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Modality and the Melodic Foreground

Roger Solie

Melodic Incipits and Diatonic Transposition

[1]
Melody-theme, tune, song, the progression of the leading voice-lies, for most listeners, at the heart of their experience of common-practice Western art music, and of most Euro-American folk and popular music as well. Yet within melody lies one of the great mysteries of music theory, the coherence of the incipit: the fact that in the opening motive or two of a successful theme, nearly any change we might propose to the pitches or their durations is distinctly and obviously for the worse (for abbreviations of work types and titles, see the appendix):

One could, of course, continue to change pitches and rhythms until one had, in effect, produced a new and possibly adequate melody; and in the rare case, a single small alteration in the incipit may leave its quality unimpaired. The fact remains, however, that in comparison with the total number of changes one could propose to the first dozen notes or so of a theme, the number that can be made without serious damage to its coherence is vanishingly small.

This virtual irreplaceability of the notes in a well-constructed melody generally diminishes as the melody continues, and as, typically, the initial ideas are modified, combined, and transformed into a more extended statement. But the unique coherence of the incipit is a major challenge for any attempt to understand melody as it is used in the great classical tradition of the West. Imagine a satisfactory account of this cohesion: what would it look like?

[2]
First comes a consideration of method: such a theory will need to be repertorial. It will be a theory of a specific corpus of melody, from which it is derived and against which it is tested. Principles deriving from one kind of melody may quite possibly coincide or overlap with those applying to other repertories, but we can't know that until we actually have such principles; and we can't genuinely establish those principles unless we confront them with the music to which they supposedly apply. We are in most cases required to search out counterexamples to whatever rule or principle is being proposed.[1]

Let us suppose that the corpus in question is a segment of the common-practice Western art-music tradition. Then presumably an adequate theory of that melody will make contact with the traditional disciplines of harmony, voice-leading, and dissonance-treatment, though it's not easy to say exactly how. It may be that these form boundary conditions, applying to the ultimate setting of the melody with its accompaniment; certainly this is true when we deal with the melody as a whole: accompanied, orchestrated, and worked out into a fully-extended statement. But in the very opening? Possibly the incipit must be constructed so as to imply, or permit, or at least not preclude, harmonization according to these traditional rules and customary schemata, and that this is part of what's wrong with this:

Another critical component of this idealized theory will deal with grouping, as influenced by duration, meter, and also, critically, by contour. Here, for example,

the change in duration of the third note seems to create an unwelcome grouping ambiguity: which way does the D-natural group? The first two notes no longer separate so cleanly from the next six. However, consider now this version:

Here the ambiguity is eliminated; the separation between the first small group and the second, between the C# and F#, is fairly complete-the grouping is as clear as can be. But now the two groups seem too disjunct, too isolated-at least given these pitches: in Mozart's divertimento for wind trio:

new notes have somehow made this rhythm and contour acceptable. Evidently what has changed is the relation between the first two small groups: from a motive plus its modified echo (in my theme), to that of a group plus its scale-pattern continuation in K.439, the implicit line across the motives being E-C#-D-B-A. Why exactly this change permits, or requires, the greater disjunction between the two groups is beyond me, and beyond any grouping theory I'm aware of. Evidently a theory adequate to deal with grouping in the melodic incipit must be quantitative and subtle; it must recognize that small separated groups of notes may cohere one with another in various ways, in order successfully to form larger complexes, and that the relation between groups goes beyond simply connected or separated or conjoined, downbeat or afterbeat or upbeat; membership or non-membership in some higher-order group.

[3]
We now, however, set these considerations aside, and consider a final distortion of Mozart's theme:

Neither the harmony, nor the durations, nor the contour, nor the meter of the original has been changed; it surely groups as before, and yet this is clearly unsatisfactory as an incipit: it has the shape of a melody, but it's immediately recognizable instead as some kind of "harmony part," not the "real tune." The sole difference is in the pitches themselves-the tune is set in a different part of the scale, and so the individual scale-degrees are treated other than in Mozart's theme.

