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Walter Piston (1894-1976) was a renowned composer, educator, and musical theorist in the United States. His composition art was complicated, boasting over 70 significant works that had earned him multiple Pulitzer Prizes and American Music Critics Awards. Notably, his pedagogical achievements were equally impressive, as he mentored a plethora of American music professionals during his tenure as departmental head at Harvard University. His theoretical treatises, including “Harmony” and “Orchestration”, were known as classics, and Aaron Copland regarded “him as one of the most skillful American composers” (Kostelanetz,2004: 180). Piston’s magnum opus, “Three Pieces for Flute, Clarinet, and Bassoon”, finished at his sojourn in Paris, serves as a seminal milestone, marking his early foray into the field of composition. This work was emblematic of his early neoclassical style. His work was a microcosm of the musical zeitgeist of the era, synthesizing both European compositional techniques and the path of American composers.
His creative journey can be divided into three phases. The first phase (1925–1940) saw Piston’s emergence as a composer, marked by the success of “Three Pieces for Flute, Clarinet, and Bassoon”, which premiered in Paris in 1925. During the time, Piston produced a number of works including the “Piano Sonata” (1926), “Symphonic Piece” (1927), “Suite for Orchestra” (1929), “Flute Sonata” (1930), “Suite for Oboe and Piano” (1931), and “String Quartet No.1” (1933). “These compositions bear Piston’s style, characterized by a great use of canon sections, melodic inversions, elusive tonal shifts, and non-functional linear harmony and a clear structure” (Zhang, 2017). Piston’s composition displays his profound reverence for European musical traditions, which he believed played a more important role on American music than the indigenous music. That attitude could be found throughout his works. “First String Quartet” earned Piston the esteemed Guggenheim Fellowship in 1935. Copland lauded Piston's bold experimentation within the framework of his two string quartets.
In 1938, Piston published his masterwork, “The Incredible Flutist”, a ballet scores that captivated audiences worldwide. Premiered by the Boston Symphony Orchestra, this opus won widespread acclaim and established Piston’s reputation as a luminary of contemporary American music. He designed the dance in the form of a suite comprising 12 selections, each with an evocative subtitle. This composition epitomizes Piston's talent for melding neoclassical sensibilities with a distinctly American ethos, thereby reinforcing its status as an enduring masterpiece in the history of American music.
During the second phase of his compositional career (1940-1959), his achievements shone brightly with his Second Symphony in 1943, a monumental work that drew critical acclaim and earned Piston the prestigious “American Music Criticism” award.
As Piston started the third phase of his compositional journey (1960-1976), "he shifted to a style of dense chromaticism and atonal elements” (Howard,1994:99). This change in his musical language is exemplified by “the Ricercare for orchestra” (1966) and “the Variations for cello and orchestra” (1967). Piston explored uncharted territories, pushing the boundaries of tonality, and embracing dissonance to evoke a complicated emotional response. Despite this departure from traditional harmonic frameworks, Piston’s underlying principle of arch structural thinking remained unchanged.
Indeed, arch-like structural thinking deeply influenced Piston’s works. This was exemplified in his five string quartets, which demonstrated his unwavering commitment to this conceptual framework throughout his life. From the meticulous craftsmanship of artificial scales to the bold experimentation with atonality and twelve-tone techniques, Piston's works presents his innovation and profound understanding of musical architecture. In conclusion, Walter Piston’s career embodies a consistent attempt of absorbing the best of tradition and innovation, underpinned by the principles of arch-like structural thinking. As he navigated through different phases of his career, from the lush harmonies of his early stage to the daring explorations of his later works, Piston’s commitment to musical craftsmanship and structural integrity remained unaltered, which greatly shaped the contour of American music.
Ⅱ. Arch-like structural thinking in music
The term “arch” is commonly used in the subject of architecture or mechanics. An arch can be either planar or three-dimensional. Apart from its symmetric feature in mechanics, an arch is also considered to distribute forces to adjacent parts and establishes equilibrium both externally and internally.
