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Fibonacci Hidden in Musical Places

Description

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

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.

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2019-12

Stravinsky for Guitar Quartet

Description

This project is an arrangement of three movements from Igor Stravinsky's most famous and beloved ballets for performance by classical guitar quartet. The movements arranged were "Augurs of Spring" from The Rite of Spring (1913), "Russian Dance" from Petrouchka (1911),

This project is an arrangement of three movements from Igor Stravinsky's most famous and beloved ballets for performance by classical guitar quartet. The movements arranged were "Augurs of Spring" from The Rite of Spring (1913), "Russian Dance" from Petrouchka (1911), and "Infernal Dance of All Kastchei's Subjects" from The Firebird (1910). Because the appeal of this music is largely based on the exciting rhythms and interesting harmonies, these works translate from full orchestra to guitar quite well. The arrangement process involved studying both the orchestral scores and Stravinsky's own piano reductions. The sheet music for these arrangements is accompanied by a written document which explains arrangement decisions and provides performance notes. Select movements from Stravinsky for Guitar Quartet were performed at concerts in Tempe, Glendale, Flagstaff, and Tucson throughout April 2016. The suite was performed in its entirety in the Organ Hall at the ASU School of Music on April 26th 2016 at the Guitar Ensembles Concert as well as on April 27th 2016 at Katie Sample's senior recital. A recording of the April 27th performance accompanies the sheet music and arrangement/performance notes.

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2016-05

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Innovative strategies used to teach mathematics: A look at educators and classrooms across six countries

Description

Mathematics is an increasingly critical subject and the achievement of students in mathematics has been the focus of many recent reports and studies. However, few studies exist that both observe and discuss the specific teaching and assessment techniques employed in

Mathematics is an increasingly critical subject and the achievement of students in mathematics has been the focus of many recent reports and studies. However, few studies exist that both observe and discuss the specific teaching and assessment techniques employed in the classrooms across multiple countries. The focus of this study is to look at classrooms and educators across six high achieving countries to identify and compare teaching strategies being used. In Finland, Hong Kong, Japan, New Zealand, Singapore, and Switzerland, twenty educators were interviewed and fourteen educators were observed teaching. Themes were first identified by comparing individual teacher responses within each country. These themes were then grouped together across countries and eight emerging patterns were identified. These strategies include students active involvement in the classroom, students given written feedback on assessments, students involvement in thoughtful discussion about mathematical concepts, students solving and explaining mathematics problems at the board, students exploring mathematical concepts either before or after being taught the material, students engagement in practical applications, students making connections between concepts, and students having confidence in their ability to understand mathematics. The strategies identified across these six high achieving countries can inform educators in their efforts of increasing student understanding of mathematical concepts and lead to an improvement in mathematics performance.

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2014-12

Original Extended Play: The Production and Marketing Plan

Description

Independent artists are thriving in the modern music industry, creating and branding their own music, and developing rich concentrations of fans. Indie artists are progressively securing positions within mainstream music while also upholding individuality. With technology advancements, to include self-recording

Independent artists are thriving in the modern music industry, creating and branding their own music, and developing rich concentrations of fans. Indie artists are progressively securing positions within mainstream music while also upholding individuality. With technology advancements, to include self-recording technology, wearable devices, and mobile operating systems, independent artists are able to extend their reach to a variety of audiences. Social media platforms' progression has further catalyzed artists' capability of growth, as they have the capacity to personalize marketing content, develop loyal fan-bases, and engage directly with potential consumers. Artists are increasingly fabricating their own unique spaces in an industry that was formerly controlled by conventions. This thesis involves the production of a three-song extended play, and ascertains how to effectively capitalize on the wide array of modern marketing platforms.

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2015-05

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Rainbow Connection: An Integrated Choir for Building Relationships

Description

Rainbow Connection is an integrated choir with members on and off the autism spectrum. It was founded in the spring of 2012 by Barrett students Ali Friedman, Megan Howell, and Victoria Gilman as part of an honors thesis creative project.

Rainbow Connection is an integrated choir with members on and off the autism spectrum. It was founded in the spring of 2012 by Barrett students Ali Friedman, Megan Howell, and Victoria Gilman as part of an honors thesis creative project. Rainbow Connection uses the rehearsal process and other creative endeavors to foster natural relationship building across social gaps. A process-oriented choir, Rainbow Connection's main goals concern the connections made throughout the experience rather than the final musical product. The authors believe that individual, non-hierarchical relationships are the keys to breaking down systemized gaps between identity groups and that music is an ideal facilitator for fostering such relationships. Rainbow Connection operates under the premise that, like colors in a rainbow, choir members create something beautiful not by melding into one homogenous group, but by collaboratively showcasing their individual gifts. This paper will highlight the basic premise and structure of Rainbow Connection, outline the process of enacting the choir, and describe the authors' personal reactions and takeaways from the project.

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2014-12

Achieving a Flow State in Piano Performance by Redefining Technical Challenges

Description

This project is a small scale investigation of various factors concerning "Flow" in Piano Performance. "Flow" is the sweet spot where ability and challenge are about equal, and usually high (Csikszentmihalyi 1990). Piano performance is a state of playing the

This project is a small scale investigation of various factors concerning "Flow" in Piano Performance. "Flow" is the sweet spot where ability and challenge are about equal, and usually high (Csikszentmihalyi 1990). Piano performance is a state of playing the piano with some intent to perform. In this case, the intent is to create something new or improvise. Improvisation is one form of expressive creativity on the piano stemming from some knowledge and extrapolation upon that knowledge (Nachmanovitch 82). Creativity is essential to the development of new music, and though extensive literature exists on both creativity and music independently, there is a gap in research regarding links between the two (Macdonald et al. 2006). This project aims to address some of these gaps by working with piano players and non-musicians of various technical skill levels to examine the "Flow" state in improvisation as well as potential factors affecting creative performance. Factors such as listening, self-confidence, frustration in methodology, and meditation practices were found to correlate positively with technical skill. Participants who completed the practice program were able to reconstruct challenges and enter the "Flow" state in improvisation regardless of high or low technical scores.

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2016-05