This paper grows out of a dissertation entitled Problems of Tonality: Schoenberg and the Concept of Tonal Expression (Columbia University, 1989). The author wishes to acknowledge the support of the Social Sciences and Humanities Research Council of Canada without which the investigation would have been severely curtailed. And he wishes to thank Patricia Carpenter, Martha Hyde, Ian Bent, Edward Lippman, and Robert Austerlitz for many timely suggestions regarding the material.
If we sum up the characteristics of the church modes, we get major and minor plus a number of nondiatonic phenomena. And the way in which the nondiatonic events of one church mode were carried over to the other modes I conceive as the process by which our two present-day modes [major and minor] crystallized out of the church modes. Accordingly, major and minor contain all those nondiatonic possibilities inherently, by virtue of this historical synthesis. (Arnold Schoenberg, Theory of Harmony)1
It seems remarkable that a composer of highly chromatic music should be concerned with the fundamentally diatonic "church" modes. For Schoenberg, however, the chromatic enrichment of the ecclesiastical modes led to modern tonality; to be precise, Schoenberg found in chromatic enrichment the cause for the abandonment of modality in favor of tonality. That a style of pitch organization such as modality should give way under the weight of chromaticism was a lesson surely not lost on Schoenberg. The goal of this article is to investigate Schoenberg's conception of modality and its decline so as to better understand his concept of a chromatically enriched extended tonality and its abandonment, ultimately for twelve-tone composition.
My principal task is to examine Schoenberg's thoughts on modality and tonality, which are scattered throughout his published writings. To accomplish this, I shall concentrate on Schoenberg's terminology, for in coining new or redefining old terms he reveals a larger conception at work. The greater part of this paper, then, will be lexical—concerned with a vocabulary from which certain fundamental concepts emerge.
The terms key and tonality are sometimes treated synonymously, but following Schoenberg, distinctions must be drawn between them. When Schoenberg speaks of tonality, he means the principle that relates a set of pitches (diatonic and chromatic) to one referential pitch—to a tonal center or tonic—the tonal principle. But he also means the set of pitches that embodies this principle. For example, in Structural Functions of Harmony he speaks of the "minor tonality" comprising two scale forms, ascending and descending, the former with chromatic sixth and seventh scale degrees.2 The minor tonality, then, is a particular concretization of the principle of tonality—a set of pitches comprising two subsets (two scales) relating to one tonal center. Hereafter, I shall use the term tonality to denote both the tonal principle and what other writers sometimes refer to as a key—a group or family of pitches (Tongeschlecht)3, one of which acts as a center and to which the others relate as diatonic or chromatic.
By eschewing key, I shall avoid a common confusion: in modern usage, one refers to the key of a whole work, or to the keys within a work. (For example: "One therefore speaks of a piece as being in the key of C major or C minor, etc . . . .The key of a movement commonly changes during its course through the process of modulation . . . .")4 I shall call the key of a whole work its tonality, and the keys within a work its regions. Following Schoenberg's principle of monotonality, a movement has only one tonality (and tonal center), though it may encompass many chromatic pitches. Schoenberg usually calls the keys to be distinguished within a movement the "regions" of a tonality, "region" denoting a diatonic subset of a chromatically expanded tonal whole. He notes that regions can be "carried out like independent tonalities" (can incorporate chromatic pitches called "substitutes"). But they are, at heart, diatonic tonal segments of one larger, encompassing tonality: "segments of [a tonality] which are carried out like independent tonalities: the regions."5
Rather than rely on pitch-letter names to label regions, Schoenberg uses a system of functional names—like subdominant, supertonic and submediant. This system is set forth in the familiar chart of the regions (see Figure 1). Schoenberg warns against applying pitch-letter names to regions, because letters are functionally neutral, showing nothing of relationship between region and the whole tonality. Functional names (showing the relationship by scale degree to the center or tonic of the tonality) are to be preferred: "A region . . . is considered a related product of a tonic. If, accordingly, a period ends in its eighth measure on V or III of C major, one must not call this a modulation to G major or E minor, but a change or movement to the dominant region or to the region of the mediant."6
Figure 1. Schoenberg's Chart of the Regions, from Structural Functions of Harmony, used by permission of Belmont Music Publishers, Pacific Palisades, California 90272.
