by Andrzej Tuchowski
This article presents one of Chopin’s methods of organizing large-scale works, dubbed by the author the “integrative pitch-axis technique.” This technique first appears in mature works of 1835, and is especially prominent in the two Nocturnes Op. 27. In the Nocturne in C sharp minor Op. 27, No. 1, the main structural pitch-axes coincide with the elements of the tonic triad, i.e. “C sharp – E – G sharp” (the other pitches are also often spelled enharmonically as “D flat” and “A flat.” Such tonal implications are absent from the design of pitch axes in the Nocturne Op. 27, No. 2; both pieces, however, mark the peak of structural coherence in Chopin’s Nocturnes. The subsequent application of the integrative technique occurs in the second Scherzo, in B flat minor, Op. 31 (1837) where the pitch axes are used independently from a sophisticated network of motivic-cellular integrative links while the coda serves as a kind of a “resume” of the all pitch axes encountered throughout the piece. The main part of the article presents a post-Schenkerian analysis of the integrative technique in Chopin’s Sonata in B flat minor, op. 35. The author points out the presence of three interconnected structural ideas in the introduction to the first movement and subtle interrelationships between the four movements, especially apparent in the widespread occurrences of overlapping minor thirds – used as nodal points in pitch motion and as vital elements of the pitch framework of the composition (highlighted by various textural and formal elements). Instances of integrative techniques similar to Chopin’s are found in the music of Karol Szymanowski (example from “Songs of an Infatuated Muezzin”) and Witold Lutosławski (example from the Fourth Symphony). Both composers highly regarded Chopin’s music and discussed its impact on their musical thinking. In this paper, Szymanowski’s statement that Chopin was “a futurist of the romantic epoch” (1923) receives a striking exemplification.
Translated by Maria Anna Harley
While looking through the 19th-century literature on Chopin one can hardly find an opinion denying Chopin’s music its originality, imaginative fantasy and emotional power. On the other hand one can hardly find a favourable critical assessment of Chopin’s constructive abilities – especially as far as large-scale structural designs are concerned. In fact, an opinion prevailed among 19th-century critics that Chopin’s large-scale musical construction lacked consistency and tended to disintegrate under the overwhelming pressure of romantic inspiration and undisciplined fantasy. This opinion, foreign to such musical authorities as Schumann and Liszt, was shared by the most influential critics and writers on music of that time: Hanslick (1869-1970), Niecks (1888), Hunecker (1900), Shedlock (1895), and Bie (1898). In some cases the criticism of Chopin’s ostensible structural inabilities was voiced in a somewhat -sharper tone. Hadow, for example, in his Studies in Modern Music (1892) accused Chopin of what could be described as “structural infantilism” by claiming that “in structure he [Chopin] is a child, playing with a few simple types, and almost helpless as soon as he advances beyond them.” Fifteen years later quite a similar objection was put forward by D’Indy who described Chopin’s op.58 as a “childish sketch,” which in spite of its undeniable beauties stands far away from the “admirable monuments of the order and harmony” discernible in works of Bach and Beethoven.
The stereotypical, one-sided image of Chopin as a master of the miniature or as an over-emotional, undisciplined romantic was overcome in the second and third decades of the 20th century with the emergence of new music theories and analytical approaches (e.g. Leichtentritt 1922; Schenker 1935). Since then, generations of analysts of various theoretical orientations have been contributing to the gradually expanding knowledge about the latent structural logic in Chopin’s works. In consequence, the long-neglected intellectual aspect of Chopin’s music (“intellectual” in the sense that its discovery requires the application of analytical methods) has been brought to the foreground – thus making the contemporary image of this composer much different from the one inherited from the previous century. It seems that a significant element of this new image is based on the growing esteem for Chopin as a “prophet” of certain 20th-century compositional techniques. Karol Szymanowski was probably the first to turn his attention to this very aspect of Chopin’s oeuvre when he labelled Chopin a “musical futurist of the romantic epoch”(1923). Szymanowski’s opinion was confirmed by subsequent scholars (e.g. Lissa 1970, Nikolska 1987) mainly in respect to Chopin’s harmonic and textural innovations and his dramatic-formal designs which, according to Nikolska, probably influenced some Polish 20th-century composers.
