. During the course of the repetitions, embellishments and other alterations would certainly be introduced by all but the least skilful (or laziest) players. For a recorded instance of such performance practices, see my collation of music from the Menuet engravings that conclude Kellom Tomlinson's The Art of Dancing (1735): Tomlinson menuet.
The proto-backgrounds applied to "Blac Danse"
(INTRODUCTION: SIX, NOT NINE). I will only present six of the nine possible readings with proto-backgrounds. I will leave out the two intervals above ^3 and the one above ^5. These three are also plausible -- in many respects, no less so than the six I will discuss -- but since my point can be made without introducing all nine readings, this web essay will be a little more efficient.
(FIRST READING: unison ^1). Spaces of the unison are, of course, the simplest and, one might say, the most forceful grounding for generative hierarchical analysis that gives its highest priority to pitch design. Every other design element comes directly under its sway. In the graphic below, the top level is the proto-background (shown as an interval, not as an isolated note). The pitch G4 has undisputed prominence in the dance's rhythms (relatively long note), meter (first bar, first beat; repeated in third bar, first beat), and form (G4 is also the final note). These three G4s are shown in the second level with half notes beamed together, representing a very basic transformation function we might call RECURrence -- in this case combined with GRouping-PROMinence (suggested in the numbers and brackets below the music in the second level).
The one high-level metric position missing, bar 5, does not abandon ^1 but transforms it with a change of register (or reaching-over in voice-leading terms). The Schenkerian term coupling could apply instead -- that would be covered by a transformation I call ADDINV (adding the inverse of the proto-background interval above it: in this case, adding the octave above the unison) -- but I regard the octave as secondary and the RECURrence of G4 as primary. Therefore, the G5 in bar 5 is shown as a kind of "prefixing" register shift within the second 4-bar group (slur from G5 to the final G4). Note that this octave is also divided by the fifth on its way.
Back in the first 4-bar group, the device of prefixing shows itself also with triadic figures down from D5 to G4 [bracketed], the pitch D5 being the secondarily prominent note in the 2-bar groups because it's on the downbeat of bar 2 and in a noticeably high register. The third level of the graphic shows that this figure is an expansion of the pickup gesture (also bracketed). I have added the assumed harmonies in the third level in order to help clarify the voice leadings that begin to emerge here.
(SECOND READING: unison ^3). See the general comments about unison proto-backgrounds under the First Reading above. The second reading replaces the attention on metric-rhythmic-formal priority with a progressive melodic figure leading by step from G4 to B4. In this case, "progressive" means "phrase-end" or "group-end," as B4 is positioned at the ending of all but the final 2-bar group. In this sense, the reading of a proto-background as the unison ^3 is in direct opposition to a reading as the unison ^1 and tends (as any reading from ^3 will) to bias the reading early on toward voice leading patterns and the "imaginary continuo" (on the latter, see William Rothstein, "Rhythmic Displacement and Rhythmic Normalization," in Allen Cadwallader, ed., Trends in Schenkerian Research, 87-113).
In order to give the progressive melodic figure as much prominence as possible in the analysis graphic, I have separated it from most other events, in particular the D5s and G5s, which are shown as the traditional cover tone (with eighth-note flags). See under the Fourth Reading for the integration of voice leading (that section also has a traditional linear analysis graph as a Schenkerian reading with Urlinie from ^3).
(THIRD READING: unison ^5). See the general comments about unison proto-backgrounds under the First Reading above. This analysis suggests that secondary metrical position, especially when it's consistent (^5 is the first pitch of bars 2, 4, & 6), combined with registral prominence (enhanced by motivic consistency: a scalewise figure goes down from every D5), is enough to undermine metric position (of G4). As with the Second Reading, the lowest level makes few voice leading connections in order to emphasize the "separateness" of the unison D5.
(FOURTH READING: third ^1-^3). See also the comments under the Second Reading (^3-^3). This reading combines pitches (in the bracketed figures of the second and last levels) that acted very differently in the first three readings: the metrical solidity of ^1, the registral prominence and secondary metrical position of ^5, and the melodic goal of ^3 are tied together in a triadic motif that replicates itself (bars 3-4) and then is reshaped in bars 5-6. Unlike the traditional Schenkerian analysis (below), the Fourth Reading does not subordinate ^1 to ^3, and thus the broadest-scale of grouping priorities is merged with -- or reconciled with -- the progressive melodic priorities: that is, G4 is background at beginning and end (not "erased" as middleground in an initial ascent).
Traditional Schenkerian reading with Urlinie from ^3:
(FIFTH READING: fifth ^1-^5). It is probably inevitable that registral processes stand out in those readings that are based on the larger intervals. In this case, I have added a level of middleground in order to highlight these processes. From the proto-background ^1-^5, a transformation enlarges the space -- ADDINV adds the inverse of the proto-background interval above it, or here, the fourth D5-G5 above the fifth G4-D5. Then the latter is set out temporally in reverse during the dance's second strain or phrase, from D5 to G4. The result is a symmetrical, arch pattern that is clearest in the third level of the analysis graphic.
(SIXTH READING: octave ^1-^8). See the comments about register and registral processes under the Fifth Reading. Like the Fifth Reading, this one shows a symmetrical registral shape, now even more starkly as it ties the beginning of the first strain to the beginning of the second, then reverses the figure to reach the end on G4 again. The transformation DIVision takes the given interval and subdivides it: here G4-G5 is DIVided at the fifth by D5.