Perhaps the term of greatest importance to the concept of modality in Schoenberg's lexicon is "character" or more frequently "characteristic" [Merkmal, Eigentümlichkeit, Charakteristik].7 "Characteristic," applied in the context of tonality, refers to a pitch that distinguishes one region from another (by its presence in one region, its absence in the other). The term is used in Schoenberg's treatment of the cadence, the minor mode, and—my present concern—the ecclesiastical modes.
Schoenberg uses both "character" and "characteristic" generally to denote the salient features of an entity. He describes the features of a motive or figure as its "character." The character of a "figure" should foreshadow its continuation: "If . . . in music, a figure is so constituted, so lacking in character, for example, or so complicated, that I cannot recognize it and remember it, then correct understanding of all that follows—all that results from it, follows from it—is impossible."8 The melodic procedure Schoenberg calls "reduction"—the alteration of a motive or melody that reduces its innate momentum in preparation for the cadence—depends on this concept of characteristic: "The melody in the cadence commonly reduces characteristic features (which demand continuation) to uncharacteristic ones."9
Characteristic, salient features are often those that distinguish one entity from another. The characteristics of a single pitch are its particular overtones, as opposed to the characteristic overtones of another pitch. Any pitch in a chromatic scale can pass as a fundamental—an embryonic tone from which everything springs10 if these characteristics are accentuated:
Each tone can pass for a fundamental if its most important characteristics are strengthened, for example, if its major third and its perfect fifth are reinforced, if the major triad which is lightly sounded in the overtone series be stressed, be awakened to life.11
I shall use Schoenberg's term "characteristic" hereafter to mean those features that distinguish one entity from another.
The importance of this notion of characteristic features to Schoenberg's concept of tonality should not be underestimated. In the tonic region, the IV—V—I or ii—V—I cadences create simple but effective expressions of a tonality, since the chords IV, II, and V taken together contain the two characteristic pitches that distinguish the tonic region of a given tonality from the tonic regions of its nearest neighboring tonalities at the fifth above and below. The two tones in question are scale degree 4 (the root of IV or the third of II) and scale degree 7 (the third of V). The presence of scale degree 4 (F) in a tonality (C major) distinguishes it in pitch content from the tonality a fifth above (G, with leading tone); the tonality a fifth above is ruled out by the presence of scale degree 4. So too, the presence of scale degree 7 (B in C major) distinguishes the tonality from that a fifth below which has a different pitch for scale degree 4 (). In other words, where scale degrees 4 and 7 are present—in the cadence, for example—there should be no confusion with tonalities at the fifth above and below:
Apart from the tonic at the beginning and the end, the characteristics of a major tonality are the 4th and 7th tones. The 4th tone represents the subdominant region (IV and II), and thus prevents the interpretation of a segment as expressing a tonality a fifth above. The 7th tone represents the dominant region (V), and thus prevents the interpretation of a segment as expressing a tonality a fifth below. To achieve a cadential effect these two tones, or their substitutes, must appear immediately before the final tonic.12
These characteristics are indispensable to tonal expression:
Should we want to establish C major in such a way that there is no doubt about it, that is, so that we can think of neither F nor G major, then we must introduce B and F. The most important means for expressing the key will thus be those that distinguish it from the keys it most resembles, that separate it clearly from its nearest neighbors. Once we have succeeded in excluding confusion even with those keys with which it could most easily be confused, then we have defined the key unambiguously.13
The instability of the minor tonality serves Schoenberg as another model for describing tonal character. For Schoenberg, the minor mode is chronically unstable—a synthetic product, as opposed to the major scale which is a direct imitation of nature.14 To distinguish it from its stronger relative, the minor requires a chromatic seventh scale degree borrowed from the parallel major—an "artificial imitation of the cadence." (The chromatic sixth scale degree follows for the sake of smooth voice leading.) Schoenberg calls this its "characteristic": "The minor scale has its particular characteristic less in the minor third than in the artificial imitation of the cadence, by means of a half step, which is found in the major scale."15
From the terms introduced here, Schoenberg's term "characteristic" in particular, one can draw conclusions about Schoenberg's concept of modality, its decline, and its replacement by tonality. I shall concentrate on the chromatic alterations made to the church modes, which serve as a precedent for the characteristic borrowed scale degrees 6 and 7 (called "substitutes" by Schoenberg) in the minor tonality. For Schoenberg, the modes were originally all diatonic—modal polyphony being based on "the seven tones of the diatonic scale," to which "the remaining five tones" were largely extraneous.16 The modes in their original form share the same seven diatonic tones and differ only according to the characteristic position of two semitones with respect to the modal final—their diatonic characteristics. (For example, Ionian, which has semitones between scale degrees 3-4 and 7-8, differs from Dorian, which has semitones between scale degrees 2-3 and 6-7.) The positions of the semitones with respect to the final, then, are the original diatonic characteristics of Schoenberg's modes.
