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For a broad range of nineteenth-century 1. Kinderman and H. Krebs Lincoln, Nebr. Harmonic space, or tonal space as defined by Fred Lerdahl, is the abstract nexus of possible normative harmonic connections in a system, as opposed to the actual series of temporal connections in a realized work, linear or otherwise. Classical tonality inhabits diatonic space; later music, it follows, inhabits chromatic space. Norton, See below, section 6.

Chromatic transformations in nineteenth-century music Table 1. Its defining aspect is the requirement of a common tone in any direct chromatic relationship. My argument will be that common-tone relationships constituted the first group of chromatic relations between triads and keys to become fully normalized in nineteenth-century harmonic practice.

Table 1. There are seven of these, six principal ones and one special case.

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They can be classified in three ways: by interval of root motion, by the absence or presence of mode change, and by the number of common tones. As the table shows, the three intervals of root relation which allow for common tones are the fifth, the third, and the prime. Names for individual relationships will be discussed below in chapter 7. Relations by each interval may occur without or with change of mode. There is an important difference, though.

With the fifth and the prime, mode preservation results in a diatonic relation, mode change in a chromatic one. With the third, it is the opposite: mode preservation results in a chromatic relation while mode change is diatonic. This gives third relations a unique profile and distinctive properties within the set of common-tone relations.

The extra relation by semitone, a chromatic one between major and minor triads, is the result of the asymmetry of the tonal system. While not part of the principal set of common-tone relations, it is recognized and employed in mid-nineteenth-century chromatic tonality see section 6. Five of the six principal common-tone relations are readily accepted in analysis. The diatonic relations and relative mode relations are basic to the harmonic system.

Fifth relations with mode change are either diatonic or else the result of commonplace alteration such as Vi in minor. Chromatic third relations, on the other hand, have always proven contentious for theory. Throughout the nineteenth and twentieth centuries, theorists have disagreed on their nature, their origin, their role within the harmonic system, and their value. They have at times been demonized as threatening the coherence of the harmonic system, or theoretically neutralized as subsidiary to diatonic phenomena.

Since I argue that, on the contrary, they serve as a cornerstone of common-tone tonality, my task is to provide a comprehensive case for their inclusion in a larger system. Straightforward theoretical explanations for these striking elements of harmony, however, have been the exception. The preferred approach in the past century has been to treat chromatic mediants as derivative entities.

Chromatic transformations in nineteenth-century music

They have been characterized as alterations or combinations of other, more basic progressions; as ornamental, secondary voice-leading events; or as incipiently degenerate coloristic phenomena, contributing to the eventual breakdown of the tonal system. I feel that these explanations fall short. My aim here is to clearly identify and describe the full range of mediant relations in the tonal system, and further to argue that chromatic third relations possess an identity and a quality which are independent of the fifth relations and diatonic third relations of the tonal system, displaying an independent functional identity.

This requires a notion of direct relation between tonic and chromatic mediants which preserves and affirms the key and makes the elaborate explanations explaining them as versions of other things unnecessary.

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To facilitate this, a straightforward taxonomic system for diatonic and chromatic third relations alike will be proposed which groups those third relations together in classes which in practice act most similarly. The ease and directness with which this terminology allows for the clear discussion of succeeding topics will serve as an argument for its utility. Mediants will be considered individually, as a group, and as part of a formal representation of the tonal harmonic system.

Developing a way of thinking which allows for direct chromatic relations suggests revisiting received notions of the nature of harmonic relationships. Toward this aim, a study of principal nineteenth-century theorists is enormously instructive. Not only were these writers contemporaneous with the music in which chromatic relations became a norm of harmonic practice, but their viewpoints toward third relations and harmonic relations in general are not what we might assume them to be, and are certainly at odds with much of present conventional understanding.

In many cases, theorists ways of dealing with third relations derived in a rational way from their conceptions of the harmonic system and the ways in which chords relate. In other cases, theorists who recognized the existence of chromatic mediant relations were. Accordingly, in order to appreciate the substance of the conflict between a comprehensive theory and an undeniable phenomenon for which it cannot easily account, we will examine notions of harmonic system and connection in general and their relation to specific ideas of third relation. Marx, and Moritz Hauptmann, all of whom advanced notions of third relations.

Hugo Riemann, who created an elaborate theory of chromatic tonality, will merit a dedicated study.


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My argument will be that the nineteenth century saw both an increasing acceptance of chromatic third relations as a class of legitimate harmonic phenomena paralleling their increasing presence in music, and, ironically, the development of theoretical constructs which were increasingly less able to accommodate these phenomena. After Riemann, as new theories emerged which focused less on classes of harmonic relation, and as chromatic practice broadened to the point by which third relations and other common-tone chromatic relations were no longer unusual or extreme, mediant relations ceased to be the subject of directed discussion.

