Master of Music (MM), Bowling Green State University, 2011, Music Theory

Puccini's Suor Angelica is a work that has received minimal attention from music theorists and analysts. James Hepokoski has proposed a rotational structure based on four of the work's forty-nine themes, though it covers only one third of the opera. Michele Girardi and Andrew Davis have made note of some motivic relationships but in an unsystematic way. Harmonic planing is a major feature of Suor Angelica yet it has not been given any specific analytical attention. This thesis expands these previous analyses by providing a detailed thematic time-line that includes all of the opera's themes, by showing that many of these themes can be unified through a three-note motive, and by exploring the types of planing Puccini used most often and the contexts in which he used them. The resulting thematic time-line shows that only fourteen of the opera's forty-nine themes are ever repeated and that James Hepokoski's rotational analysis explains only a small portion of the entire work's thematic structure, leaving thirty-five themes unaccounted for. The motivic analysis demonstrates a relationship between many of the opera's themes and demonstrates that the opening and ending of the opera have a particularly strong motivic connection, though themes including a recurring three-note motive are shown to occur consistently throughout the opera. Themes containing the motive are then proven to occur consistently throughout the opera when its appearances are placed against the thematic time-line. Finally, a survey of all passages involving planing, identifying their location, the type of planing and the type of chords used, reveals that planing is likewise a consistent feature of Suor Angelica.

Committee: Nora Engebretsen PhD (Committee Chair); Gene Trantham PhD (Committee Member) Subjects: Music

Doctor of Philosophy, The Ohio State University, 2022, Mathematics

We explore lattice point counting and the method of stationary phase through the lens of questions about the number of lattice points on and near surfaces with vanishing curvature. Our focus is on spheres arising from the Heisenberg groups. In particular, we prove an upper bound on the number of points on and near large dilates of the unit spheres generated by the anisotropic Heisenberg norms for α ≥ 2. We accomplish this through a transformative process that takes a number theory question about counting lattice points and translates it into that of an analytical estimation of measure. This process relies on truncating and scaling the n-dimensional integer lattice to produce a fractal-like set. By introducing a measure on this resulting set and using elementary Fourier analysis, the counting problem is transformed into one of bounding an energy integral. This process uses principles of fractal geometry and oscillatory integrals. Primary challenges that arise are the presence of vanishing curvature and uneven dilations. Following a discussion and formal estimate of the curvature of the Heisenberg spheres, we utilize the method of stationary phase to compute a bound on the Fourier transform of their surface measures. Our work is inspired by that of Iosevich and Taylor (2011) and Garg, Nevo, and Taylor (2015). We present an extension of the main result in the former to surfaces with vanishing curvature. Furthermore, we utilize the techniques developed here to estimate the number of lattice points in the intersection of two such surfaces. Additionally, we present a mini-course on the basics of stationary phase—a quick-start guide to stationary phase in practice. This includes a discussion of the formulation of oscillatory integrals and their solutions with a focus on the impact of geometric properties (e.g. curvature) on the estimates for the decay of the Fourier transform. It further serves as a supplement to [Shakarchi and Stein, Functional Analysis: Chapter (open full item for complete abstract)

Committee: Krystal Taylor (Advisor); Rodica Costin (Committee Member); Barbara Keyfitz (Committee Member) Subjects: Mathematics

Master of Science, The Ohio State University, 2012, Mathematics

The purpose of this study was to show how mathematics can be used to analyze effects on sound. Our hope is that this may inspire student interest in mathematics. We analyzed five common industry standard effects. Research data was gathered using Mathematica and GarageBand software. Three versions of each effect were used to alter pure tone sound waves of ten different frequencies using GarageBand. Then using Mathematica's Fourier command, the frequency spectrum of each altered sound wave was generated. Through observation of each set of 30 frequency spectra, the most prominent and common pure tone components were determined. For each effect, Mathematica's Fit command was used to determine a best fit model of the magnitude of each component as a function of frequency. Our models provide descriptions of the effects that are consistent with the traditional descriptions of the industry standard effects in our study. If similar research is to be conducted, our recommendation is that more versions of each effect, a wider range of input frequencies, and a higher sampling rate would produce function models that are even more consistent with traditionally accepted effect descriptions. Furthermore, an understanding of the hardware and software design used to build effects on sound is highly recommended.