Clearly, then, there must be modal principles at work in this repertory: certain scale-degrees are used in certain ways and in certain situations where other scale-degrees are not.[2] Some of these ways are of course already familiar: the fact that non-modulating melodies usually conclude on the tonic (the first scale degree, hereafter notated 1°), for example, or that in Classic thematic constructing the antecedent of an antecedent-consequent construction generally cadences on the 2°. But the operation of "diatonic transposition" or "translation" we've performed on Mozart's concerto theme, and its unhappy result, implies that there must be other principles at work too, at least in the critical opening measures of a melody.

[4]
Trying to discover a few of these principles, for the major mode only, is the object of this study.[3] (Corresponding regularities in the use of the minor mode, in the Classic style or elsewhere, no doubt overlap to some degree with those for major, but this determination will have to be left to future study.) The repertory under consideration is thus composed of major-mode Viennese classic melody: themes drawn from most of the mature (or nearly-mature) work of Haydn, Mozart, Beethoven, and Schubert. In Haydn's case, I have included only the instrumental music, reaching back to about 1770. The Mozart considered excludes the church sonatas and the vocal or choral music outside the operas; in most categories reaching back to 1772 or 1773. The Beethoven works go back to 1783 in most genres (where possible); the only significant excluded categories are songs without opus number and the canons. For Schubert, the choral works (sacred or secular), and most stage works were not considered, and only a portion of the songs-most of the famous ones, and all the song-cycles. In most Schubert categories, we go back as far as 1814. These restrictions were imposed in an attempt to cut the number of themes to be examined down to a somewhat-manageable size, without affecting the conclusions to be drawn, but it is of course still possible that, for example, Haydn's style in his operatic works is so different from the rest of his music that the conclusions set out below might need to be seriously modified. Nevertheless, in total we have the incipits of roughly 6300 themes or melodies upon which to begin to construct a modal theory for this music. The process of assembling the repertory in the first place, of extracting themes from larger works, was carried out as far as possible without preconceptions, that is, on an entirely intuitive sense of what a melody or a theme is. This intuition is, of course, what a theory of melody must try to explicate.[4]

[5]
We are, moreover, going to concern ourselves only with the way the nontonic notes of the major scale-the pitches 2°, 4°, 6°, 7°, and also #4°-are treated; and we will do that in terms of traditional dissonance treatment.[5] That is, we will make the simplifying assumption that the whole incipit occurs within tonic harmony-even though a significant minority of these themes begin with extended non-tonic harmony, and of course on the literal musical surface a non-tonic melody note will be quite often be supported with harmony of its own. We will then look at what happens when these nontonic pitches occur as various kinds of "dissonances" to that assumed tonic harmony; that is, as unprepared nominal "appoggiaturas" ("APs"); or as "neighbor tones" ("NTs"), departing from and returning to a tonic pitch; or as "passing tones" ("PTs"), occurring between two tonic pitches a third apart. To diagram these situations (with the black note representing the nontonic pitch):

Along the way we will also have some things to say about grace-notes. We won't by any means arrive at a complete theory of melodic modality in the incipit of Viennese Classic themes; but we should be able, by examining many incipits, to come up with at least a few elements in such a theory.

APs in the incipit

[6]
We shall turn first to situations in which a nontonic pitch in the incipit precedes an adjacent tonic pitch (1°, 3°, or 5°), and is itself preceded by a leap, or (when it is the very first note of the theme) by nothing at all. A genuine nonharmonic tone in this situation would be called (in some usages anyway, including mine) an appoggiatura, and so these "unprepared" quasi-nonharmonic tones we will call "APs." Note that this has nothing to do with rhythmic grouping: whether the AP groups with the ensuing tonic pitch does not concern us here; all we care about is the sequence of events: gap, nontonic pitch, adjacent tonic pitch.

We will need to distinguish between "strong" APs-those metrically strong relative to the ensuing tonic note, which are treated quite freely (¶ [9])-and "weak" APs, the more restricted variety.

