The Role of Vagrant Harmonies in Selected Lieder by Wolf, Strauss and Schoenberg1

William S. Cratty


Vagrant chords represent an important step in the development of tonality. Vagrant chords, a term coined by Schoenberg in his book Theory of Harmony, are defined as wandering, ambiguous harmonies. Schoenberg refers to examples from the musical literature only sparsely and some of his theories remain unclear (especially in Structural Functions of Harmony), therefore, a need exists to examine examples from musical literature, and expand and clarify these unique harmonic functions. Many of these vagrant chords are chromatic transformations of common major and minor triads. From these transformations there emerge two classes of vagrant harmonies defined by: 1) our understanding of their physical nature or intervallic content, and 2) our understanding of their changing and multiple interpretations. Any sonority which wanders away from the central tonality or has multiple meanings within a harmonic context may be considered a vagrant chord.


Vagrant harmonies distinguished by their intervallic constitution include the augmented triad, diminished seventh chord, whole-tone chord, and perfect-fourth chord.2 These four types of chords all share three characteristics: 1) they all have the same interval between adjacent degrees, 2) they do not have, because of their physical nature, a single comprehensible root, and 3) they all are capable of multiple meanings and resolutions.



Example 1: Inversions of Perfect Fourth Chord


The second class of vagrant chords are not based on equal intervallic construction but on the possibility of more than one interpretation. A vagrant chord of this type, then, may allow more than one harmonic resolution. Enharmonic spelling of one or all the pitches within a chord may create multiple interpretations and different resolutions. These vagrant harmonies include German and Italian augmented sixth chords which can be reinterpreted as dominant seventh chords. As one can see in Schoenberg's theoretical writings, any chord may have the potential for multiple meaning, including the major triad.3

Both classes of vagrant harmonies, whether based on their constitution or not, are referred to as vagrant chords because they all have multiple resolutions, provide easy access to distant regions, and can contribute to tonal instability. Vagrant harmonies enrich a composer's harmonic palette, offering a greater harmonic variety with which he can express his ideas. The chords in classical tonality had a more or less rigidly defined harmonic function. With the addition of vagrant harmonies as a prominent part of the harmonic structure, the function of the chord became more flexible, pointing toward the emancipation of the chord itself from a given tonal context. Composers of the later 19th and early 20th century, such as Wolf, Strauss, and Schoenberg, provide examples of vagrant sonorities in their lieder of this transitional period. Although they were not the first composers to use vagrant harmonies, they are important because they used vagrant chords as a common harmonic resource, rather than on an occasional basis threatening traditional concepts of tonal stability.


Hugo Wolf’s Das Verlassene Magdlein


In Wolf's lied, "Das Verlassene Magdlein," one can find vagrant harmonies in the form of augmented triads used as independent sonorities for their expressive color and pivotal facility.4 The first augmented triad occurs in the middle of this fifty-two bar song on E flat in the piano accompaniment (Wolf begins with two-measure units which remain, for the most part, consistent throughout the entire song.) in the third line of the second verse (measure 20) under the words "so darein." One should notice how Wolf has arranged these augmented triads (in Example 2) so that they are structurally conspicuous by their simplistic rhythmic motion, their blocked chordal style, and their sheer repetition.


Example 2: Wolf's Das Verlassene Magdleln, ms. 20-26


The last line in the second verse (bars 22 and 23) repeats the two-measure unit including the E-flat augmented triad one more time. The E-flat augmented triad represents the dominant of the preceding A-flat major triad with an altered fifth. Because augmented triads have multiple leading tones, they do not direct the ear toward a single resolution, yet the E-flat augmented triad functions as a substitute dominant, subordinate to its temporary tonic, A flat. This seemingly traditional I - V progression, however, does not return to the tonic between measures 22 and 23. Instead, it moves to a distantly related tonic through a two-bar sequence transposed down a major second in the upper voice. -Each tone of the augmented triad functions as a leading tone to the next chord providing a supple chromatic connection, but not in a V - I relationship (see Example 2, measures 22 and 23).


The progressions of bars 22 and 23 are parallel to those of 30 to 31. Thus a harmonic, thematic, and rhythmic sequence occurs in the piano accompaniment in the last two lines of the third verse, in the augmented triads on A flat and B natural. Immediately following the end of the third verse, the piano solo breaks away from the two-measure unit through liquidation of its harmonic and rhythmic components. This becomes the first real confirmation of the central tonality (A minor) before Wolf returns to the opening dyads which accompany the last verse.