Committee: Bart Snapp (Advisor); Herb Clemens (Committee Chair); James Cogdell (Committee Member) Subjects: Mathematics Education

Doctor of Philosophy, The Ohio State University, 2006, Mechanical Engineering

Serpentine belts are widely used for efficient power transmission in automobiles and heavy vehicles, but they suffer noise and wear problems that have their roots in system vibration. The primary goal of this work is to develop mathematical models for serpentine drives with nonlinear elements and implement vibration analysis to understand certain nonlinear dynamic behaviors and provide guidance for practical design. Nonlinear one-way clutches integrated with accessory pulleys are effective devices to decouple the motions of an accessory and its pulley during disengagements and mitigate the rotational pulley vibration problems. A mathematical model of a one-way clutch in belt-pulley systems is established, where a wrap-spring type of clutch is modeled as a nonlinear spring with discontinuous stiffness. Analysis of steady state and transient vibrations exhibits the mechanisms behind one-way clutches' effectiveness, and identifies where the one-way clutch works most effectively to reduce vibration and noise. The method of multiple scales is employed to approximate the steady-state periodic solutions. This study evaluates the validity of the perturbation method for such strong nonlinearity through comparison of analytical and numerical solutions. A one-way clutch that functions based on the relative velocity of the driven pulley and its accessory is common in applications. This type of one-way clutch is included in a hybrid continuum-discrete model incorporating span vibration and pulley rotation. The engagement/disengagement status transitions lead to a piece-wise linear system with alternate locked clutch and disengaged clutch configurations. The dynamic response and dynamic tension fluctuations are examined for varying system parameters. A tensioning system, consisting of a rigid arm pivoting around a fixed point and an idler pulley rotating at the free end of the arm, is typically used in belt drives to maintain belt tension as operating conditions change. Dry frict (open full item for complete abstract)

Committee: Robert Parker (Advisor) Subjects: Engineering, Mechanical

PhD, University of Cincinnati, 2021, Arts and Sciences: Mathematical Sciences

This thesis presents two sets of new sharp estimates in harmonic analysis united by a common theme: they are both related to $A_p$ weights, they are both treated with the use of Bellman functions, and they both develop new technical tools that go beyond established theory. The first part concerns estimates for a family of Carleson sequences related to dyadic $A_2$ weights; the corresponding Bellman functions do not arise as solutions of a PDE and have a new, non-infinitesimal kind of optimizers. The second part deals with lower $L^p$-estimates for logarithms of $A_\infty$ weights as an indirect way of estimating the constant of exponential integrability of $\BMO^p$ for $0 Committee: Leonid Slavin Ph.D. (Committee Chair); Michael Goldberg Ph.D. (Committee Member); Nageswari Shanmugalingam Ph.D. (Committee Member) Subjects: Mathematics

PhD, University of Cincinnati, 2018, College-Conservatory of Music: Theory

This dissertation is the first comprehensive study of the harmonic theories of German composer and music theorist Sigfrid Karg-Elert (1887–1933), whose two major treatises date from the early 1930s. The dissertation's subtitle highlights the four principal components of Karg-Elert's theoretical project: its three-dimensional just intonation pitch space, and its acoustic derivation; its expansion of Hugo Riemann's function theory, encompassing a variety of fifth-, third- and seventh-based chord relationships; its complete and consistent system of common-tone transformations, which operates independently from harmonic function; and finally, its ultimate presentation of the entire system as a model of harmonic perception. The appendix to the dissertation is a complete annotated German-English edition of Karg-Elert's 1930 treatise Akustische Ton- Klang- und Funktionsbestimmung (“Acoustic Determination of Pitch, Chord and Function”), translated here for the first time. Karg-Elert's treatises synthesize three strains of thought in late nineteenth-century German theory that were previously somewhat self-contained: a model of pitch and harmonic space derived from the pure intervals of just intonation; major-minor dualism (which Karg-Elert termed polarity), shaped especially by the work of Arthur von Oettingen; and the concept of harmonic function, first presented in Riemann's Harmony Simplified of 1893. Building on that scholarly foundation, Karg-Elert introduces several innovative ideas, including the addition of a third dimension to the pitch space, based on the pure or concordant seventh (4:7); a network of direct major and minor third transformations; and transformations involving the concordant seventh, which enable direct connections among dominant and half-diminished seventh chords. In total, Karg-Elert proposes 23 transformations among triads and seventh chords, all of which retain at least one common tone (conceived as a unique location in the three-dimension (open full item for complete abstract)