Arch-like structures were also used in music at the Baroque and Classical periods, as exemplifed by compositions such as Bach’s fugues and Mozart’s “Piano Sonata in D major” (K.311). Typically, structural symmetry featured in arch-like musical structures. However, at the early stage of musical history, the application of arch-like structures was more rooted in the established practices of music and culture rather than caused by an intentional choice of artists. In the 20th century, composers began to extensively apply arch structural thinking in their works. They changed this structure from a classical form of physical structure to a mode of thinking in composition. This transformation empowered arch-like structures by using them in composition, and influenced the history of music.
“Arch-like structures have undergone centuries of development. In the 20th century, composers have elevated them from classical forms to a mode of thinking applied in composition, exerting a significant influence on the direction of musical evolution”. (Li, 2020:)
The arch-like structure is typically divided into five basic parts (or more): the springing, the haunches, the crown, the haunches again, and the springing, as illustrated below (Example 1): Each of these components plays a crucial role in providing stability and distributing forces within the arch, ensuring its structural integrity and balance.
Example 1
In geometric structures, arch exhibits a salient characteristic of symmetry and tripartite division. More significantly, an arch-like structure represents a curved or segmented form that primarily bears axial pressure, which is balanced by distributing the force at its ends. While displaying symmetry in its overall form, it also provides structured support to specific points under stress, maintaining internal equilibrium through thrust balance. However, in the realm of music, this characteristic cannot be simply understood as an apt proportion of different parts of a structure. The structure of music consists of elements such as time (rhythm), space (pitch), and logical arrangement (pitch organization). The true essence of arch-like structures applied in music lies in their capacity to incorporate all these elements and to present a holistic outcome. Through the unique structural characteristics, this enables the seamless progression of music, facilitating the presentation of logical coherence and the creation of three-dimensional sonic spaces. This structure also maintains internal equilibrium at crucial structural points, thereby achieving a certain degree of harmony within the overall composition.
Between 1930 and 1931, Béla Bartók composed his “Second Piano Concerto”, which cleverly employed arch-like structures. Scholars coined the term "Bartókian form" to define this unique application of symmetric proportional structures. His success lied in the symmetrical arrangement of thematic material across the movements, creating macroscopic resonance. Additionally, the interplay and variation of specific materials exhibited reflective relationships, forming microscopic resonances. The exploration of arch-like structures contributed to the success of the work.
Ⅲ. The Arch-like Structural Thinking in the Trio for Flute, Clarinet, and Bassoon
The chamber music piece “Three Pieces for Flute, Clarinet, and Bassoon” was completed in 1925, during Walter Piston's studies with Nadia Boulanger at the Paris Conservatoire (he returned to Harvard University in 1926). According to Piston himself, the “Three Pieces” composed during his studies with Boulanger represents his “first period” (neoclassical) of compositional style, notable for its presentation of color and dissonant harmonic progressions. The opening chapter of the book “Harvard Composers Walter Piston and His Students, from Elliott Carter to Frederic Rzewski”, published by Harvard University Press, mentions that “Three Pieces for Flute, Clarinet, and Bassoon” is his first successful work that was recognized in public. Therefore, the study of this piece is important to understanding Piston's formative stylistic period and as a starting point in his career as a professional composer.
3.1 The manifestation of arch-like structures in the macro-structure
This chamber music piece, which was published in 1925, consists of three movements. The first movement spans 123 bars. From a morphological perspective, it is undoubtedly a work with a rondo-like characteristic—the ABACABA structure. The structural characteristics of this form express the essential elements of a classical arch-like structure (Example 2). As mentioned earlier, the essence of arch-like structures lies not only in a balanced proportion of different parts but also in the simultaneous conformity of important elements, which shapes the musical force. These arch-like structural characteristics are one of the key factors contributing to the success of the work in terms of macroscopic architecture.