Wolf demonstrates, with the augmented triads in parts of the second and all of the third stanzas, a harmonic contrast to the more traditional harmonies in the outer verses. He also shows how the augmented triad can have a two-fold meaning functioning both as a tonic and/or a dominant alternating with each other much in the manner of a traditional harmonic progression: I - V. But most importantly, the vagrant chords demonstrate the effort to make use of the chromatic scale, to express the text, and to obtain more convincing, more swift, and more supple chord connections between distant tonal regions.


The second class of vagrant harmonies, not based on their equal intervallic construction, but on their change of interpretation, are also prevalent in Wolf's Das Verlassene Magdlein. The most interesting vagrant chord of this group is the C-sharp dominant seventh of F-sharp minor. It is first heard during the two-measure piano interlude between verses one and two (measure 14). The previous measure (bar 13) which begins the two-measure unit contains the first unequivocal statement of the tonic chord in the parallel major, A. The A major triad is immediately followed by the C-sharp dominant seventh. The unit is then repeated twice at the beginning of the second stanza (bars 15-18).

By measure 19, Wolf makes an abrupt harmonic shift progressing to the distant region of A-flat major rather than the indirect but close region of F-sharp minor implied by the C-sharp dominant seventh. Wolf manages this abrupt movement through the changing interpretation of this vagrant dominant seventh chord. By examining the enharmonic equivalence of just the triad of the C-sharp dominant seventh and retaining the seventh degree, B natural, one finds a German augmented sixth chord in the key of F minor: D flat, F natural, A flat, and B natural.


Of course, bar 19 is not the typical classical resolution of the German augmented sixth chord. It does not conform to any traditional i 6/4 - V - i cadential formula; the progression does not contain these chords. In addition, the German augmented sixth chord occurs at the end of the phrase (bar 18). Instead, the German augmented sixth chord progresses irregularly to an incomplete A-flat chord (the fifth, E flat, is omitted), rather than the F minor i 6/4 chord as expected. If the A-flat chord had been followed by the V of F minor, one could assume the A-flat chord was a rootless F-minor triad. The E-flat augmented triad functions as the V and confirms the temporary region of A flat in bar 20. Thus by respelling the chord at bar 18, one perceives this modulation as less distant. A flat is also the relative major to F minor, therefore, the progression is not too far­fetched. Thus the C-sharp dominant seventh chord can be related to the present region of A minor, and simultaneously through its multiple and changing interpretations, it points toward a region which is both indirect and remote: A-flat major.



Richard Strauss’s Ruhe Meine Seele


Like Wolf's lied, Das Verlassene Magdlein, Strauss also uses an equal-intervallic vagrant chord, the diminished seventh, as an expressive sonority and as an independent chord freed from any type of orthodox progression. Unlike Wolf's treatment of the augmented triad, Strauss incorporates this vagrant sonority very sparsely in his song Ruhe, Meine Seele. The diminished seventh first appears about mid-way through the song (measure 20) at the end of the fifth line of the text on the word "wild." It is first introduced sforzando on the root F sharp, sustained as a whole-note throughout the entire measure and echoed in the following bar pianissimo. Strauss elects, in this forty-three bar song, to use the fully diminished seventh only once in the entire work. The diminished seventh chord built on F sharp does appear again at the climactic point of this song at measure 30. However, it is transformed slightly by the addition of the root, D natural, heard in the lowest register. Thus it becomes a D dominant minor-ninth chord which relinquishes its vagrancy by constitution. However, at bar 20, Strauss does not use it for modulatory purposes or in any standard harmonic progression. Rather, Strauss chooses to use this ambiguous chord to express and intensify the word "wild." He destroys its traditional function of resolution by repeating it, and, above all, never resolving it to any of the eight appropriate regions for resolution. Instead it progresses chromatically to a dominant seventh of B-flat major (bar 22).



Example 3: Strauss' Ruhe, Meine Seele, ms. 16-25

The vagrant nature of this diminished-seventh chord is therefore compounded by its constitution, and by its unorthodox progression.