In the present study I would like to point out another “futuristic” aspect of Chopin’s œuvre: structural coherence understood as a latent logic of the unity in multiplicity. Studies of transformational changes in Chopin’s style (c.f. Gołąb 1993, Tuchowski 1996) reveal that structural coherence achieved by means of motivic-cellular connections (which belong to the “foreground” type of integrative links) reaches its high point in Chopin’s music during the early 1830s and remains more or less the same later on, with the exception of a “post-romantic turning point” in the early 1840s. On the other hand, the same research indicates a growing role of integrative techniques in the structural background of the music as Chopin’s style progressed towards its full maturity. Indeed, in some works written about the year 1835 and after that date, one can find astonishingly strict, ingenious structural designs, something which could be hardly expected from a romanticist who was commonly considered a master of imaginative fantasy and emotional power.
The purpose of the present study is to highlight a certain integrative technique (one of the many utilized by Chopin) which anticipates the 20th century “constructivism” – thus providing a bridge between the 19th-century concept of “organicism” and structural designs that function in post-tonal music. I shall call this particular device the INTEGRATIVE PITCH-AXIS TECHNIQUE; it relies on far-reaching aural capabilities of the listeners, the “Fernhoeren” – as Heinrich Schenker would have put it. This technique, signalled in the Mazurka Op. 6, No. 1 (1830-32) and in the Mazurka Op. 17, No. 3(1833) appears in its fully-fledged shape in the Nocturnes Op. 27 (1835). Let us, then, commence the analysis from the Nocturne in C-sharp minor op. 27, no. 1.
As the following graph indicates, in the melodic line of section A there are some pitches of a special structural prominence. A closer scrutiny reveals that these are “border pitches” (or “nodal points”) of the melodic motion. “C-sharp” and “G-sharp” limit the expansion of the motion in both directions, up and down. It is interesting that these nodal points of the motion design are given a strong emphasis by means of texture, sonority and dynamics, as if Chopin wanted these particular pitches to be well remembered. Another proof of their perceptual and structural significance can be found in the two-bar introduction with its motion-trajectory limited to these very pitches. Certainly this particular gesture helps to fix the two pitches in the mind of the listener (see Example 1).
As the graph suggests, there is yet another pitch, “E,” that appears to have structural significance. This pitch initiates the melodic line and functions as a sort of “symmetry axis” for the design of the melodic motion (“a sort of” since the distance between “C-sharp” and “E” is not equal to the distance between “E” and “G-sharp.” We have to keep in mind, however, that this construction is adapted to the requirements of the tonal system.) Therefore, there are two main pitch axes, “C-sharp” and “G-sharp,” as well as one subsidiary pitch axis, “E.” Needless to say, together they form the tonic triad of C-sharp minor. In measure 29, when the contrasting section B starts, we can discern a phenomenon described by Felix Salzer in 1970 as “a heightened drive” upwards, towards “G-sharp.” As it follows from the graph, the progressions which start at bar 29 are organized in such a way that both pitches “C-sharp” and “G-sharp” receive a strong emphasis. What happens next is even more interesting: the trajectory of the modulatory passage is strictly controlled by the pitch axes of the previous section. Therefore, up to the return of section A we find the following tonal centres: “E” (m. 46), “A-flat” (m. 49) – an enharmonic equivalent of “G-sharp” – and “D-flat” (= C-sharp) which enters in m. 65. In terms of statistical distribution, the tonal centres equivalent to the pitch axes of “C-sharp” and “G-sharp” predominate. At the same time, in sections B and C of the Nocturne the pitch-axis “E” continues to have a subsidiary role.
