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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.
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.
ContributorsFerry, Courtney (Author) / Knowles, Kristina (Thesis director) / Buck, Nancy (Committee member) / School of Music (Contributor) / School of Mathematical and Statistical Sciences (Contributor) / Barrett, The Honors College (Contributor)
Created2019-12
Description
This project is a visual presentation on the value of music education in public schools. With cutbacks in funding for education, arts programs such as orchestra or band are often the first to face budget restrictions or be eliminated altogether. Many schools and administrators deem arts programs as less essential to a student’s education because they do not directly teach core subjects such as math, science or reading. This project explains why reducing or eliminating funding for arts programs is ultimately detrimental to students. A high quality musical education brings great developmental benefits in a variety of skills such as language development, memory learning and special understanding. Students trained in music also have shown higher scores on standardized tests. Additionally, music programs provide a creative outlet for students that can help relieve stress and provide an opportunity for personal expression and a sense of identity. This project is organized into three sections. Part I discusses the lack of funding for fine arts programs in schools and the affordability of playing a stringed instrument. Part II dives into the academic, cognitive and behavioral benefits of an education in music. Finally, Part III discusses potential solutions to the problem and showcases examples of out-of-school music programs. The final form of the project is displayed online through a program called Readymag, a digital tool for presenting projects, which allows for the written aspect of the project to fall seamlessly with the visual component. The visual component of the project is made of photographs captured on site at interviews, performances and practices, as well as in a studio.
ContributorsAtzenweiler, Stella Alexander (Author) / Dolin, Penny (Thesis director) / Buck, Nancy (Committee member) / Graphic Information Technology (Contributor, Contributor) / School of Art (Contributor) / Barrett, The Honors College (Contributor)
Created2019-05