Although the F dominant-seventh chord in bar 22 is not vagrant by its constitution (as was the previous chord), it is important to show that its unusual resolution to the distant region of B minor in the next measure (bar 23), demonstrates the other type of vagrant harmony. The F dominant seventh has no apparent function in the region of B minor, but this irregular resolution is achieved convincingly above a pedal tone and chromatic voice leading (see Example 3, measures 22 and 23). Both vagrant chords, wandering in succession, smoothly slip away from the central key are directed to strong linear goals on C and G (tonic and dominant of the central tonality) amid the chromatic tonal ambiguity.


The F dominant-seventh chord is not, by any means, the only vagrant chord of the second class in this song. Throughout Strauss' lied, he treats most of the dominant sevenths as vagrant chords as they undergo irregular resolutions. For example, the opening dominant-seventh chord in first inversion (V 6/5 of IV), in the three measure introduction of the song, clearly demonstrates how a vagrant chord's irregular resolution can lead to a distant region and undermine the central tonality.


Example 4: Strauss' Ruhe, Meine Seele, ms. 1-5

Unlike the dominant seventh at measure 14 in Wolf's song, which demonstrated changing and multiple interpretations, Strauss' opening dominant-seventh chord has only one interpretation. However, through its unusual resolution, the central tonality (C major) is obscured from the onset of the piece and placed in conflict with the rival region of F#. The unequivocal statement of the tonic chord is avoided until the end of the song.


Although the opening chord is the tonic of the key, it is not heard as tonic, but as a secondary dominant. The C dominant seventh, however, does not resolve to its subdominant F. Rather, it deceptively resolves to an F-sharp minor-seventh chord in third inversion. The distant region of F‑sharp minor is achieved through common-tone and chromatic voice leading, identical to the example in bars 22 and 23. Strauss is, therefore, able to quickly move to a distant region, the supertonic's minor mediant, without sounding abrupt, using the chromatic pivot as a recurrent voice-leading logic throughout the piece.

Arnold Schoenberg’s Ghasel


In Schoenberg's early tonal composition "Ghasel", op. 6, no. 5 in F major we see how even a simple major triad can be treated as a vagrant chord of multiple interpretations within a complex harmonic context. At the climactic point of "Ghasel", bar 33, Schoenberg includes an A-flat major triad which has multiple interpretations.

Example 5: Schoenberg's Ghasel, ms. 31-34

There are many factors involved which contribute to the vagrant nature of the A-flat major triad. Three chords prior to the vagrant chord, clearly establish the region of E minor (Example 6).5



Example 6: Root movement of measures 30-31


However, Schoenberg immediately abandons this region and, without any transition, progresses to a region of four flats, (F minor/A-flat major). This unusual harmonic progression can only be explained through the multiple meanings of the vagrant A-flat major triad. The simultaneous occurrence of a "sharp and flats" notation is another factor which indicates that there are two functions for this chord. At bar 32, the piano accompaniment introduces the A-flat major triad, while the voice sustains a high G sharp (see Example 5, measure 33, beat one). The vocal part is at its highest point, accented agogically and dynamically (it is the loudest point of the song), creating a conspicuous moment suited for the dramatic use of a vagrant harmony.


Initially, the A-flat major triad appears to be a flat submediant of the region C in its progression to a dominant of C on beat four via chromatic passing tones. Its resolution on an F dominant-seventh chord, however, immediately dispels this reference to C and perhaps represents a brief intervention of the ultimate region of F. The climactic progression from the B dominant seventh to the A-flat mediant major sonority appears to be a Schoenbergian extension of traditional deceptive resolutions. The ambiguity of the deceptive resolution is reinforced notationally with the G# referring to the preceding region and the A flat referring to the emerging tonality. The A-flat major triad, however, can be closely related to the region of F minor. It progresses smoothly to the region of F major without an F minor chord ever appearing via the interchangeability of major and minor modes. Through its descending root movement, it progresses to an altered II chord which finally concludes the phrase on an altered tonic in bar 33.


The progression from a dominant on G to a sonority rooted on F which permeates Ghasel is further exploited in the codetta. However, in the codetta the vagrant chords progress one after the other in close proximity. At the second measure of the piano's codetta (bar 40), Schoenberg includes four different types of vagrant harmonies: the diminished seventh, augmented triad, partial whole-tone chord, and German augmented sixth chord.