[7] Weak APs away from db0 ("downbeat 0")
We will look first at APs which are metrically weak relative to the ensuing tonic note, and which are normally in the midst of a theme, "away from db0 " ("downbeat zero")-that is, those in which the tonic "note of resolution" is not the very first downbeat of the theme ("db0").

The governing principles of weak APs away from db0 appear to be:

To flesh out these principles in detail and with examples, we'll discuss weak APs in order of freedom:

7-1°: These are free and commonplace; the examples here are drawn just from the piano sonatas of the four composers under discussion: EX 7-1. Notice the seventh example, Pf Son Op.49#1/i, 16: even though the B-natural which is marked as the AP, the immediate predecessor of the C, is itself preceded by several repetitions of the same B, I have interpreted it as an AP, since the onset of the repeated B-naturals is itself preceded by a leap, from F-natural . A directly-repeated pitch, in other words, is considered to arrive at its first appearance, and to persist until it is replaced. (However, this principle does not extend to distinguishing between strong and weak APs; see ¶ [9] below.)

6-5°: This is also treated freely; EX 7-2 gives examples drawn just from the chamber music (excluding the baryton and lyra organizzata works of Haydn).

#4-5°: Unrestricted as such, but usually used quickly and sparingly for tonal reasons; moreover, leaps to #4° are themselves rare: representative examples given in EX 7-3.

4-3°: Free; the first eight instances in EX 7-4 conform to patterns analogous to those given below for the more restricted 2-1° APs: 6-4|3° and 4|3-2° (where the | "barline" indicates that the note before it is relatively weak metrically, the pitch after it relatively strong) but the last five incipits show the 4-3° AP handled more freely.

2-1°: Common enough, but quite strictly controlled: the 2-1° AP in effect occurs only in the 4-2|1° formation, or in the 2|1-7° formation (typically at the barline with tonic harmony and a 4-3 suspension) EX 7-5 or in the 7-2|1° formation: EX 7-6. The only exceptions I can find to this are shown in EX 7-7; most are (quasi)-sequences, lie across a phrase boundary, etc.

2-3°: These are essentially avoided, except in 4-2|3° formations (EX 7-8). Most of the exceptions to this are in sequence, in implied polyphony, or across a phrase-boundary (EX 7-9); the more genuine counterinstances to this principle are given (all I could find) in EX 7-10.

4-5°: This basically does not occur as a weak AP (or even as a strong AP; see below). A few possible exceptions result from sequence, quasi-sequence, or imitation (representative examples in EX 7-11). EX 7-12 shows the real exceptions, all the weak-beat 4-5° APs I could find; notice even here that three of them are from the Schubert keyboard dances, where the arpeggiated style suggests several contrapuntal lines at once, and the 4-5° succession is an AP only on the most literal interpretation.

It's not obvious that these rules flow from any deeper principles, but as we shall see with grace-notes and elsewhere, the care with which the rising whole-step to a tonic pitch is used, especially in the rhythmic sequence weak -strong, seems basic to the style.


Notes

[1] Explicitly repertorial music theory is not common, theorists usually preferring to analyze just a few pieces at a time, presumably leaving to the reader the extension of their methods to other works of a similar kind; a few writers have, however, grounded their investigation of melody in a specific and homogeneous body of music. A series of articles by Sundberg and Lindblom (1970, 1973, 1976, 1991) attempted to formulate principles (inspired by the Chomsky-Halle rules for English intonational patterns) describing a small melodic corpus-53 of the (quite stereotyped) Swedish nursery songs of Alice Tegnér-sufficiently detailed to "generate," that is synthesize, the melody-line of these songs along with similar-sounding melodies; and also to apply these principles to multiple versions of a Swedish folk-song. While it's difficult for a reader unfamiliar with the original repertory to decide whether the synthetic melodies presented really are successful imitations, or whether the rules (somewhat laconically presented) really do unequivocally produce these melodies, and also all of Tegnér's, nevertheless one must admire Sundberg and Lindblom's attempt to take the "generative" aspect of "generative grammar" seriously.