Example 2
The symmetry of artificial scale across the work features in the first piece of composition. At the zenith point B, the rhythm undergoes a swift change into a polyphonic crescendo with a triumvirate of voices, namely, a calculated avoidance of unison motifs. Subsequently, the motif music of point A reappears at “arch shoulder”, but the mirror part is omitted and followed by the interlude. Herein, the transitional motif plays a pivotal role in displaying a coherent pitch logic, showing a harmonic echo with the antecedent "arch spring" section, acting as a pivotal conduit between the celestial and terrestrial tonal realms. In particular, Bassoon's melodic motif in this transitional phrase produces a meticulously curated 1:5 structural ratio, which is based the judicious application of artificial scales to ensure continuity and fluidity while the flute traverses a whole-tone scale, the clarinet navigates through semitone intervals—a calculated compositional stratagem that echoes the 2:2 and 1:1 artificial scale paradigm respectively in the introduction. This approach based on the artificial scales is used across all three instrumental domains mitigates tonality, while amplifies logical congruity.
In terms of vertical alignment, the composer keeps minor thirds and major seconds among the tripartite voices to produce a vertical resonance, reflecting the harmonic architecture of the concluding triad. The composer pays attention to both horizontal development and proportional relationships of pitch material, coupled with the vertical superposition and spatial arrangement. That epitomizes Piston's consummate compositional skill and demonstrates archetypal structural integrity.
3.2 The manifestation of arch-like structures in the micro-organization
Throughout the 20th century, Impressionist composers shattered the hegemony of major and minor keys, with pioneering figures like Schoenberg and Berg who challenged the use of tonality and explored new forms of musical structure. This transformative period saw a shift in how people engaged with music, prompting significant changes in perception, understanding, and analysis.
“Due to the rapid and diverse development of music throughout the 20th century, significant changes naturally occurred in the way people engage with music, their perspectives on music, standards of understanding music, and procedures for analyzing music. One important change is the emphasis on viewing each ‘element’ or ‘event’ in a musical work with an 'equivalent' perspective.” (Peng, 2011:3) As a professor at Harvard University, Walter Piston embarked on a creative journey that distinguish him from his predecessors and contemporaries, which echoed the zeitgeist and uttered his unique voice. This quest for originality contributes to a balance between academic rigor, technical prowess, and sonic innovation which defined the standards of excellence in composition.
In his seminal work, Piston employs a sophisticated architectural metaphor to display a vivid sonic landscape. At the heart of this composition lies the concept of "artificial scales," that evokes a sense of symmetry and proportion. The deliberate use of pitch ratios—1:5, 1:3, 1:2, and 2:1—creates a tapestry of sound that transcends traditional tonal boundaries, offering audience a place where harmony and dissonance coexist in perfect equilibrium.
For example, in the first movement, in the A section, the core theme (Example 3), a symmetrical sequential pattern played by the bassoon, follows a 1:1:1:1:2:1:1:1:1 interval structure.
Example 3
In the third movement, the thematic phrase, played by the clarinet (Example 4), is presented in the middle section, following a symmetrical sequential pattern with a 1:2:1 interval structure.
Example 4
In the bass section of the first movement, the bassoon maintains a fixed melodic pattern (Example 5), presenting a sequence of intervals characterized by a 2:5:2 structure.
Example 5
In the second movement, the central rhythmic motif is performed by the flute and bassoon, as illustrated in Example 6. The flute section shows a mechanical and evenly paced rhythmic motion, while the bassoon section presents a rhythmic model formed by a certain symmetrical proportion. This interplay between the flute’s mechanical precision and the bassoon's symmetrical rhythm creates a dynamic and engaging rhythmic texture, enriching the musical fabric with its intricate patterns and nuanced expression.