Example 7: Schoenberg's Ghasel, ms. 39-43


In Example 7, bar 40, Schoenberg has a root position A-sharp diminished seventh, leading tone of B (the raised fourth degree of the final F major tonality), the A sharp in the bass ascending chromatically to an augmented triad on B on beat two. The B natural octave in the bass, the third of the G augmented triad, ascends chromatically to C natural, following traditional voice-leading. However, in a traditional progression, the C would represent the root of the dominant in the key of F. Schoenberg chooses not to harmonize the C in the bass with the expected tones, but with D natural, F sharp, B flat and C natural forming a vagrant whole-tone sonority. The tones above the octave C may be interpreted as a D augmented chord with the C as the added seventh or possibly as sonorities on B flat (with an added ninth) or on D (a possible altered dominant of the supertonic).


The whole-tone chord (bar 40, beat three) progresses chromatically in contrary motion to a German augmented-sixth chord on D flat resolving in the traditional manner chromatically across the bar-line to a I 6/4 chord. The concluding phrase, however, never fulfills its complete resolution on the dominant. Instead, Schoenberg chromatically alters the traditional augmented sixth to form an altered II chord (analogous to G B D-flat F), creating a vagrant harmony through its multiple meanings. When the root G is added (in m. 41) it acquires a function as in the context of the imminent F-major conclusion. These simultaneous interpretations of the chord as both an augmented sixth and an altered II chord work together to intensify the drive toward the V, but throughout "Ghasel", Schoenberg avoids the conventional ii - V - I progression at cadences by frequently substituting for it a II - I progression. As in all the previous II - I cadences the dominant is omitted and through this rationale, the II - I harmonic movement, which Schoenberg established early in the song, remains consistent throughout the piece. The final phrase of the codetta, of course, concludes the song with a more conspicuous II - I progression which is elaborated through passing tones and chromatic neighbors.



Arnold Schoenberg’s Arnold Schoenberg’s Ich Darf Nict Dankend

Like Ghasel, which experiments with a partial whole-tone chord, Schoenberg's lch Darf Nicht Dankend, op. 14 no. 1, explores a new vagrant harmony: the perfect-fourth sonority as a three- and sometimes four-note chord. Like the partial whole-tone chord or the incomplete dominant seventh, one does not need to use all possible tones of the chord. In op. 14, Schoenberg never uses quartal harmonies of more than four tones. In Schoenberg's earlier works, however, one can find the perfect-fourth chords constructed with more than four tones. Two good examples are Schoenberg's first use of quartal harmony in his symphonic poem Pelleas und Melisande6 (1902-03) and later in his Kammersymphonie, op. 97 (1906). Both works used this vagrant harmony, as Schoenberg described it, as an "expression of a mood."8 However, in Schoenberg's op. 14, his last songs to incorporate a key signature, the perfect-fourth chord becomes the primary structural unit. Op. 14 is a transitional piece which tries to create a relationship between fourths and thirds. Schoenberg tries to integrate the perfect-fourth chord with tertian harmony, and establish it as a tonal identity.

Because their intervallic contents are equidistant, the root will always be ambiguous. However, Schoenberg shows in an inconspicuous and ingenious way how this vagrant chord, in context with voice leading and other added contrapuntal lines, may have an implied root. In addition he also tries to convey a sense of stability through the perfect-fourth chords.

The first stable perfect-fourth chord is on beat two of the piano introduction. The ear is confronted with three equidistant tones suggesting any one of them as a root. However, the E sharp, on the weak beat of two in the bass, resolves chromatically to F sharp. The added contrapuntal line therefore suggests a harmonic root in D - the tone A below represents the dominant, and the tone G above, the (unresolved) subdominant.


In the song Ghasel, Schoenberg compresses traditional harmonic progressions by eliminating the dominant in most ii - V - I progressions. In op. 14, he compresses a traditional IV - V - I progression by including vertically with the tonic, the fourth and fifth degrees. In this way, Schoenberg verticalizes the important structural degrees of the reference to D major in a new independent sonority.


                Example 8: Schoenberg's Ich Darf Nicht Dankend, ms. 1-4

The previous chord also contributes to the stability of the perfect-fourth chord in beat two. It is, by its spelling, an altered fourth chord comprised from bottom to top, an augmented fourth and a perfect fourth (see Example 8, measure one, beat one). The two uppermost tones are merely a double appoggiatura to the central chord in beat two, while the lowest tone remains as a pedal. The three-part perfect-fourth chord is its resolution. The progression of these two chords is repeated five times in the first verse at various tonal levels. Through its repetition, the ear becomes acclimated to this sound. Therefore, in this sense the perfect fourth chord, vagrant only by its constitution, becomes the stable triad which can function on various degrees.