As the individual church modes evolved, they took on artificial chromatic characteristics borrowed from or in imitation of other modes. Dorian, for example, took on a chromatic (raised) seventh scale degree, as well as a chromatic (lowered) sixth scale degree (a descending leading tone to scale degree 5), like the characteristic scale degrees of the melodic minor. The chromatic seventh scale degree of Dorian was borrowed from the Ionian mode (as is the chromatic scale degree 7 of melodic minor), where it was a diatonic characteristic:
The church modes had a tendency to imitate a certain characteristic of the Ionian, whose seventh tone is an ascending leading tone [scale degree 7] . . . .17
The practice of mixing the characteristics of several modes in an artificial hybrid was, for Schoenberg, the cause of the decline of modality. The church modes could not sustain chromaticism and maintain their original character; through the application of accidentals to produce such artificial chromatic characteristics, "their distinguishing [original modal] characteristics were thereby cancelled out . . . . "18 They gave way to two new chromatically expanded tonal modes, major and minor, which encompassed the various characteristics of all the old church modes and in doing so became modern tonalities. Schoenberg accounts for this as follows:
The individual modes became so similar to one another that in the end only two main types were left that are clearly distinguishable: major, which brought together the characteristics of Ionian and the other major-like modes; and minor, which brought together those of Aeolian and the other minor-like modes.19
The product of this development was extended tonality—the tonal principle extended to cover not only diatonic tones but also chromatic tones in one given tonality. Schoenberg describes an extended C major tonality comprising both diatonic pitches and the following added chromatic pitches (see Example 1): and modelled on the alterations made to the Dorian mode on D to make it resemble Aeolian and Ionian, from the Phrygian mode on E (as a curious leading tone to the modal fourth scale degree [a sort of hypo-leading tone]) to make it resemble Aeolian,20 from the alteration to the Lydian mode on F to make it resemble F Ionian, as a raised seventh degree from G Mixolydian to make it resemble G Ionian, and both and as characteristic raised sixth and seventh scale degrees of A Aeolian borrowed to make it resemble A Ionian. His C-major tonality is thus enriched by the tones , , , (and ), as well as , all of which find precedent in characteristic alterations to the church modes.21 It is but a small step from this chromatic modality enriched by characteristic tones borrowed from other diatonic modes to a modern chromatic tonality enriched by characteristic tones borrowed from diatonic regions. To describe extended tonality, Schoenberg's term "substitution" must be introduced and briefly defined.
EXAMPLE 1 "The Derivation of Substitute Tones in C major," from Structural Functions of Harmony, ex. 29a, used by permission of Belmont Music Publishers, Pacific Palisades, California 90272.
Substitution is the procedure of introducing into a region a chromatic pitch in lieu of, or to substitute for, a diatonic pitch of the same letter name. The diatonic pitch is a member of the tonic region, which I shall call a target region. The chromatic substitute is borrowed from what I shall call a source region (the region where the substitute is diatonic).
An excerpt from the second movement of Beethoven's Second Symphony, reproduced in Structural Functions of Harmony, will serve to illustrate substitution (see Example 2). The excerpt is set in A major. The and in the second half of the example are borrowed from the region of the tonic minor (the , from the "descending form" of the minor) to substitute for the and of the tonic major region. Schoenberg draws attention to the substitution by analyzing the second group of four bars in tonic minor. He does so with the lower-case letter "t," the symbol for the region of tonic minor, which tells us that the substitutes and are borrowed from the tonic-minor region. This symbol must not be taken to indicate a modulation or change of tonality, nor should it be taken to imply a mixture of modes.
Example 2. Substitution in Beethoven's Symphony No. 2, Larghetto, from Structural Functions of Harmony, ex. 74a, used by permission of Belmont Music Publishers, Pacific Palisades, California 90272.