Committee: Steven Cahn Ph.D. (Committee Chair); David Carson Berry Ph.D. (Committee Member); Cristina Losada Ph.D. (Committee Member) Subjects: Music

Master of Science in Engineering, Youngstown State University, 2017, Department of Electrical and Computer Engineering

Power distortion has been a rising concern in the industrialized society nowadays due to the increasing number of non-linear power electronic devices. Power distortion refers to the existence of unwanted frequency harmonics in power systems, which is dangerous and may cause serious problems such as fires, electromagnetic interfaces, and equipment damage. Therefore, detecting harmonics is a critical part of determining the efficiency and the safety of an electrical system. The objective of thesis was to develop a real-time harmonic detection system that can detect the harmonics in a single-phase AC electrical system by using digital hardware. The proposed harmonic detection system was designed with VHSIC Hardware Description Language (VHDL), which can be implemented on a Field-Programmable Gate Array (FPGA) chip. Fast Fourier Transform (FFT) was utilized to get the values for the 1st, 3rd, 5th, 7th, and 9th harmonics of the signals. In this thesis, two artificial harmonic components were constructed to create two test signals using MATLAB to match real life scenarios. Additionally, one actual electrical signal was recorded for comparison. The three signals were then simulated and analyzed through the proposed system. Signals were also processed using MATLAB to get the theoretical values of the harmonics. The digital hardware simulation results of the proposed real-time harmonic detection system matched the theoretical simulations from MATLAB.

Committee: Frank Li PhD (Advisor); Jalal Jalali PhD (Committee Member); Eric MacDonald PhD (Committee Member) Subjects: Electrical Engineering

Doctor of Philosophy, The Ohio State University, 1958, Graduate School

Committee: Not Provided (Other) Subjects: Biology

Master of Music, University of Akron, 2015, Music-Theory

Summary, Data Conclusion: The purpose of the analyses explained in Chapter III was to recognize the relationship, if one exists, between the overlying emotion/purpose of the song and its intervallic complexity. Similarly to classical operatic structure, rock ballads, like arias, often stop time to further explore a singular emotion. The rock musical version of aria's counterpart, recitative, is the rock anthem which is inordinately trying to send a message - often one of passion, angst, or revolt. With a message as powerful as this, the music may fall prey to the text so as not to distract from the persistence of revolution. The Total Average Interval (TAI) data of Tables 5 and 6 indeed shows that the vast majority of songs classified as ballads or anthems lie on opposite ends of the spectrum, with ballads containing the largest intervallic totals and anthems the smallest. Another interesting correlation arose among songs that had repetitive texts. As aforementioned in the background of the study, Leonard Bernstein (famous for both the melodic tritone and the melodic minor seventh in his songs from West Side Story, "Maria" and "Somewhere," respectively), attended a production of Hair when it premiered on Broadway and was said to have walked out at intermission. His objection was that the lyrics reminded him of mere "laundry lists" which is an analysis not lacking in accuracy. Of the songs from Hair analyzed here, three stand out as having a majority of lyrics that incorporate the recitation of a series of nouns: the title song, "Hair," "I Got Life," and "Ain't Got No." "Hair" boasts forty different styles/types of hair, including, "polka-dotted," "confettied," and "spaghettied." In the same fashion, "I Got Life" specifies thirty-five "things we've got," the majority of which are body parts, while "Ain't Got No" spells out thirty-six "things we ain't got," including, "culture," "schoolin'," and a "draft card." When consulting Table 5, it seems that th (open full item for complete abstract)

Committee: Nikola Resanovic (Advisor); Brooks Toliver (Committee Member) Subjects: Music

PHD, Kent State University, 2015, College of Arts and Sciences / Department of Mathematical Sciences

I consider the following problems from Tomography. Suppose that the projections (sections) of two given bodies onto (by) every subspace of a fixed dimension are related by a certain condition. Does this imply that the bodies satisfy a similar condition in the ambient space? There are two major parts to this dissertation. The first one is on bodies with directly congruent projections or sections. The second part is about containment of two bodies and relations between their volumes, provided the projections (sections) of the first body can be rotated to be contained in the corresponding projection (section) of the second one.

