(Original posted on April 9, 2002)
This is a research book that analyzes the characteristics of Bartók’s musical works through the “Golden Ratio” and “Fibonacci sequence.” It delves into representative works such as “Music for Strings, Percussion and Celesta,” “Piano Concertos,” and “Mikrokosmos,” using musical examples to reveal Bartók’s unique compositional methodology, demonstrating that these works are not merely atonal or simple quotations of folk music, but are based on meticulous mathematical and structural principles.
Bartók left very few writings about his own compositional techniques. Therefore, the principles underlying the depths of his music were shrouded in mystery. The author, Lendvai, boldly tackled this mystery, and by meticulously analyzing his works, sought to “discover” a unique compositional principle that Bartók himself may not have recognized, or perhaps intentionally never spoke of. In this respect, the book possesses a depth and an engaging sense of inquiry not found in similar works.
One of the theories proposed by the author is the “Axis System.” This is the author’s unique theory that extends and assigns the harmonic functions of “tonic,” “subdominant,” and “dominant” found in classical tonal music to all twelve tones of the chromatic scale.
According to this Axis System, all twelve tones belong to one of three functions (tonic axis, subdominant axis, dominant axis). The author states that this enables free harmonic progressions unbound by traditional tonality while still maintaining a sense of tonality. He claims that through this system, it becomes possible to logically explain characteristics of Bartók’s music such as “remote modulations” and “ambiguous tonality.”
Whereas Schoenberg’s twelve-tone technique aimed for atonality and constructed a completely new system, Lendvai’s Axis System is conceived as a system encompassing all twelve tones by broadly reinterpreting traditional tonal functions. This can be seen as the author’s own answer to the complex sonority of Bartók’s music, which is “not completely atonal, yet cannot be fully analyzed by traditional harmonic theory.”
Furthermore, by actively applying concepts like the “Golden Ratio” and “Fibonacci sequence” – which have long been used in visual arts and architecture – to the temporal and structural aspects of music, and by providing abundant concrete analytical examples, the book clarifies the structural characteristics of Bartók’s works. Thus, the very idea of introducing the Golden Ratio into perceived time was highly original and groundbreaking.
However, questions have now been raised about the validity of applying the Golden Ratio to “musical time” (perceived time), and there are slight suspicions of self-serving interpretations in his arguments. Nevertheless, the historical significance of its success in clarifying the uniqueness of Bartók’s compositional technique has not diminished.
For those familiar with Bartók’s music or composers кто wish to grasp a part of his world of sonority, the concrete analytical content of this book will likely serve as a catalyst for application. Note that this book is not the type to teach Bartók’s compositional techniques step-by-step. Basic knowledge of music theory fundamentals and harmony is essential.
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Bartók reorganized elements that are major forces in traditional Western musical composition, such as “dominant chords,” the “circle of fifths,” and “leading tones,” from his own unique perspective, and composed based on that. As Bartók himself stated, “All art should have its roots in the art of preceding ages. And not only should it have them, but it must grow out of them,” he aimed to root his work in Western music and further cultivate it from there.
According to the author, a major influence on Bartók in this endeavor was the “Golden Ratio (1:0.618…)” found in nature. The Golden Ratio is widely applied in architecture and a_rt for its visual naturalness and beauty of balance, but Bartók is considered the first to have actively applied it to music. What was actually used in music was the “Fibonacci sequence (1, 2, 3, 5, 8, 13…),” which generates the Golden Ratio, and this was mainly applied to intervals.
Now, as for what kind of music was born from that, you simply have to listen to it yourself. In my personal opinion, it is “transparent and austere music.” Incidentally, converting “13” from the Fibonacci sequence into an interval results in a “minor ninth (an octave, 12 semitones + 1 semitone),” an interval that is “harsh to the ear.” And indeed, minor ninths appear frequently in his actual compositions. However, strangely enough, one feels a sense of transparency in Bartók’s music. This is one of the wonders of music.
Interestingly, Bartók’s melodies and harmonies bear a strong resemblance to jazz sounds. Why don’t you explore Bartók’s sound with this book?
Table of Contents for “Bartók’s Compositional Technique”
- Principles of Tonal Organization
- The Axis System
- Principles of Form
- Golden Section
- Fibonacci Sequence
- Application to Chords and Intervals
- Chromatic System
- Diatonic System
- Appendices I, II, III
- Translator’s Afterword
About the Author
Ernő Lendvai
Ernő Lendvai was born in 1925 in Kaposvár, a small city in southwestern Hungary. He majored in composition and theory at the Liszt Academy of Music in Budapest. After graduation, he taught at music vocational schools in Szombathely, Győr, Szeged, Budapest, and other cities. He also worked for a radio station for a time, and is currently (at the time of this book’s writing) a lecturer at the Budapest Music College. (Quoted from this book)