Generally speaking, the structural background design of the Nocturne, Op. 27, No. 1 articulates Chopin’s way of using the integrative technique discussed here. As one may notice in the graph, this technique (at least in the case of the Nocturne, Op.27, No. 1) is fully adapted to the requirements of the tonal system. The nodal points of the pitch motion design in section A coincide with the root and the fifth of the tonic chord, i.e. with the pillars of the “Naturklang” in Schenker’s terminology. Nonetheless, such a conjunction of pitch axes with tonal elements is not a general rule. In the Nocturne, Op. 27, No. 2, for example, we may discern an attempt to separate the network of the integrative pitch axes from the set of pitches, the structural importance of which depends on the laws of the tonal system. Since the form of this Nocturne has been based on the alternation of two contrasting musical thoughts, the integrative links connecting the first projection of these ideas are taken into account in the following diagram (see Example 2).
The nodal points of the melodic pitch motion design have been beamed above the upper stave; these points articulate moments of change of direction of motion and the highest points in pitch contours. With the exception of the initial “F” which constitutes the head-note of the “Chopin passage” (descending, beamed group) none of these pitches belong to the set of pitches, whose structural importance stems from tonal harmony. Moreover, while the “B-flat” in m. 4 receives a strong emphasis by means of dynamics, duration and sonority, the pitch “C” passes almost unnoticed (hence its graphic representation in brackets). As if to compensate for the harmonic weakness of these pitches and to make sure that they will be remembered by the listener, both of these pitches are repeated an octave lower, functioning as the terminal points of the octave progressions (indicated by downward beamings on the upper stave). The graph illustrates that exactly the same pitches open the successive stages of melodic progression in the contrasting theme, with the pitch class “G-flat” assigned a dramatic role of the climactic point of tension (note that the high “G-flat” continues to serve in this climactic role throughout the piece, for instance in mm. 42-45 and 57). It is striking that the integrative pitch axes are emphasized by all possible means – exactly as in the Nocturne, Op. 27, No. 1. Therefore, one may safely assume that the connections indicated above do not result from a coincidence.
Indeed, Chopin’s Opus 27 marks the peak of structural coherence in the genre of the nocturne: the discussed technique may be found in its complete form only in the works from Opus 27. Other nocturnes are structurally integrated by means of more or less complicated networks of motivic-cellular links which are typical for 19th-century organicism and, as such, are not discussed here. However, after completing the composition of Opus 27, Chopin apparently decided to apply the pitch axis technique to larger forms. The most interesting example is provided by his second Scherzo, in B-flat minor,, Op. 31 (1837) where the pitch axes are used independently from a sophisticated network of motivic-cellular integrative links. The prominent role of the pitch “F” in the structuring of motion in the first exposition (up to m. 262) has been pointed out by many analysts of various methodological orientations (Schenker 1935, Eibner 1960, Kinderman 1988). Let us note that this pitch provides a destination point for all the phrases, all the linear progressions up to measure 34. In m. 46 “F” closes the first section of the main theme, then it provides the starting point of the second theme (m. 49). In m. 65 the same pitch initiates the lyric theme; here, the melodic line extends between the initial “F2” and the final “F2,” with “F3” serving as a peak within the trajectory of motion. Generally, one may say that all the nodal points in this section’s structural-formal design are marked by the pitch axis “F.”
Interestingly, the closure of the first exposition coincides with the end of the integrative role of the pitch axis “F;” afterwards a new axis – “D-flat” – emerges. In m. 262 this pitch axis is enharmonically transformed into the “C-sharp,” thus serving as an integrative force which brings together sections in distant key areas. In the second exposition, this new axis plays exactly the same role as the former axis in the first exposition. In m. 299, however, the pitch axis “D-flat” is simultaneously “pushed” – so to speak – in both directions: a perfect fifth upward and a perfect fourth downwards (this may be seen as an analogy to the concentric motion of the first theme). As a result, a new pitch-axis, “G-sharp,” is created. In the following segment of the piece, a sort of “interplay” between both axes may be seen: a brief return to “C-sharp” in m. 317 is followed by a return of “G-sharp” in a brilliant, virtuoso segment, based on the “Chopin passage” (m. 334). The stormy and unstable – as far as tonality is concerned – developmental section of the Scherzo brings in a suspension of all pitch axes. Nevertheless, when we look at the starting points of the successive stages of the development we can discern a striking regularity: most of these segments begin with strongly emphasized pitch classes that have, so far, served as the integrative axes. The developmental section of the Scherzo (m. 476) starts with a highlight on the pitch class “C-sharp.” The beginning of the next segment (m. 516-517) features an emphasis on “G-sharp” (i.e. “A-flat”) while the final segment of the development starts with a high “D-flat” (m. 544) and ends with a strongly exposed “F” (m. 580-582). The recapitulation brings back all the tonal and structural relations of the first exposition.