Similar aims motivated the attempt of Baroni and Jacoboni (1978) to specify the rules governing a repertory composed of the first two phrases in the melody-line of 60 duple-meter, non-modulating Bach Chorales. Again, the attempt was to "generate"-synthesize-melodic phrases, in this case ones that sounded as much like the chorale-tunes as possible (using mostly left-to-right, non-hierarchic rules between beginnings and cadences already chosen), an enterprise requiring quite a large number of rules (56 of them, many with multiple clauses). A computer was used to produce the actual melodic examples, some of which seemed chorale-like, and some of which did not (see note 6 below). A later report (Baroni and Jacobi 1984) on the continuing project briefly describes MELOS 2, a computer program dealing with a corpus of 100 chorale-melodies, but only one synthesized example is given.

More recently, David Temperley (2001) has produced a set of principles, based on the "preference rule" model of Lerdahl and Jackendoff (1983) and embodied in computer algorithms, which performs several kinds of low-level (but by no means simple or straightforward) analyses on a musical surface: identifying metrical structure, simple melodic phrase-structure, "contrapuntal structure" (assigning notes to multiple simultaneous voices), pitch-spelling, harmonic analysis, and key-structure (including modulation). These analyses, for the most part, are readily confirmable by introspection (and in some cases notation), and though this is a different kind of inquiry from describing or synthesizing a repertory, from ruling out impossible themes or specifying obligatory features of them, Temperley does refer his principles to several kinds of corpus-a collection of folk-songs for sight-singing, for example, and an anthology of 46 classical music excerpts for classroom analysis-against which they are tested.

[2] The starting point for a discussion of modality-trans-historical, cross-cultural-remains the article "Mode" by H. Powers et al. in The New Grove (2001): "mode can be defined as either a 'particularized scale' or a 'generalized tune', or both, depending on the particular musical and cultural context. If one thinks of scale and tune as representing the poles of a continuum of melodic predetermination, then most of the area between can be designated one way or another as being in the domain of mode. To attribute mode to a musical item implies some hierarchy of pitch relationships, or some restriction on pitch successions; it is more than merely a scale." (my emphasis) For a discussion of melodic modal behavior undertaken in much the same spirit as the present study, see Day-O'Connell (2002), which surveys a characteristic "non-classical" treatment of the sixth degree in plagal cadences in the later 19th century. Day-O'Connell writes that even though Western music theory has focused primarily on group-theoretic or acoustic properties of the western scale, "nevertheless, 'modal' or 'syntactic' aspects of the major and minor scales reside firmly within the intuition of competent musicians, and we can therefore attempt to delimit these aspects with the hope of illuminating analytical and style-historical issues."

[3] It may be necessary to add that what is being attempted here is music theory, rather than music psychology. What we seek to characterize is the practice of certain composers; equivalently, we aim to describe, with some economy and precision, an aspect of the music they write (namely, the treatment of scale-degrees in thematic incipits). How exactly the composer goes about writing what he does, or how (or even whether) the listener grasps it, are things which will concern us only indirectly. This contrasts with many recent theoretical works seeking to produce, in the words of one of the most ambitious and influential of them, "a formal description of the musical intuitions of a listener who is experienced in a musical idiom" (Lerdahl and Jackendoff, 1983, p. 1). One of the common criticisms of Lerdahl and Jackendoff's A Generative Theory of Tonal Music and similar efforts has been the difficulty of deciding whether the more abstract and complex analyses presented there do, in fact, represent our intuition: such analyses are often beyond simple introspective confirmation, and for the most part controlled psychological experiments have naturally concentrated on considerably more immediate features of the music. Among the aspects of melodic perception which are readily available to introspection, however, are not only the kind of analyses considered in Temperley (2001), mentioned above, but also the yet-simpler discrimination implied when we say, this theme sounds fine, this alternative (produced when we change one of Mozart's notes) does not; this is a melody, this is a melody missing something, this is just a nonsense string of notes. Since the perceptual judgments here are primitive-yes, no, I don't know, maybe-and since we can produce at will a great many more inadequate themes than adequate ones, the focus shifts from characterizing the more recondite output of the listening apparatus-its parsings, its groupings, its mappings and hypotheses and expectations, all those things that analysis tries to depict-to characterizing the input: what is it about the notes that separates successful from unsuccessful themes, wonderful melodies from the mediocre and from the ludicrous, melodic sense from nonsense? A similar point is made by Sundberg-Lindblom 1991: "[Lerdahl and Jackendoff] do not address the issue of describing musical style in the sense of what is possible and what is impossible."