At measure three, there is an elision between the ending of the piano introduction and the beginning of the vocal part. On beat one, just before the voice begins, the tonic perfect-fourth chord is heard again. Unlike measure one, there is no counterpoint in the bass line to determine its root. Instead, the tone G acts as an appoggiatura in the upper part of the chord. This momentarily indicates the root, D (see Example 8, measure three), but it can be seen that the sonority changes immediately to B minor through the upward movement from the A natural, thus exposing a tonal ambiguity which is central to the meaning of the piece.


Op. 14 shows how perfect-fourth chords can be integrated tonally within chromatic tertian harmony. Through tones of harmonic support and as goals of contrapuntal lines, and voice leadings, they provide structural stability. By including fourth chords in his extended harmonic principles, Schoenberg created a sophisticated tonic which simultaneously includes the dominant and subdominant degrees. This compression of traditional tonal function similarly gives rise to new, more central functions for sonorities that are not part of tertian harmony. This is one of many innovations which signals the breakdown of tertian harmony.


During the 19th century, as chromatic harmony developed, vagrant chords became an important tool in undermining traditional, classical tonality. Vagrant harmonies, based on their equal intervallic contents or their changing and multiple interpretations, generally functioned as subservient chords to conventional harmonic progressions. But as these chords were explored to their utmost potential, as seen in selected lieder of Wolf, Strauss, and Schoenberg, they became an ingredient which undermined the tonal expectations of traditional harmony. When the framework of tertian harmony is maintained, the equal-intervallic chord generally has the potential for multiple meaning. However, when tertian harmony is on the verge of destruction, as seen in op. 14 where perfect-fourth chords invaded the harmonic structure, the equal-intervallic chord can become the most stable element of the harmony. This is even more evident in Schoenberg's later songs from The Book of Hanging Gardens, op. 15, where Schoenberg finally abandons the key signature and frees himself from traditional tonality. This is an example of the inevitable progression from a tertian harmony weakend by vagrant chords to the complete dissolution of a tertian hierarchy. Through the prominent use of vagrant harmonies in the music of Wolf, Strauss, and Schoenberg, the first step is taken toward the emancipation of the chord.



Dahlhaus, Carl, "Harmony", The New Grove Dictionary of Music and Musicians, vol 8, Macmillan Publishers Limited, London, 1980, pp. 175-188.

Krenek, Ernst, Music Here and Now, Russell and Russell, New York, 1939.

Leibowitz, Rene, Schoenberg and His School, Philosophical. Library, New York, 1949.

Salzman, Eric, Twentieth-Century Music: An Introduction, Prentice-Hall, Inc., New Jersey, 1967.

Samson, Jim, Music in Transition: A Study of Tonal Expansion and Atonality, 1900-1920, Dent, London, 1977.

Schoenberg, Arnold, Structural Functions of Harmony, W. W. Norton and Company Inc., New York, 1954.

Schoenberg, Arnold, Style and Idea, University of California Press, Berkeley and Los Angeles, 1975.

Schoenberg, Arnold, Theory of Harmony, University of California Press, Berkeley and Los Angeles, 1978.


1This paper is excerpted from a longer study of the same title which is available at the Department of Music of the University of California, San Diego.

2The diminished seventh, augmented triad, and whole-tone chord (constructed only by superimposed major seconds) do not change their intervallic contents when inverted. The perfect-fourth chord, however, is only recognized as a vagrant chord by its intervallic contents when it is constructed in superimposed fourths. When it is found in its inversion, unlike the diminished seventh, augmented triad, and whole-tone chord, it is no longer vagrant by its constitution.

3Arnold Schoenberg,Structural Functions of Ilarmony, W. W. Norton and Company, New York, 1969, p. 165.

4Arnold Schoenberg, Theory of Harmony, University of California Press, Berkeley and Los Angeles, 1978, p. 238.

51n Schoenberg's Structural Functions of Harmony, p. 22, he says, "three or more of the characteristics of a region should be present."

6Four-part quartal harmony is found in the third and fourth measures before rehearsal no. 9 in Pelleas und Melisande.


7A linear passage of perfect fourths is found in measures five and six of the Kammersymphonie.

8Arnold Schoenberg, Theory of Harmony, University of California Press, Berkeley and Los Angeles, 1978, p. 403.