More interesting phenomena, however, are discernible in the concluding section of the piece. The coda serves as a kind of a “resume” of the all pitch axes encountered throughout the piece. The following pitches create strongly exposed nodal points in the design of melodic motion in this section: “C-sharp” in mm. 716, 720, “F” in m. 724, “A-flat” in mm. 732-747 and “F” from m. 756 to the end of the piece. It is significant that the final chord of the Scherzo is a D-flat major triad with its third, i.e. the pitch “F,” in the treble position. It is also worth noting that all the pitch axes, that are so consistently recapitulated in the coda, add up to – together with their enharmonic equivalents – the D-flat major triad, i.e. the tonic chord of the key which has been described by many analysts as predominating in this work (Schenker 1935, Eibner 1960, Gołąb 1991, Samson 1988, Kinderman 1988). 
As mentioned, the pitch-axis technique appears in the Scherzo in B-flat minor quite independently from the foreground net of motivic-cellular connections. In the next analytical example (i.e. Chopin’s Sonata in B-flat minor; 1837-39) both integrative aspects of the structure are closely interrelated. During the eighty years since the first serious analytical studies of the structural logic in this astonishing work had been undertaken (Leichtentritt 1922), successive generations of analysts have examined aspects of structural coherence in the work that was so frequently criticised by 19th-century theorists for its apparent lack of unity. Here, we should only mention the facts that have a certain significance for the present study. Most modern analysts point out that the Funeral March had been composed before other movements of the Sonata and that it should be considered a source of thematic ideas for the whole work. Undoubtedly, it is true – Alan Walker (1967) found such thematic relationships in the first and the third movements; such findings have been confirmed by other analysts (Leikin 1992, Bollinger 1981, Helman 1993).  The present study’s focus on the perceptive rather than the creative aspects of the music requires that we survey the Sonata in its entirety from its first notes onwards. Let us start from the introduction. It contains three closely interconnected structural ideas:
- the “embryonic” progression of minor thirds “B-flat – D-flat” = “C-sharp – E” (it seems possible that the enharmonic change serves to emphasize the relation of the minor third)
- the intervallic cell consisting of a minor third followed by a minor second (marked on the following graph as an “X”) which is of crucial importance for the thematic material in the whole Sonata (it provides a significant integrative element in the foreground)
- two pitch axes: “B-flat” and “D-flat” (a significant integrative element in the background)
The structural importance of the interval of the minor third and its inversions/variants is striking. The diagram in Example 3 indicates the presence of the minor third in the nodal points of the motion trajectory of the first theme (i.e. its melodic line and the bass). The nodal points in the trajectory of motion of the highest voice of the texture consist of three elements: two overlapping minor thirds, “B-flat – D-flat” and “A – C,” plus another minor third “E-flat – G-flat.” The bass line features a different set of minor thirds: “B-flat – D-flat” and “E – G.” It is striking that two overlapping minor thirds, “F – A-flat” and “E-flat – G-flat” constitute a frame for the head motive in the second theme (see Example 4).
In addition, the minor third “A-flat – F” makes its imprint on the framework of the trajectory of pitch motion in the core of this theme (see Example 5).
The minor third as a frame of the main integrative cell X mentioned earlier (with an emphasis on the most prominent pitches of “B-flat” and “D-flat”) influences the trajectory of motion in the first phrase of the third theme in mm. 81-84 (see Example 6).