As Schoenberg puts it, the regions are carried out like, but only "like," independent tonalities: their characteristic pitches are used as substitutes, thus creating the impression (but only the impression) of a change of tonality, of modulation.22 Modulation between tonalities within a piece of tonal music is an illusion in this respect: substitution only suggests or feints modulation—a region carried out as if it were an independent tonality. True modulation, if it happens at all, takes time, according to Schoenberg:
Intermixing of substitute tones and chords with otherwise diatonic progressions, even in non-cadential segments, was considered by former theorists as modulation. This is a narrow and, therefore, obsolete concept of tonality. One should not speak of modulation unless a tonality has been abandoned definitely and for a considerable time, and another tonality has been established harmonically as well as thematically.23
Just as the tonality cannot move easily between regions through modulation, neither can two regions be completely dissolved into one another; every region remains a distinct entity. With reference to the Beethoven excerpt cited, tonic A major and its parallel minor are not fused to form one mixed-modal hybrid, A major/minor. The region of tonic major, identical in tonic and quality with the tonality of the movement, constitutes what I called a target region into which substitutes from other distinct regions are inserted.
Tonality, accordingly, is not a melting pot in which chromatic and diatonic pitches commerce freely without allegiance. Tonality is a multifaceted and uneven terrain built of separate though adjoining planes—the regions. Every region relates to the tonality by the scale-degree interval between its tonic and the tonal center, and every region contributes some characteristics to the tonal crucible, as substitutes introduced into the tonic region. These substitutes refer back from the referential plane of the tonic region to their source regions (which they affirm in doing so). Tonality, then, is built of many orientations; it is metaphorically a parliament of pitches reflecting various regions through characteristic representatives brought together in a central governing region.
The concept of substitution is a missing clause in the current definition of Schoenberg's term "monotonality." In monotonality, the tonic region is the central frame of reference; after all, without some exclusively diatonic referential collection of pitches, nothing can be referred to as chromatic. All substitutes orient monotonally to this one original diatonic collection as replacements for diatonic pitches; there must, after all, be some ultimate or privileged set of diatonic pitches which chromatic substitutes stand in lieu of. In monotonality such a collection ought to comprise tones diatonic to the tonal center from which the tonality takes its name; any other region presupposes chromaticism and, thus, substitution. It follows that the pitch that constitutes both the tonal center and the tonic of the tonic region forms a central reference point in monotonality; chromatic pitches are simply substitutes for scale degrees that relate diatonically to this pitch.
It follows as well that the more expansive the tonality (the greater the number of substitutes), the more attenuated becomes the ability of the tonic region as a vessel to encompass chromatic tones and the tonal center to serve as a frame of reference. In a truly expanded tonality, the characteristics of the tonic region would be simply overwhelmed by the borrowed characteristics of other regions, much as the characteristics of the individual modes were overwhelmed by substituted characteristics borrowed from other modes; the tonic region ceases to be a "distinct" entity; and in effect the tonal vessel shatters.
Following the concept of substitution, chromaticism does not inhere in any given pitch but instead is produced by transferring the characteristics of one region to another and thereby expanding the tonality. The model and, following Schoenberg, the historical antecedent for this procedure of transferring tonal characteristics is the substitution of modal characteristics that leads to the decline of modality. This lesson of history was presumably not lost on Schoenberg as he tried to come to grips with chromatic tonality in the works of Brahms, Wagner, and Reger, and its continued evolution in his own work. Chromaticism can be conceived of as a monotonal "problem" of perspective: how to describe the relationships among the regions from which substitutes are borrowed and their relationship to the tonic region and tonal center.24 A spatial perspective is implicit in Schoenberg's use of functional names, which show relationship by interval—distance measured by scale degree. (This tonal space is represented in the geometry of the chart of regions.)25 As tonality expands, so this perspective broadens; distances can be reckoned through a number of paths, some of these not leading directly from the tonal center but wandering instead through intermediate points of reference. Eventually, when too many paths are explored in the domain of a given piece, the spatial perspective tonality affords us breaks down.