Example 6
As key components, these sequences, with their intricate structural variances, serve as exemplars of diverse tonalities and technical complexities. They have a spectrum of acoustic effects and stylistic nuances, presenting a great challenge to achieving uniformity and control, which Walter Piston resolves with great effort. He integreats them into a coherent framework, namely the arch-like structure, a sophisticated compositional device that establishes overarching musical logic and presents nuanced expression and structural cohesion. Through strategic arrangement of different sections within the arch-like structure and adept utilization of transitional passages, Piston cleverly presents a holistic structure of harmony and balance, presenting a fluent expression of different ideas. Piston recognized the importance of concise material in composition, an insight that resonates with the legacy of composers such as Beethoven, Schumann, Brahms, and Mahler. He adeptly controls various pitch materials to form a distinctive "neo-classical" style, creating the work with continuity and coherence while pushing the boundaries of traditional tonal frameworks. This underscores Piston's remarkable compositional skill and meticulous logic, affirming his status as a visionary composer whose work heralds the dawn of a new era in music composition.
3.3 The manifestation of arch-like structures in the sonic architecture
Besides a musical analysis of arch structure thinking, this paper shows this phenomenon through an analysis of waveform and spectrum of performance versions (Example 7). From a signal processing standpoint, the analasis of the waveform and spectrum reveals the structural proportions, waveform trends, and threshold intensities, which illuminates the formation of arch-like structure in composition. By examining the amplitude variations and temporal patterns of waveform, recurring motifs, dynamic contrasts, and thematic developments within the composition are revealed. Similarly, frequency spectrum analysis helps identify dominant frequencies, harmonic relationships, and spectral density distributions, revealing the harmonic architecture and textural intricacies in composition.
Example 7
The analysis of the relationship betwen waveform and spectrum reveals the hierarchical organization of musical elements and how motifs and themes develop and transform in the process of the composition. Through quantitative analysis of structural proportions and waveform, the research reveals the architectural framework of the composition, highlighting the symmetrical arrangements, thematic contrasts, and developmental trajectories that underpin its arch-like structure.
By assessing threshold intensities and amplitude envelopes, the moments of climax, tension, and resolution are displayed, as well as the narrative arc and emotional contour of the musical discourse. Overall, waveform and frequency spectrum analysis supplement the traditional musicological approach with a new empirical one, enriching our understanding of the arch structure in composition and its seminal role.
The analysis of the first movement’s performance rendition focuses on frequency spectrum, disclosing a multitude of intricate features that sheds light on the features of arch-like structure in Walter Piston’s works. The analysis of waveform reveals a symmetrical arrangement, with the pivotal “Marker 46” as a focal point which follows the feature of an arch structure.
Considering the waveform trends between structural segments, a remarkable consistency could be found, exemplified by the waveform progression from “Marker 2” to “Marker 19”. The relationship between these two can be regarded as repetition. However, “Mark 19” only presents a reduced version of the waveform in the point A, as the mirroring section omitted. The change from “Mark 59” to “Mark 82” was similar to that from “Mark 2” to “Mark 29”, both of which played a role of “springing” and “arch shoulder” in an arch structure.
In terms of pitch distribution analysis, the extreme pitch revealed a pattern of mathematical elegance. The positions of “Marker 18” and “Marker 72” shows a symmetrical arch structure of the extreme pitch #G. Piston also carries the idea of arch structure in the overall composition and pitch layout.
The patter of golden-ratio extreme pitch in Piston’s piece is achieved by positioning the auditory key points at the most semialr structure, which locates at the intersection of golden section ratio of both progressive and regressive directions. This produces a sense of order and logic in spatial and temporal aspect, while achieves the unity and balance of structure and content. The golden section ratios also contribute to a balanced holistic structure with a dichotomous feature. This paper not only reveals the intricate interplay between waveform dynamics and pitch distribution within Piston's composition, but also underscores its aesthetic sophistication of arch structure thinking in composition.
The analysis of third movement comprising 191 bars (as illustrated in Example 8) is based on frequency spectrum and waveform smoothing techniques. This paper finds a waveform morphology inherently aligned with the arch-like structural attributes and characterized by symmetrical dual peaks and an axisymmetric configuration. In particular, the composer strategically positioned extreme pitches at pivotal structural junctures, the “Arch Shoulder”. This arrangement of extreme pitches highlights the structural integrity of the composition. Similar to the structural characteristics of the second movement, a duality is found and shows the inherent dichotomy of arch structure composition.