[4] Works are identified by Hoboken numbers (for Haydn) without the Roman numerals of the larger subdivisions (thus the second movement of the String Quartet H.III/70 is referred to simply as "SQ H.70/ii"); by the traditional (pre-Einstein) Köchel numbers (Mozart); by opus number or "WoO" number (Beethoven); or by Deutsch catalog number (Schubert). Where not otherwise specified, the melody in question is that at the beginning of the movement; otherwise it is identified by the measure number in which it begins. To facilitate comparison, all examples below have been transposed to C major. A complete list of works in the examples, with a list of abbreviations used, can be found in the Appendix.

[5] There is a tradition of "scale-degree" tendencies attributed to these tones going back at least to Percy Goetschius (1900/23); see the useful surveys in Burdick (1977, chapter 4), and in Day-O'Connell (2002). Burdick derives some of these notions from the customary voice-leading of dominant-to-tonic resolutions in figured-bass practice and standard harmonic theory, but credits Goetschius with the first attribution of intrinsic tendencies to scale-degrees apart from specific harmonic circumstances. Goetschius calls 2°, 4°, 6°, and 7° the "active" scale-degrees, while 1°, 3°, and 5° are "inactive"; by a tendency which Goetschius likens to gravitational attraction, the 7° is disposed to move toward the tonic, the 6° to the 5°, the 4° to the 3°, and the 2° is "evenly balanced" between 1° and 3° (because it is equidistant from both). His diagram of these resolution-tendencies is apparently the first of many:

(Goetschius 1900/23, p.2)

These innate tendencies may be counteracted by scalewise motion, by arpeggiation, by deferred resolution, or by a leap of a third to another active scale-degree (which then should resolve "properly"); later he also allows for the complicating effects of motivic repetition and sequence.

Some such scale-diagram has been a textbook commonplace ever since Goetschius, and Burdick (1977) sets out to investigate whether in fact the "tendencies" they aim to illustrate are borne out in practice. He is interested, however, not in immediate note-to-note movement, but with progressions between "structural tones," which he devises a systematic and plausible way to identify (based on consonance, stress, precedence, metric position, etc.). Burdick produces in this way, from a repertory of 513 thematic passages in Haydn, Mozart, Schubert, and Chopin, a corpus of lightly-reduced, consonant, rhythmic-melodic skeletons, similar to Leonard Ratner's (1980) "basic structural melodies," and to the "melodic germs" which Goetschius (1900/23, §121-123) imagines to be the scaffolding behind more elaborate melodies. In these reductions, Burdick finds that nontonic scale degrees do indeed most often progress to their tonic "proper resolution" as given by Goetschius, but not overwhelmingly so, and that the many "irregular resolutions" to be found can for the most part be systematically categorized in terms similar to those of Goetschius (delayed resolution, sequence or repetition, progressions across a phrase boundary, etc.). He also finds that "irregular resolutions" occur more often at the beginning and the middle of phrases, while closer to points of closure the nontonic scale-degrees tend to progress more reliably to their "natural" pitch of resolution.

While Burdick's work differs from the present effort in several ways-the abstraction from the musical surface to a sequence of "structural tones," and the investigation essentially of two-note melodic progressions (a nontonic pitch and its successor), rather than of three-note figures such as passing-tone and neighbor-tone configurations-it does anticipate an essential aspect of this study, the examination of idiosyncratic scale-degree treatment in themes drawn from a sizable and homogeneous body of music.


Continue to Section II
References and Appendix

©Roger Solie, 2006

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