Evaluation of the readings and choice of ^1-^5
(ALL READINGS POSSIBLE) None of the seven readings of "Blac Danse" given above -- six based on proto-backgrounds and one Schenkerian graph -- is implausible, that is, none of them can be rejected outright as failing to be a reasonably possible hearing of this basic form of the dance melody, nor can the analysis graphics be mechanically wrong, within the normally informal limits of all linear analysis. Thus, the seven readings satisfy Lewin's requirement in his comparative analysis exercise for a Schumann song (cited at the beginning of this essay), in that they are musically plausible and mechanically adequate on their own terms. If we leave it at that, we assert a pluralist viewpoint that is also relativist -- necessarily tolerant because it is not deemed possible to evaluate different assertions of value. Is the voice leading bias in Schenker closer to "truth" than the register preference in the proto-background readings, most obviously the Fifth and Sixth?
(FIFTH READING PREFERRED) The admirable tolerance of relativism, however, is unsatisfying. Although it is quite possible for me to hear the "Blac Danse" in terms of any of the analyses given here -- or, for that matter, in any of a number of other ways -- that fact doesn't mean that all of them match my own "best fit" for this melody. Nearly sixty years ago, Milton Babbitt said, in reference to Schenkerian modes of linear analysis, that "There is no authority of ultimate validity beyond the formed, informed, and intelligently experienced musical perception" (cited in the MTS article). I could hear the "Blac Danse" as a carnival of different guiding shapes -- different "themes" in the language of literary analysis -- but in fact I hear it most readily in a particular way, one conforming most closely to the Fifth Reading. And that is because I hear the dance as a melody for dancing as much as -- or more than -- I hear it as an autonomous musical composition. As I put it in paragraph 11 of Contredanse and Classical Finales,
(ANALOGY TO LISTENING FOR DANCING) In order to give a better sense of how I would hear the "Blac Danse" by analogy with music for dancing, I will employ a graphic construct that I have already used elsewhere in connection with the "leap" from the particular to the general (see the second part of the web essay Frames for another example and citation to a published article). For a dancer, this leap represents a run from clues in the first moments of the music to a quick judgment of the dance's genre (perhaps, "This is a waltz"), necessary for the dancer to know how to begin and at what pace. For the listener, the analogy would be a quick guess at genre, style, era, or composer ("This sounds like Gershwin") or a pitch-design or metric schema ("The basic idea seems to be neighbor-note figures about ^3").
In the first figure below, the music has begun (1), and from that I make a quick judgment (2) that the opening strongly suggests a registral and voice-leading frame of ^1-^5 ("The frame or generating interval seems to be ^1-^5"). Given this, I have a number of expectations about likely continuations. including a first significant (but internal) formal articulation (3), some kind of continuation, most likely involving a level of contrast (4), and an ending involving a formula cadence (5), at which point -- if all has gone well -- I would assume that my initial judgment would be confirmed (6).
Steps (2) and (3)--see below: This example is not as clear as it might be because it doesn't highlight the "looping" that occurs from (2) through (3) back to (2). Step (3) shows an answer (in the musical notation) to the question posed about the ending of the first strain. Because that ending leaves the background/middleground shape unchanged, it feeds back through step (2) as "tending to confirm" (2)'s snap judgment about the proto-background.
Conclusion
Analysis using the proto-backgrounds as initial structures for generative hierarchies must be informal -- certainly compared to formal devices and systems elsewhere in music theory. Because the work is based on a top-down hierarchy, it is highly dependent on the choice of the initial or highest-level figure. Such figures are what David Lewin calls "metastable" (see the citation in the MTS article): not universals but acting pragmatically as if they were for the sake of the work of analysis or interpretation. They are, in other words, identical in function to the themes that a reader engenders to gather and guide reading and interpretation of a poem, story, play, or other text. For example of themes in the analysis of literary works, see Rebecca and Genre Clerk.
Apart from its practical value in aiding the construction and comparison of analyses made on differing assumptions, the notion of "theme" can also be tied to an argument about the historicity of linear analysis. From the article: "The thematic analogy -- that is, theme as the equivalent of the contents of the background, last stage of reduction, or other 'summary' in a hierarchical model -- helps to align a traditional practice of linear analysis with practices in literary interpretation current at the time that Schenkerian analysis was in process of being adopted in the United States." The point is elaborated at some length in the article.
All original material copyright David Neumeyer 2009.
Return to proto-background
Source: Library of Congress American Memory: Dance Manuals: Landrin, Recueil danglaise [c1760-1785]. 
If two measures mark the basic step-unit in the menuet, they must mark more rigidly the passage of time in the contredanse, whose figures have multiple elements that must be accomplished within a single strain. Since these are lively group dances, one couple's failure of timing can create problems for the others . . . For example, in [one set of dance instructions,] the second strain (ten measures, as five two-measure units) asks the dancers to "clap hands sides, all four [couples] turn [single] then clap hands with your Partners and cast off, then lead through and cast off again." One need not understand the details of each action to recognize that a great deal is being asked in a relatively short time. Under the circumstances, it is not surprising that music for the contredanse puts a premium on clarity and symmetry -- and, to help accomplish that, on regular hypermetric patterns.
Therefore, metric clarity at all levels is a high priority. The First Reading certainly fits the bill, but it ultimately can't compete with the Fifth Reading, which accounts not only for the 2-bar groups but for the individual bars as well. 
Go to essay on Mozart, K. 602, no. 4.
Go to essay on Beethoven, WoO10, no. 2.
Home