In contrast, the second phrase presents a different sequence of overlapping minor thirds (see Example 7).
Another method of pairing minor thirds appears in the developmental section. Its dramatic climax in measures 138-153 is based on the following pairs of chords:
- G minor – B-flat minor (mm. 138-141)
- F minor – A-flat major (mm. 142-145)
- E minor – G major(mm. 146-153)
- D major/minor – F major (mm. 150-153)
When put together, the roots of these chords (emphasized by powerful octave doublings in the bass) constitute a familiar progression of overlapping minor thirds, the same progression which controls the trajectory of motion in the head sections of both main themes of this movement. Still another way of juxtaposing minor thirds in a linear fashion underlies the frame of the main theme in the Scherzo. Needless to say, the emphasis rests on two pitches, “B-flat” and “D-flat” (see Example 8).
Another, rather ingenious way of turning the attention of a listener towards both pitches appears in the central section of the Scherzo, Piu lento (see Example 9).
While in the first movement of the Sonata both pitches control the overall tonal design, in the second movement they determine the construction of the main nodal points of the trajectory of motion, and in the third, i.e. the Funeral March, they assume both roles.
In addition, here both pitches receive – as far as this Sonata is concerned – an unprecedented emphasis by means of their obsessive repetition in the bass line. It is interesting that the full exposure of both axes by all possible means coincides with the dramatic climax of the Sonata brought about in the Funeral March. When this full exposure is over, both axes are suspended and – what is especially striking – this suspension goes hand in hand with a partial suspension of the laws of tonality. This is exactly what we may observe in the mysterious, enigmatic Finale, one of the most prophetic works written in the 19th century. As it is known, this Finale posed many problems for those analysts who tried to read it in terms of functional harmony (e.g. Riemann 1901, Leichtentritt 1922, Bronarski 1935, Chomiński 1960, Benary 1985, Cholopow 1987).
It seems, however, that we should rather take into account the standpoint of Zofia Lissa (1970) who postulated considering the Finale in terms of 20th century rather than 19th century compositional techniques. In this context, it is worth noting some remarks of Irina Nikolska (1987) who tried to compare Chopin’s dramatic narrative to that of Lutosławski.  According to Nikolska both composers share the same reluctance to reveal “a true sense of music” before the final stage of the work. Although Nikolska does not specifically refer to the Sonata in B-flat minor, it seems that her remarks are directed to this particular work. Her thesis may be applied not only to the dramatic but also to the structural design of this Sonata. Only its Finale presents an ultimate and full realization of the potential constructive possibilities latent in the structural “matrix” of the introduction. In fact, there are only “enclaves” in the Finale where the laws of tonality are unchallenged; vast stretches of musical discourse take place – so to speak – in a tonal void. What fills this tonal vacuum? As the following graph suggests certain INTERVALIC MOTION PATTERNS appear; these patterns are based on progressions of the minor third, transformations of the cell “X” and on the chromatic line. Needless to say, all these patterns result from the multiplication of elements which constitute the structural “matrix” displayed in the introduction. Example 10 illustrates how these patterns work up to m. 8.
The following example presents the development of the tertian patterns in mm. 8 to 11 (see Example 11).
In both cases the music that might be heard results from a process of “composing out;” the deeper structural level consists of pitches indicated on both graphs by means of beaming. This deep structural level is controlled by the patterns which can be numerically described as: 1+3 (i.e. a minor second plus a minor third, or their enharmonic equivalents), 1+1, or 3+3, or as a combination of all these patterns. This intervallic structuring brings us directly to 20th-century music. Similar intervallic patterns provide the outlines of pitch motion in certain pieces by Karol Szymanowski. In his “Songs of Infatuated Muezzin” (1918), for example, these patterns (as in Chopin’s Sonata, Op. 35) appear as successive stages of transformation of the structural “matrix” which is discernible in the introductory passage to the first work of the cycle. This introduction (and, more precisely, its melismatic invocation “Allah, Akbar”) defines Szymanowski’s usage of the pitch axis technique (see Example 12). In this case, however, the application of integrative techniques examined in my paper stems from their semantic dimension which results from Szymanowski’s reading of Iwaszkiewicz’s poetic text. 