Schoenberg's precedent for substitution, as I have noted, lies in substitutes borrowed from one mode to stand in lieu of the diatonic pitches characteristic of another. So Schoenberg referred to five chromatic substitutes in the diatonic modal polyphony of the "Netherlanders":
The secrets of the Netherlanders, strictly denied to the uninitiated, were based on a complete recognition of the possible contrapuntal relations between the seven tones of the diatonic scale . . . the remaining five tones were not included in these rules, and, if they appeared at all, did so apart from the contrapuntal combination and as occasional substitutes.26
Accordingly, Schoenberg refers to the modal chromatic pitches of Example 1 as substitutes:
It must be kept in mind that the minor tonality is a residue of one of the modes, the Aeolian. As such, it uses the seven tones of the diatonic (Ionian) scale [equivalent to the relative major], and produces all its characteristic differences by means of substitutes.27
To reiterate, it is but one small step in musical evolution according to Schoenberg to move from substitutes borrowed from the modes to substitutes in the minor tonality, and another step to substitutes in extended tonality—substitutes borrowed from regions.
To follow this evolutionary course, the problem of extended tonality, of a chromatic perspective—how to orient chromatic tones spatially to one and only one tonic region and tonal center through substitution—eventually becomes unsolvable. Given the weight of chromaticism, extended tonality simply ceases to function. Schoenberg rehearses the "dethroning" of tonality by chromaticism (and dissonance) in the essay "Composition with Twelve Tones (1)":
In the last hundred years, the concept of harmony has changed tremendously through the development of chromaticism. The idea that one basic tone, the root, dominated the construction of chords and regulated their succession—the concept of tonality—had to develop first into the concept of extended tonality. Very soon it became doubtful whether such a root still remained the centre to which every harmony and harmonic succession must be referred . . . . tonality was already dethroned in practice, if not in theory.28
Following this path of evolution, Schoenberg presumably set to one side a monotonal orientation in favor of twelve points of reference and new spatial perspectives drawn from them: the row and its forms.
I will not argue about the propriety of Schoenberg's concept of modality to our own, nor speculate upon its origins. (He, himself, suggests it was derived from Max Loewengaard,29 although examination of that theorist's work has proven largely fruitless in this respect.) The end to which Schoenberg's train of thought moves is patent: if modality gave way under the weight of chromatic substitutes (which obscured the characteristic diatonic differences upon which the modes are based), then surely diatonic tonality would give way too as it extended to encompass a full twelve tones, and a new system of relation among tones would have to be devised. Whether we agree with Schoenberg's conception of the modes or not, it should inform nonetheless our appreciation of that common Schoenbergian term, "extended tonality"—which means not a loose mixture of chromatic and diatonic elements but rather a precisely articulated tonal field comprising regions distinguished by characteristic pitches and related by their tonics to a tonal center. Schoenberg's modal conception should inform, as well, our appreciation of his evolving twelve-tone method and its tonal antecedents.
* * *
The questions addressed in this article have been largely of an historical and lexical nature, and not of any immediate application in analysis or theory. Schoenberg's concept of characteristic can be applied, however, to the question of tonal orientation, a question of some concern to the field of music perception. Richmond Browne, in the essay entitled, "Tonal Implications of the Diatonic Set," refers to "rare" intervals, the tritone in particular, that aid in "position finding," in tonal orientation.30 Browne speaks of new rare intervals "not contained in the diatonic collection of the moment," which herald a change of tonal orientation. For example, modulation from C to G will be preceded by the new, rare-interval tritone C to .
Tonal orientation was a constant concern of Schoenberg. Indeed the Harmonielehre can be considered not only a manual for creating harmony but also a treatise on how harmony is perceived through a process of tonal orientation not unlike Browne's, but from a different perspective. Browne, working with intervals and within a single diatonic collection, distinguishes rare intervals from larger entries in the interval vector. Schoenberg, working within an enlarged diatonic field comprised of diatonic regions (expanded tonality), could be said to distinguish "rare" and thus characteristic pitch classes proper to one region from more numerous pitch classes shared by that region and its neighbors. For Browne, the appearance of a new rare interval necessitates a change of orientation, and so too for Schoenberg the appearance of a new rare pitch would necessitate a change of orientation and herald a new collection.