The preeminence of scale-step or scale-degree conceptions in twentieth-century theory led to theories as divergent as Schenkers and Schoenbergs, both of which will be seen to devalue chromatic third relations among others as ultimately dependent on other musical factors. Scale-degree thinking has also led to the modern textbook approach wherein chromatic mediants are presented as variants of diatonic ones, or as coloristic events with no definite harmonic meaning. Some contemporary American theory has tackled the problem of third relations. Solutions range from ones which adopt a Schenkerian point of view and work from the assumption that chromatic mediants destroy the integrity of the key, to others which offer alternative explanations of chromatic mediants which presuppose their coherent participation in tonal processes.

Some propose classification systems; others concentrate less on classification and more on analysis and explanation. Relevant aspects of this work will be discussed and analyses considered where appropriate. The recent development of transformation theory will be reviewed, and will provide a model for my approach, inspiring a modification to existing systems to reflect direct chromatic relations as integral processes. An investigation of practical aspects of chromatic third relations follows this survey. The discussion will treat common types of mediant relations on different levels of musical organization.

Drawing on numerous musical examples and providing some 4. Thomas Christensen cautions against navely tracing the development of a single theoretical concept through history without taking account of its context. For the most part he cites musical and cultural forces external to the theoretical texts, but the larger concerns, goals, and structures communicated by the texts themselves also provide contexts for the expression of individual concepts. Bernstein and C.

Hatch Chicago: University of Chicago Press, , pp. The present study will focus on the latter type of context. Loosely put, the term function signifies harmonic meaning. But notions of this meaning may take many forms. We commonly associate the idea of function itself with the thought of theorists ranging back to Rameau. Typical is the following comment on Gottfried Webers work by a mid-twentieth-century historian of nineteenth-century harmonic theory: The author believes Weber to be the first theorist to use Roman numerals as function signs.

However, such habitual assumptions about the idea of function are misleading. During the common practice period, a well-defined notion of function in harmony had not yet been introduced, although aspects of what we would consider to be functional theory were of course present in the work of many theorists. Not until the end of the nineteenth century was a full-fledged concept of harmonic function formulated and named Funktion by Hugo Riemann, following two decades of painstaking theoretical groundwork. For Riemann himself, as I will show, the concept provided a means to explain how all chords, diatonic and chromatic alike, draw their meaning in a key from their shared membership in one of three functions defined by the three principal triads.

In a related conception also identified with Riemann, function inheres in the three chords themselves rather than in the categories they define. A corollary notion of ours absent from Riemanns theory locates harmonic and functional identity directly in scale degrees I, IV, and V, on which these principal triads are based. In our time, functional power and harmonic meaning of chords are often attributed instead to each of the seven diatonic scale degrees and sometimes their variants, serving as the roots of a variety of chords and identified by Roman numerals. VI in C major.

The author means that Weber was the first to use Roman numerals to label scale degrees in a systematic way, associating chords with keys. For an exploration of ways in which we understand notions of function in earlier theory see my On the Function of Function, Music Theory Online, 1. Each scale degree has its part in the scheme of tonality, its tonal function.

New York: Norton, , p.

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Scale degree is a concept inimical to Riemann, for whom, for example, a chord based on the third scale degree may function as tonic, dominant, or dominant of the relative minor, depending on context. The term function may also be used to signify a concept of the intrinsic potentiality of a given chord to progress in a particular way or to a particular chord, such as the notion of the dominants innate propensity to progress to the tonic.

Or we may associate function with specific outcomes rather than with scale-degree identity. More generally, we may use the term function to denote meaningfulness or meaningful relation within a key, as opposed to color, which signifies a relation without meaning in the tonal system. An important traditional index of meaning within a key is diatonic pitch content, or else, in the case of chords with chromatic content, direct relation or resolution to a chord with diatonic content.

The principal chords of a key satisfy the first condition; chords such as secondary dominants, diminished sevenths, and augmented sixths satisfy the second. Chromatic third relations are often dismissed through this rationale as non-functional color events pointing only to themselves or away from the tonic, or else as out of the plane of tonal relations.

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The presence of non-ornamental chromatic tones in these mediants and the distance between their associated keys and the tonic are attributes which for many theorists disqualify these chords from expressing harmonic function. But in fact chromatic mediants often do satisfy the second condition, relating directly to their tonic or dominant, not as applied chords, but in a coherent way which preserves the sense of tonic key. This coherence derives from smooth relations involving common tones and root connections, along with other factors.

Harmonic relationships between chords are not simple, single-faceted connections but rather complex linkages whose effect results from the interrelation of a number of processes. Consider Dahlhaus also observes that Riemann is not clear about the distinction between function as category and function as chordal archetype. In some cases, IV proceeds to a I chord. More frequently, IV is linked with ii. New York: Alfred A. For Rameau, who did not use the term function, these are respectively represented as a triad, a seventh chord, and an added-sixth chord.

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Chromatic Transformations in Nineteenth-Century Music

Lester is careful to distinguish his use of the term from modern usage. At the end it is a goal of motion, thus a closing tonic. New York: Harcourt, Brace, and Jovanovich, , p.