This research project dug into mathematics in music, exploring the various ways a number series was used in the 20th century to create musical compositions. The Fibonacci Series (FS) is an infinite number series that is created by taking the two previous numbers to create the next, excluding 0 and 1 at the very start of the series. As the numbers grow larger, the ratios between the numbers of the FS approach the value of another mathematical concept known as the Golden Mean (GM). The GM is so closely related to the series that it is used interchangeably in terms of proportions and overall structure of musical pieces. This is similar to how both the FS and GM are found in aspects of nature, like to all too well-known conch shell spiral.
The FS in music was used in a variety of ways throughout the 20th century, primarily focusing on durations and overall structure in its use. Examples of this are found in Béla Bartók’s Music for Strings, Percussion, and Celeste (1936), Allegro barbaro (1911), Karlheinz Stockhausen’s Klavierstück IX (1955), and Luigi Nono’s il canto sospeso (1955). These works are analyzed in detail within my research, and I found every example to have a natural feel to them even if its use of the FS is carefully planned out by the composer. Bartók’s works are the least precise of my examples but perhaps the most natural ones. This imprecision in composition may be considered a more natural use of the FS in music, since nature is not always perfect either. However, in works such as Stockhausen’s, the structure is meticulously formatted in such that the precision is masked by a cycle as to appear more natural.
The conclusion of my research was a commissioned work for my instrument, the viola. I provided my research to composer Jacob Miller Smith, a DMA Music Composition student at ASU, and together we built the framework for the piece he wrote for me. We utilized the life cycle of the Black-Eyed Susan, a flower that uses the FS in its number of petals. The life cycle of a flower is in seven parts, so the piece was written to have seven separate sections in a palindrome within an overall ABA’ format. To utilize the FS, Smith used Fibonacci number durations for rests between notes, note/gesture groupings, and a mapping of 12358 as the set (01247). I worked with Smith during the process to make sure that the piece was technically suitable for my capabilities and the instrument, and I premiered the work in my defense.
The Fibonacci Series and Golden Mean in music provides a natural feel to the music it is present in, even if it is carefully planned out by the composer. More work is still to be done to develop the FS’s use in music, but the examples presented in this project lay down a framework for it to take a natural place in music composition.
Ernest Bloch’s Suites for Solo Cello (B. 93, 94, 97) contain a melodic-harmonic language unlike any other twentieth-century unaccompanied work, and when transcribed for viola, become meaningful additions to the existing viola repertoire. Each movement within these three works has its own distinct dancelike character, much like J.S. Bach’s Suites for Solo Cello (BWV 1007-1012). The melodies contain a persistent lyrical quality, and the harmonies are modal and reminiscent of folk music. Rather than compose an appropriate ending to Bloch’s incomplete Suite for Solo Viola (B. 101), a transcription of Bloch’s Suites for Solo Cello provides violists with more variety and opportunity for musicianship. These works present technical challenges such as rapid string crossings, sudden and vast register changes, complex rhythms and meter, and offer interpretationally rich passages. The level of these difficulties can prepare violists for more challenging twentieth-century works; thus, transcribing the Bloch Suites provides an opportunity to bridge a pedagogical divide in solo viola repertoire.
This project includes the transcriptions of Bloch’s Suites for Solo Cello, a performance edition, and a recording. Included is an overview of why these works are suitable for the viola, how these arrangements help fill a pedagogical gap in the unaccompanied viola repertoire, and insight into the transcription process. The performance recording captures the accessibility of these works for violists wishing to perform them and shows the integrity and variety of each piece by programming them all on a single recital.
Works for clarinet in the twentieth century exist in abundance; furthermore, the number of extant works from the Classical period is substantial. However, works for solo clarinet in the late-Romantic style are lacking; most of the significant literature for clarinet is contained in orchestral works. Therefore, the purpose of this project is to add to the solo clarinet repertoire of the late Romantic-style through the transcription of works written originally for viola. The four works transcribed for this project are by York Bowen. Bowen was a British composer and pianist who taught at the Royal Academy of Music in England. Although his career flourished in the twentieth century, his music reflects the music of the late-Romantic style. The project includes a transcription of Bowen's Sonata No. 1 in C minor, Op. 18 for viola and piano, Sonata No. 2 in F major, Op. 22 for viola and piano, Romance in D-flat for viola and piano, and Phantasy in F, Op. 54 for viola and piano. Additionally, a brief examination of Bowen's life, an overview of each piece, details regarding transcription parts, a list of changes made to the original part, and a recording of each transcription is included in the document.
This handbook is aimed to develop a violist’s technique as they move from Georg Philipp Telemann’s Concerto for Viola, Strings, and Basso Continuo in G Major, TWV 51: G9 and begin the Carl Stamitz's Viola Concerto in D Major, Op. 1. Ten etudes and related exercises introduce and highlight various techniques, providing a comprehensive and methodical transition from one concerto to the next. These etudes are based on fragments of the Stamitz Concerto in an effort to directly relate technical development with performance skills.