Let us consider a simple example of rare pitches at work (and thereby expand upon Schoenberg's concept of the cadence, as discussed above): in an extended C major tonality comprising at least the three closely related regions of tonic, subdominant, and dominant, the pitches and occur in one region each, and occur in two regions, and C, D, E, G, and A are common to all three. In this sense, and are "rare," and their presence individually at any given moment would distinguish the tonic region from the dominant region (in the case of ), and the subdominant region (in the case of ). (In effect, the cadence IV—V—I in the tonic region rules out the rare pitches and .) In this context, the pitches C, D, E, G, and A are incapable of such distinctions, or to quote Browne: "Rare intervals [and rare pitches] aid position finding. Common intervals [and common pitches] do not."31
The notions of rare intervals and rare pitches are abstract theoretical concepts. Tonality, of course, is a tangible quality of a piece, and so we might ask: "How, in terms of tangible experience, would the notion of characteristically rare pitches account for tonal orientation and reorientation?" David Butler has pointed out the complexity of tonal orientation, and, drawing upon Browne, has proposed a model of an intervallic hierarchy of intervals that
takes the dynamic form of perceptual rivalry . . . . Any tone will suffice as a perceptual anchor—a tonal center—until a better candidate defeats it. The listener makes the perceptual choice of most-plausible tonic on the basis of style-bound conventions in the time ordering of intervals that occur rarely in the diatonic set; that is, minor seconds (or enharmonics) and the tritone.32
Butler contrives an example: any given pitch G in its own right will serve as a tonic—a perceptual anchor—lacking a better candidate. An added to this G will usurp the role of tonic, "in as much as half steps are found below tonics, but not above them."33 The addition of a tritone to either G or would set up another perceptual rivalry: what is the tonic? (posed by adding D to ) or (adding to G)? To put it in spatial terms, the addition of a rare interval—semitone or tritone—determines a critical path toward a tonic, a path chosen from among other less plausible paths.
Let us recast this argument: Schoenberg, I think, would have agreed with Butler's point that "any tone [G, for example] will suffice as a perceptual anchor—tonal center—until a better candidate defeats it." The addition of Schoenberg might have seen, however, as opening up both and tonics, since the semitone G to occurs in both those keys. The conflict would be decided at the tritone by adding a pitch characteristic to one key (and accordingly not to the other)—D to the key of , and to the key of . All other pitches are common to both keys and would not serve this orienting function. In other words, the addition of a characteristic pitch—D or —determines the critical path toward a tonic, a path chosen as most plausible from among other paths.
With the notions of rare intervals and characteristically rare pitches, Browne, Butler, and Schoenberg would seem to be taking a similar stance on tonal orientation. Do these models account for perception? Yes, but I would compound them to yield an extended tonality.
Let us expand upon Butler's example: Instead of adding a tritone to the collection of G and , let us add another rare semitone below G—the pitch , characteristic of neither nor . Does this not give rise to a more complex tonal rivalry, within and between two groups of tonics: the tonics and (implied by the common pitches G and ), and the tonics , , , and (implied by and )? It would do so with great economy, to great effect and with few resources. While Butler's conflict invokes only two tonics by exchanging tritones or characteristic pitches, the addition of another rare minor second by means of the uncharacteristic pitch (in the context of and ) creates a conflict of at least six tonics (implying a rivalry between at least six tritones). By adding a minor second to a minor second, I have produced a major second, a spectacularly common interval. It would seem, however, that the intermingling of rare and common intervals produces a rivalry of some complexity. Accordingly, the addition of the major second to the semitone /G opens a wider domain of key relations, not simply to include another rival key but rather a domain comprised of several tonal regions.
While there is a certain efficacy to laboratory experiments deciding between two keys, surely our ears are more agile and juggle three, four, perhaps even more keys—domains or regions—as potential and even plausible at any given moment. Let us postulate a model of tonal orientation built not only upon two distinct keys involved in a conflict of tonics (through the disposition of rare intervals and characteristic pitches) but also involving clusters of keys. As I listen to a piece, my ear decides not between individual tonics but rather assembles a tonality comprised of many keys. Keeping a tonal referential frame comprising such a group of keys, my ear adds certain tonics (individually or in groups) to the frame as plausible and casts others aside.
To illustrate, I shall turn to the not so plausible metaphor of a card game. Imagine that my initial experience of a tonality is rather like the experience of opening up a hand. Being certain of a tonality is like finding four or more cards characteristic of some winning combination (high, of the same suit, etc.), which entails by default the elimination of cards characteristic of other combinations. As I ponder my hand, I make critical decisions pointing to one optimal grouping; I look for rarities—a flush, a straight, four of a kind—but also combinations of rarities and not-so-rare cards that will allow me flexibility on the second deal. So too, as a piece proceeds I listen for characteristic tones leading to an optimal grouping; I look for rarities—tritones, semitones, chromatic pitches—but also combinations of rarities and those common intervals or pitches that will allow me flexibility as the piece proceeds. I then make a critical decision (unless I am very lucky), casting aside those cards or characteristic pitches that cannot plausibly lead to a winning hand or to a firm tonal orientation. But I retain in my hand the characteristics of what could be several winning combinations, much as I retain potential rare intervals or pitches (and not-so-rare intervals or uncharacteristic pitches) that could lead to several tonal orientations. It is only in the subsequent hand that I am forced to select one combination of possible orientations, and it is only as I am lead through a cadence that I know whether my tonal orientation pays off or not. The laboratory is rather like being dealt one final hand; in truth the musical experience is far more complex and exciting.