Example 8
This paper provides evidence of the architectural design structure within the third movement of Piston’s composition based on frequency spectrum analysis, coupled with waveform smoothing techniques. With waveform dynamics and pitch distribution, Piston demonstrates his deep understanding of musical structure, and this example also shows the rise of arch-like structural design in contemporary composition technique.
Ⅳ. Conclusions
The developmental history of composition technique represents a lasting journey towards idea of “beauty”, a process which seeks to balance between musical principles with artistic objectives. This perspective, articulated in a conversation between Wang Shaoming and Zhao Songguang on October 10, 2017, at Zhao Songguang’s residence at Guangzhou University, underscores the philosophical and aesthetic value of music creation.
Walter Piston was a pioneer of his era, who upheld classical aesthetic principles and adopted the state-of-the-art technique. His tools encompassed a wide range of sophisticated musical components, including atonality, polytonality, compound rhythms, and artificial scales. While he was not the first to creatively use these elements, Piston's works exemplified his mastery of skills and his commitment to artistic integrity, especially the principles of balance and order.
The arch-like structure, a classic architectural motif, plays an important role in modern composition technique and analysis. Piston’s seminal work, “Three Pieces for Flute, Clarinet, and Bassoon”, presents the arch-like structure both macroscopically and microscopically, designing an intricate relationship between elements in a harmonious equilibrium. Indeed, Piston's works also demonstrates the influence of history, and his aeththetics and techinique not only reflect an individual taste but also implies the zeitgeist.
References
[1] Hegel, Georg Wilhelm Friedrich. Aesthetics. Translated by Zhu Guangqian. Beijing: Commercial Press, 1996.
[2] Li, Xiaonuo. A Study on Arch-like Music Structure. Shanghai: Shanghai Conservatory of Music Press, 2006.
[3] Peng, Zhimin. A Course on New Music Works Analysis. Changsha: Hunan Literature and Art Publishing House, 2010.
[4] Piston, Walter. Orchestration. Translated by Dun Xing. Shanghai: Shanghai Literature and Art Publishing House, 1962.
[5] Schoenberg, Arnold. Composition with Twelve Tones. Translated by Chen Shibin. Beijing: People’s Music Publishing House, 2013.
[6] Song, Jin. From Modern to Postmodern Western Music. Shanghai: Shanghai Music Publishing House, 2006.
[7] Strauss, Joseph Nathan. Introduction to Post-Tonal Theory. Translated by Qi Yan. Beijing: People’s Music Publishing House, 2014.
[7] Wang, Cairong. Discourses on World Philosophy. Beijing: China Times Economic Press, 2010.
[8] Yang, Jian. The Structural Features and Causes of the 20th Century Western Instrumental Performance Styles—Based on a Study of Computer Visualization of Acoustic Parameters. Shanghai: Shanghai Conservatory of Music Press, 2011.
拱形结构思维在辟斯顿《为长笛、单簧管、大管而作的三部作品》中的运用
滕海峰（大真大学、广州科技贸易职业学院）
摘 要：拱形结构广泛存在于自然界与人类社会，是一种经典力学结构。在20世纪音乐当中，相当多作曲家使用该结构进行创作，以此获得某种音乐的控制。辟斯顿一生的创作丰富，相当多的作品运用了拱形结构思维，并将其作为结构整体与结构力重要部分共同看待。
关键词：拱形结构思维；辟斯顿；三重奏
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【JET征稿贴士】《教育教学研究论丛》（JET）2024年重点选题 & 征稿启事
【IJMS征稿贴士】《国际马克思主义研究学刊》（IJMS）青年学人支持计划
【征稿贴士】一心九刊，总有一刊适合你~涵盖教育、马理论、法学、语言文学和音乐学及人文社科综合类~~