Therefore, some of the pitch axes or motion patterns refer to symbolic and expressive subtleties of the represented world, with its interconnections between mysticism and eroticism. A different, even more striking example of affinity with Chopin’s integrative techniques is provided by late works of Witold Lutosławski who uses these techniques in the context of his 12-tone system, and who endows them with an almost mathematical strictness. Let us, for example, consider the most “romantic” passage in Lutosławski’s music, the introductory paragraph to his Fourth Symphony (see Example 13).
Structurally speaking, the point of departure for the first section of this work is the hexachordal aggregate consisting of minor thirds and perfect fourths. It emerges by gradual accumulation of pitches starting from the low “E” in the bass. A closer scrutiny allows us to separate this basic pitch from the higher pitches that create a symmetrical intervalic structure of “5-3-3-5.” This division, marked on the graph with a brace, has repercussions for the layout of tone-colors, i.e. instruments and instrumental groups (on the diagram, the significant events in this segment are marked by vertical arrows).Thus, the initial sonority of the aggregate coincides with the first entry of the strings; furthermore, the appearance of the first pitch of the symmetrical segment of the aggregate coincides with the entry of the harp, while the last pitch of the aggregate – “B” – coincides with the entry of the clarinet. As the graph indicates, the first pitch in the work (“E”) is sustained until Fig. 3, while the symmetrical segment of the initial harmonic structure is composed-out according to a consistently observed principle of motion, i.e. the successive appearance of a semitone plus a minor third, or its enharmonic equivalent, in various combinations of ascending and descending patterns. In addition, other intervals than those indicated by the main pattern, i.e. the hexachordal aggregate result from the presence of octave transpositions in the highest part (i.e. the clarinet).
It is hard to believe that this strikingly beautiful, opulent harmony and the nostalgic melody played by the clarinet result from a sophisticated, multi-layered application of a single motion pattern of 1+3. When we separate the “filling-in” layer controlled by the 1+3 patterns from its constructive frame (by means of post-Schenkerian reduction technique) the result is a short fragment of an overall background design in terms of pitch motion. The following graph (in Example 14) presents this fragment in a different perspective. Here we may observe the background frame of the pitch motion design of two complementary musical ideas which constitute the departure points for the succession of musical events in the Symphony’s introductory section.
The prominent position of the pitch “E” is immediately notable. Later on in the Symphony this pitch axis is temporarily suspended, only to be restored in the final sections of the work. Therefore, the overall background design may illustrate how Lutosławski’s pitch-axis technique works. It is striking that exactly the same overall design (in terms of the structural importance of the pitch “E”) may be recognized in other mature works by Lutosławski, e.g. Livre pour orchestre or his Third Symphony.
As is well known, Chopin was the only one of the early romantic composers whom Lutosławski held in the highest esteem. In a conversation with Tadeusz Kaczyński, Lutosławski stated: “I go back to his music from time to time in various ways. I listen to it, or play it or study it. Even today […] I find in the course of my everyday work that his music refreshes my imagination in certain ways. But probably nobody would guess that Chopin’s music had anything to do with the works which finally emerge from that relationship”  . Although it can not be proved, it seems quite possible that it was Chopin’s structural discipline, his “constructivist” skill, which could have stimulated Lutosławski’s imagination. Let us note that the aesthetic attitudes of both Polish composers were similar in respect to the matter of the autonomy of music. It seems that this very attitude promoted their concentration on the abstract, specifically musical phenomena. There is no doubt that the structural coherence understood as a latent logic of the unity in multiplicity belongs to these very phenomena. Therefore, Lutosławski’s statements and works confirm Szymanowski’s opinion about Chopin as a futurist of the romantic epoch, especially in terms of the history of Polish 20th century music.