To the primarily historical and lexical observations drawn here, let me add that Schoenberg's notion of characteristic has a certain relevance to perceptual models of tonal orientation. Schoenberg did speak of a rivalry of tonics,34 but this took place within an extended tonality that would seem to encompass a multitude of tonics. How can we accommodate the narrow (two tonics) and the broad (the multitude) in modelling the process of tonal orientation? The process is one of gradual selection between orientations, of deciding some pitches are rare and characteristic, while some are not, of paring down the multitude to a critical group. In this respect, extended tonality is neither a level playing field, a free intermingling of forces, nor a field divided clearly by a frontier. Tonality, characteristically, is an uneven field slanted dramatically in several directions and filled with dead ends, through which one moves cautiously by choice between rival attractions, while holding one's options to the final moment—being always at the mercy of the dealer.
1Arnold Schoenberg, Theory of Harmony, Roy E. Carter trans. (Berkeley: University of California Press, 1978), 427-28; translation of Harmonielehre, third ed. (Vienna: Universal Edition, 1922). Cross references in these footnotes are to the seventh German edition, published by Universal Edition, 1966.
2Arnold Schoenberg, Structural Functions of Harmony, rev. ed. Leonard Stein ed. (New York: W. W. Norton, 1969), 9. In Theory of Harmony, Schoenberg refers to the two "regions" of the minor tonality, its ascending and descending forms (p. 124).
3Riemann Musiklexikon, twelfth ed., W. Gurlitt and H. H. Eggebrech, eds. (Mainz: B. Schott's Söhne, 1967), Sachteil, s. v. "Tonart."
4The New Grove Dictionary of Music and Musicians, ed. Stanley Sadie (London: MacMillan, 1980), vol. 10, s. v. "Key (i)."
5Schoenberg, Structural Functions, 19.
6Arnold Schoenberg, Models for Beginners in Composition, rev. ed., Leonard Stein ed. (Los Angeles: Belmont, 1972), 55.
7The three terms are used in several ways in Theory of Harmony and the essay "Problems of Harmony," in Style and Idea: Selected Writings of Arnold Schoenberg, L. Stein ed., L. Black trans. (Berkeley: University of California Press, 1984). And, see the German-language edition, "Probleme der Harmonie," in Styl und Gedanke: Aufsätze zur Musik, Ivan Vojtech ed., vol. 1 Gesammelte Schriften (N.p.: S. Fischer, 1976).
Merkmal, in Theory of Harmony, 95 (from Harmonielehre, 110) to denote characteristics of the minor mode.
Charakteristik, (i) in Theory of Harmony, 96 (from Harmonielehre, 111) to denote the distinctive quality of a thing; (ii) but more particularly with reference to the character of the minor mode—Mollcharakteristik—in Theory of Harmony, 124 (from Harmonielehre, 145), and see "Problems of Harmony," Style and Idea, 272 (Styl und Gedanke, 222).
Eigentümlichkeiten, (i) in Theory of Harmony, 95, 222, 427 (footnote to p. 175) (from Harmonielehre, 110, 267, 206) to denote the characteristics of the church modes—Kirchentonarten-Eigentümlichkeiten; (ii) in "Problems of Harmony," Style and Idea, 273 (Styl und Gedanke, 222) to denote the characteristic overtones of a fundamental.
8Arnold Schoenberg, "New Music: My Music," in Style and Idea, 103.
9Arnold Schoenberg, Fundamentals of Musical Composition, G. Strang and L. Stein eds. (London: Faber and Faber, 1970), 30.
10Schoenberg, Theory of Harmony, 28.
11Schoenberg, "Problems of Harmony," in Style and Idea, 273; "Probleme der Harmonie," Styl und Gedanke, 222.