Committee: Dmitry Ryabogin (Advisor); Artem Zvavitch (Committee Member); Joseph Diestel (Committee Member); Feodor Dragan (Committee Member); Peter Tandy (Committee Member) Subjects: Mathematics

Doctor of Philosophy (PhD), Wright State University, 2012, Computer Science and Engineering PhD

The scope of this research is concentrated on analytical winding size optimization (thickness or diameter) of high-frequency power inductors wound with foil, solid-round wire, multi-strand wire, and litz-wire conductors. The first part of this research concerns analytical optimization of the winding size (thickness or diameter) for the inductors conducting a sinusoidal current. Estimation of winding resistance in individual inductor layers made of foil, taking into account the skin and proximity effects is performed. Approximated equations for the winding power loss in each layer are given and the optimal values of foil thickness for each layer are derived. A low- and medium-frequency approximation of Dowell's equation for the multilayer foil winding is derived and analyzed. A new closed-form equation for the optimum foil thickness at which the global minimum of the winding ac resistance occurs is derived and an equation for the foil winding hill thickness at which the local maximum of the winding ac resistance is obtained is given. An analytical optimization of solid-round-wire windings conducting a sinusoidal current is performed. New closed-form analytical equations are derived for the normalized valley diameter, normalized hill diameter, and normalized critical diameter. An approximate model for multi-strand wire winding, including litz-wire winding is presented. The proposed model is evaluated using Dowell's equation. The model takes into consideration the existence of proximity effect within the litz-wire bundle, i.e., between the strands as well the skin effect. New closed-form analytical equations are derived for the normalized strand diameter to achieve the local minimum of the ac winding losses for sinusoidal current. The second part of this research concerns analytical optimization of the winding size (thickness or diameter) for the inductors conducting harmonic currents with and without dc offset. Analytical winding power loss minimizati (open full item for complete abstract)

Committee: Marian K. Kazimierczuk PhD (Advisor); Raymond E. Siferd PhD (Committee Member); Sayiu Ren PhD (Committee Member); Ronald Riechers PhD (Committee Member); Ronald Coutu PhD (Committee Member) Subjects: Engineering

DMA, University of Cincinnati, 2007, College-Conservatory of Music : Clarinet

John Adams's clarinet concerto Gnarly Buttons, now more than ten years old, fuses post-minimalism, post-Stravinsky techniques, and American vernacular idioms, holding a unique place in the clarinet repertoire and serving as an important marker in Adams's evolution of compositional style that began in the 1990s. The stylistic point of departure is his 1991 opera The Death of Klinghoffer, and Gnarly Buttons is among the pieces that continues to develop the textural and melodic innovations that Klinghoffer started. Thus, full comprehension of the style and aesthetic of Gnarly Buttons depends on an understanding of the stylistic traits established by Adams's compositions from the 1980s combined with an examination of innovations in the 1990s. This document offers an account of the history of the work, centered on information of those interviewed for this project, including John Adams, Michael Collins, Paul Meecham and William Helmers. The performance guide that follows also incorporates information from recent performances, especially from the January 2007 performance with the Los Angeles Philharmonic, John Adams conducting, and Derek Bermel as soloist. The last section of the document offers analysis, tracing Adams's style from Nixon in China, through The Death of Klinghoffer, and finally to Gnarly Buttons, showing how the concerto both incorporates and builds on Adams's own compositional past.

Committee: Dr. Robert Zierolf (Advisor) Subjects: Music

Doctor of Philosophy, The Ohio State University, 2008, Music

Function is one of those words that everyone understands, yet everyone understands a little differently. Although the impact and pervasiveness of function in tonal theory today is undeniable, a single, unambiguous definition of the term has yet to be agreed upon. So many theorists - Daniel Harrison, Joel Lester, Eytan Agmon, Charles Smith, William Caplin, and Gregory Proctor, to name a few - have so many different nuanced understandings of function that it is nearly impossible for conversations on the subject to be completely understood by all parties. This is because function comprises at least four distinct aspects, which, when all called by the same name, function, create ambiguity, confusion, and contradiction. Part I of the dissertation first illuminates this ambiguity in the term function by giving a historical basis for four different aspects of function, three of which are traced to Riemann, and one of which is traced all the way back to Rameau. A solution to the problem of ambiguity is then proposed: the elimination of the term function. In place of function, four new terms - behavior, kinship, province, and quality - are invoked, each uniquely corresponding to one of the four aspects of function identified. The meanings of these new terms are elucidated by such harmonic topics as secondary dominants and six-four paradigms. A notation system is developed for behavior, in particular, which is used in conjunction with two standard systems of harmonic analysis to form a Three-fold System of Analysis that yields deeper explanations of harmony characteristics. Part II of the dissertation reveals how my theory of behavior leads to new explanations for chromatic harmonies. A definition of tonicization is proposed based on behavior paradigms. The models suggest that tonicization is a better explanation than is mixture for many chromatic notes and harmonies that are typically explained with mixture. Further, so-called linear or voice-leading chords (such as augme (open full item for complete abstract)