. See: Oscar Bie. A History of the Pianoforte and Pianoforte Players, transl. by E. Kellet and E. Naylor (New York: 1966; original edition: Munich, 1898); Eduard Hanslick, Geschichte des Concertwesens in Wien(Vienna: 1869-1870); James Hunecker, Chopin: The Man and His Music (New York: 1900); Friedrich Niecks, Friedrich Chopin als Mensch und als Musiker. (Leipzig: 1890); J. S. Shedlock, The Pianoforte Sonata: Its Origin and Development (London, 1895). [Back]
. William H. Hadow, Studies in Modern Music, (London: 1892), vol. 2, p. 155. [Back]
. Vincent D’Indy, Course de composition musicale, (Paris: 1909; vol. 2, p. 407-410). [Back]
. Hugo Leichtentritt, Analyse der Chopin’schen Klavierwerken, (Berlin: 1921-1922); Heinrich Schenker, Der freie Satz, (Vienna, 1935). [Back]
. Karol Szymanowski, “Fryderyk Chopin,” Skamander 1923 (no. 28, p. 22-27 and no. 29/30, p. 106-10). Reprinted in K. Szymanowski, Pisma [Writings], vol. 1 Pisma muzyczne [Musical writings], Kornel Michalowski, ed. (Krakow: PWM, 1984), 89-103. This is Szymanowski’s first essay devoted to Fryderyk Chopin. The manuscript is held in the Karol Szymanowski Collection, Archives of Polish Composers, Library of the Warsaw University (BUW). English translation by Maria Piłatowicz forthcoming in After Chopin: Essays in Polish Music, ed. Maria Anna Harley (Los Angeles: USC Friends of Polish Music). [Editor’s note][Back]
. Zofia Lissa, “Harmonika Chopina z perspektywy dżwiękowej XX wieku” [Chopin’s Harmony from the point of view of the 20th century]. In Zofia Lissa, Studia nad twórczością Fryderyka Chopina [Studies in Chopin’s music] (Kraków: PWM, 1970); Irina Nikolska, “Dramaturgia i forma u Chopina a polska muzyka XX wieku: wybrane aspekty.” [Chopin’s dramaturgy and form in view of Polish 20th century music], Rocznik Chopinowski(no. 19, 1987). [Back]
. Maciej Gołąb, Przemiany stylu Chopina [Transformational changes of Chopin’s style], (Kraków: Musica Iagellonica, 1993); Andrzej Tuchowski, “Integracja strukturalna w świetle przemian stylu Chopina” [Structural coherence in view of the transformational changes of Chopin’s style], (Kraków: Musica Iagellonica, 1996). [Back]
. Felix Salzer, “Chopin’s Nocturne in C-sharp Minor, Op. 27, No. 1,” The Music Forum vol. 2 (1970): 290-291. [Back]
. Schenker,, Op. cit.; Franz Eibner, “Die Stimmfuhrung Chopins in der Darstellung Heinrich Schenkers,” in The Book of the First International Musicological Congress Devoted to the Works of F. Chopin, Zofia Lissa, ed., (Warsaw: F. Chopin Society, 1960); William Kinderman, “Directional tonality in Chopin, in Chopin Studies, Jim Samson, ed., (Cambridge: Cambridge University Press, 1988). [Back]
. Schenker,, Op. cit.; Eibner,, Op. cit.; Kinderman,, Op. cit.; Jim Samson. “The Composition-Draft of the Polonaise-Fantasy: The Issue of Tonality.” In Chopin Studies, Jim Samson, ed.,(Cambridge: Cambridge University Press, 1988); Maciej Gołąb, Chromatyka i tonalność w muzyce Chopina [Chromaticism and tonality in Chopin’s music], (Kraków: Musica Iagellonica, 1991). [Back]
. Alan Walker, “Chopin and musical structure,” in Frederic Chopin. Profiles of the Man and the Musician. Alan Walker, ed. (New York: 1967); Anatole Leikin, “The Sonatas,” in The Cambridge Companion to Chopin, Jim Samson, ed. (Cambridge: Cambridge University Press, 1992); John S. Bollinger, An Integrative and Schenkerian Analysis of the B-flat Minor Sonata by F. Chopin, (DMA Thesis, Washington University, 1981); Zofia Helman, “Norma i indywiduacja w Sonatach Chopina” [Norm and individuality in Chopin’s Sonatas], in Przemiany stylu Chopina [The transformational changes in Chopin’s style], M. Gołąb, ed. (Kraków: Musica Iagellonica, 1993). English translation forthcoming in Polish Music Journal vol. 2 no. 2, Winter 1999. [Back]