12Arnold Schoenberg, Preliminary Exercises in Counterpoint, L. Stein ed. (London: Faber and Faber, 1963), 73; and see Structural Functions, 12-13.
13Schoenberg, Theory of Harmony, 130; Harmonielehre, 152.
14Schoenberg, Theory of Harmony, 23, 95, and see pp. 184-85. Compare Heinrich Schenker, Harmony, Oswald Jonas, ed., Elisabeth Mann Borgese, trans. (Cambridge: MIT Press, 1973), 54, 247-48.
15Schoenberg, "Problems of Harmony," 272; "Probleme der Harmonie," 222. Schoenberg's minor tonality and the voice-leading procedure called "neutralization," are treated at length in my article entitled "Schoenberg's Concept of Neutralization," Theoria: Historical Aspects of Music Theory 2 (1987): 13-38.
16Schoenberg, "New Music, Outmoded Music, Style and Idea," in Style and Idea, 117.
17Schoenberg, Theory of Harmony, 95; Harmonielehre, 110.
18Schoenberg, Theory of Harmony, 95.
19Schoenberg, Theory of Harmony, 95; Harmonielehre, 110-11.
20The derivation of chromatic pitches from the Phrygian "church" mode (section c) seems puzzling in Example 1. The example tallies the various chromatic additions to C major. Section g of the example contains a , which could only be derived as a leading tone, raised scale degree 7, of Phrygian. Schoenberg, however, in the example omits the from section c, his Phrygian scale, and uses instead a , thereby leaving the unaccounted for. A passage from the Theory of Harmony only compounds this puzzle: "Phrygian (starting on the third tone, E) gives B, , (it was not commonly used in this form) and E, D, C, B." See Theory of Harmony, 175.
21See: Schoenberg, Theory of Harmony, 175-78.
22Schoenberg, Structural Functions, 19.
23Schoenberg, Structural Functions, 19. The principle of monotonality—one single extended tonality—would seem to rule out modulation, but the quotation suggests otherwise. And see Models for Beginners, 55.
24The concept of a tonal problem—raised in "New Music, Outmoded Music," 123—provides a powerful conceptual tool for envisioning a work as a whole, the working out of a problem of tonal relation: for example, the problem posed by tonally ambiguous substitute tones. It has been addressed in Patricia Carpenter's writings. See the following:
Patricia Carpenter, "Grundgestalt as Tonal Function," Music Theory Spectrum 5 (1983): 21, 24; "Musical Form and Musical Idea: Reflections on a Theme of Schoenberg, Hanslick, and Kant," in Music and Civilization: Essays in Honor of Paul Henry Lang, E. Strainchamps, M. R. Maniates eds., with C. Hatch (New York: Norton, 1984), 418 (where she speaks of balance and imbalance); "Aspects of Musical Space," in Explorations in Music, the Arts, and Ideas: Essays in Honor of Leonard B. Meyer, R. Solie and E. Narmour eds. (Stuyvesant, N. Y.: Pendragon Press, 1988), 352; "A Problem in Organic Form: Schoenberg's Tonal Body," Theory and Practice: Journal of the Music Theory Society of New York State 13 (1988): 39.
25Fred Lerdahl refers to Schoenberg's "regional space." See "Tonal Pitch Space," Music Perception 5, no. 3 (1988): 343. And see Carpenter, "Aspects of Musical Space."
26Schoenberg, Style and Idea, 117.
27Schoenberg, Structural Functions, 30.
28Schoenberg, "Composition with Twelve Tones (1)," Style and Idea, 216.
29Schoenberg, Theory of Harmony, 95.
30Richmond Browne, "Tonal Implications of the Diatonic Set," In Theory Only 5, nos. 6-7 (1981): 3-21.
31Browne, "Tonal Implications," 8.
32David Butler, "Describing the Perception of Tonality in Music: A Critique of the Tonal Hierarchy Theory and a Proposal for a Theory of Intervallic Rivalry," Music Perception 6, no. 3 (Spring 1989): 238. See as well, Carol L. Krumhansl, "Tonal Hierarchies and Rare Intervals in Music Cognition," Music Perception 7, no. 3 (Spring 1990), 309-24, and David Butler, "Response to Carol Krumhansl," Music Perception 7, no. 3 (Spring 1990), 325-38.
33Butler, "Intervallic Rivalry," 238.
34Although he speaks of chords, not individual pitches. See Style and Idea, 123, and "Problems of Harmony," 275.