Committee: Gregory Proctor PhD (Advisor); Graeme Boone PhD (Committee Member); Lora Gingerich Dobos PhD (Committee Member) Subjects: Music

Doctor of Philosophy, The Ohio State University, 2005, Mathematics

Let F be a number field or a p-adic field. We introduce in Chapter 2 of this work two reductive rank one F-groups, H1, H2, which are twisted endoscopic groups of GSp(2) with respect to a fixed quadratic character varepsilon of the idele class group of F if F is global, F* if F is local. If F is global, Langlands functoriality predicts that there exists a canonical lifting of the automorphic representations of H1, H2 to those of GSp(2). In Chapter 4, we establish this lifting in terms of the Satake parameters which parametrize the automorphic representations. By means of this lifting we provide a classification of the discrete spectrum automorphic representations of GSp(2) which are invariant under tensor product with varepsilon. The techniques through which we arrive at our results are inspired by those of Kazhdan's in [K]. In particular, they involve comparing the spectral sides of the trace formulas for the groups under consideration. We make use of the twisted extension of Arthur's trace formula, and Kottwitz-Shelstad's stabilization of the elliptic component of the geometric side of the twisted trace formula. If F is local, in Chapter 5 we provide a classification of the irreducible admissible representations of GSp(2, F) which are invariant under tensor product with the quadratic character varepsilon of F*. Here, our techniques are also directly inspired by [K]. More precisely, we use the global results from Chapter 4 to express the twisted characters of these invariant representations in terms of the characters of the admissible representations of Hi(F) (i = 1, 2). These (twisted) character identities provide candidates for the liftings predicted by the local component of the conjectural Langlands functoriality. The proofs rely on Sally-Tadic's classification of the irreducible admissible representations of GSp(2, F), and Flicker's results on the lifting from PGSp(2) to PGL(4).

Committee: Yuval Flicker (Advisor) Subjects: Mathematics

Bachelor of Science, Marietta College, 2008, Mathematics and Computer Science

We seek to extend the applicability of the tools of complex analysisthat have been developed to deal with problems in two-dimensional harmonic field theory. In order to ease the reader who has only a basic understanding of complex analysis into a working knowledge of its relevant applications to field theory, this material is introduced through the use of vector fields as common ground. Opportunities for using the mathematical tools being developed to solve physical problems are also highlighted by examples in order to aid comprehension and foster intuition. Established techniques used in solving problems involving point sources are then generalized to handle those involving interval sources.

Committee: Mark Miller (Committee Member); Craig Howald (Committee Member); Cavendish McKay (Committee Member) Subjects: Mathematics; Physics

Master of Music, University of Akron, 2009, Music-Theory

The purpose of this Thesis is to explore and compare four works by two recognized leaders of the Tin Pan Alley style. This includes the songs “They Say It's Wonderful” and “A Pretty Girl is Like a Melody” by Irving Berlin, and “You're a Bad Influence on Me” and “Wunderbar” written by Cole Porter. Through comparison and analysis I will attempt to pinpoint characteristics that made their music more appealing to the performers, the public, and everyone considered. These characteristics include aspects of rhythm, phrase structures, harmonic analysis, and performance practices.The phrase ‘Tin Pan Alley' was supposedly first used by Monroe Rosenfeld in 1903, in his series of articles about the area around 28th street in New York City. The sounds of the composers pounding away on cheap pianos all day were said to resemble the sound of beating on old tin pans. Tin Pan Alley actually came into being in the 1880's, when music publishers and writers began moving to a central location in New York City. 1 The location of Tin Pan Alley changed over the years, originating around East 14th St. near Union Square, shifting to West 28th St. around the turn of the 20th century. Later, after World War I, it moved further uptown to around West 50th St. and Broadway.2 1 Ewen, David, All The Years of American Popular Music (Englewood Cliffs, NJ: Prentice-Hall, Inc., 1977) 152-3. 2 Ewen, David, The Life and Death of Tin Pan Alley (New York, NY: Funk and Wagnalls Co., 1964) 294-5.

Committee: Nikola Resanovic PhD (Advisor) Subjects: Music