. Hugo Riemann, Geschichte der Musik seit Beethoven, (Berlin: 1911); Leichtentritt, 1922,, Op. cit., Ludwik Bronarski, Harmonika Chopina [Chopin’s Harmony], (Warsaw, 1935); Józef Chomiński, Sonaty Chopina[Chopin’s Sonatas], (Kraków: PWM, 1960); Paul Benary, “Ein Fall von Fehlinterpretation?” (Musica no. 1, 1985); Yuri Cholopow, “O zasadach kompozycji Chopina: zagadka finału Sonaty b-moll” [On compositional principles in Chopin: The mystery of the finale of the Sonata in B-flat minor], (Rocznik Chopinowski, No. 19, 1987). [Back]
. Zofia Lissa,, Op. cit., 1970. [Back]
. Nikolska,, Op. cit., 1987, p. 185. [Back]
. I further discuss the structural relationships and pitch organization in Szymanowski’s Songs of Infatuated Muezzin in my chapter of Alistair Wightman, Zofia Helman and Teresa Chylińska, eds. Szymanowski’s Songs, Kraków: Musica Iagellonica, forthcoming; English version, Los Angeles: Friends of Polish Music; Polish Music History Series, vol. 7). For other studies of Szymanowski’s songs see: Stephen C. Downes, Szymanowski as post-Wagnerian: The Love Songs of Hafiz,, Op. 24 (New York: Garland, 1994); Alistair Wightman “Szymanowski and Islam” Musical Times vol. 128, no. 1729 (March 1987): 129-132. [Back]
. Tadeusz Kaczyński, Conversations with Witold Lutosławski, transl. Yolanta May, (London: Chester, 1984; rev. 1995), 171. Originally published as Rozmowy z Witoldem Lutosławskim, (Kraków: Polskie Wydawnictwo Muzyczne, 1972). Printed in German as “Gespräche mit Witold Lutosławski, mit einem Anhang von Bálint András Varga,” tr. L. Fahlbusch & C. Rüger, in Neun Stunden bei Witold Lutosławski, (Leipzig, 1976, 163-230). [Editor’s note]. [Back]
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Andrzej Tuchowski, born in 1954, is a Polish musicologist and composer. He graduated from the Music Theory Department(1978) and the Composition Department(1983) of the Academy of Music in Wrocław. In 1981-1982 he conducted postgraduate musicological studies at Southampton University (England). After attending the Seminar in Music Theory and Aesthetics of Prof. Zofia Helman at the Institute of Musicology University of Warsaw, Tuchowski received his Ph.D. for a dissertation on the symbolic language of the operas by Benjamin Britten (1988, published in book form in 1990 by the Pedagogical College in Zielona Góra, Poland). In 1997, Tuchowski presented a monograph on Structural Integration in the Light of Transformational Changes in Chopin’s Style at the University of Warsaw to receive his professorship in musicology (i.e. “habilitacja”). Meanwhile, he wrote a book on Benjamin Britten (Benjamin Britten – Tworca, dzielo, epoka; Kraków: Musica Iagellonica, 1994), and numerous musicological articles published in Polish, English, and Russian. In addition Tuchowski’s compositions received two mentions at two national composers’ competitions (in Warsaw, 1984 and in Czechowice-Dziedzice in 1991). Tuchowski’s scholarly interests include, besides Britten and Chopin, also the music of Lutosławski, Szymanowski, and Panufnik. He is currently a professor of music theory at the Institute of Music Education, Pedagogical College in Zielona Góra and, simultaneously, at the Academy of Music in Wrocław, Poland.