This dissertation explores the influence of melody on harmonic function in pop and rock songs from around 1950 to the present. While authors define the term "function" in several ways, none consider melody in their explanations, and I contend that any discussion of harmonic function in rock must include melody. I offer a novel perspective on function by defining it through what I call tension-as-anticipation, and I define a "melodic function" that accounts for the sense of tension and relaxation a melody creates within a particular moment in a track. My dissertation defines two types of melodic function—dominant and tonic—based on the melody's goal-directed scale-degree content, position within a phrase, and relation with the harmony. Dominant-melodic function results in two musical phenomena that I call the "imposed dominant" and the "dominant remainder." An imposed dominant occurs when a dominant-melodic function is initially dissonant with the harmony and resolves over a tonic. A dominant remainder occurs when a dominant-melodic function occurs over a harmonic resolution to the tonic, creating a slower dissipation of tension. Tonic-melodic function produces a phenomenon I call the "tonic anticipation," where a melody outlines a tonic mode over a pretonic harmony, creating a maximum sense of tension-as-anticipation. By including melody in considering harmonic function, we can more adequately describe the cycles of tension and resolution found in pop styles.

The aim of this thesis is to establish the principal properties for the theory of ordered compactifications relating to connectedness and to provide particular examples. The initial idea of this subject is based on the notion of the Stone-Cech compactification.The ordered Stone-Cech compactification oX of an ordered topological space X is constructed analogously to the Stone-Cech compactification X of a topological space X, and has similar properties. This technique requires a conceptual understanding of the Stone-Cech compactification and how its product applies to the construction of ordered topological spaces with continuous increasing functions. Chapter 1 introduces background information. Chapter 2 addresses connectedness and compactification. If (A;B) is a separation ofa topological space X, then (A 8 B) = A 8 B, but in the ordered setting, o(A 8 B)need not be oA 8 oB. We give an additional hypothesis on the separation (A;B) tomake o(A 8 B) = oA 8 oB. An open question in topology is when is X -X = X. Weanswer the analogous question for ordered compactifications of totally ordered spaces. So, we are concerned with the remainder, that is, the set of added points oX -X. Wedemonstrate the topological properties by using lters. Moreover, results of lattice theory turn out to be some of the basic tools in our original approach. In Chapter 3, specific examples and counterexamples are given to illustrate earlierresults.

Diss. Upps. phil. / [E.U. 1699-56].

Doctorat en Sciences / info:eu-repo/semantics/nonPublished

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It is the purpose of this paper to study the approximation to real functions by certain power series. Specifically, Taylor's series and generalizations of Taylor's series are considered. The importance of the behavior of the remainder, defined in chapter 1, demands a study of the difference between a function and the terms of an approximation sequence. Thus, this paper is devoted to the presentation of various forms of the remainder term when the approximation is by Taylor's expansion or some of its generalizations. / "May, 1955." / Typescript. / Advisor: B. F. Hadmot, Professor Directing Paper. / "Submitted to the Graduate Council of Florida State University in partial fulfillment of the requirements for the degree of Master of Science." / Includes bibliographical references (leaves 72-73).

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The study aimed at evaluating tree and shrub vegetation concerning the slope of the soil in Seasonal Deciduous Forest. The vegetation assessment was conducted in 14 plots systematically distributed in the forest and divided into subplots of 10 x 10 m, in which individuals with circumference 1.3 m of soil (CAP) ≥ 30 cm were observed. These individuals represented class I while individuals with a CAP ≥ 15 < 30 cm represented class II. Vegetation was analyzed by means of the TWINSPAN (Two-way Indicator Species Analysis) method to classify groups, within which the horizontal structure of the forest was studied. In 36 subplots, morphological description of the soil profile was carried out, samples were collected for chemical analysis and clay was determined at three depths (0-10, 10-20 and 20-30 cm), as well as slope, which was classified as low slope (1 ≥ 15), medium slope (15 ≥ 35) and high slope (≥35). The relationship between clusters of vegetation, slope and soil characteristics was studied by means of Principal Component Analysis (PCA). In G1, indicator species were Trichilia claussenii, Cupania vernalis and Crysophyllum marginatum and, in G2, Luehea divaricata and Sebastiania commersoniana. In terms of horizontal structure, these species were among the three best represented ones. Both clusters occurred in areas of variable slope, however, G2 took place in an environment which was more susceptible to interference in the vegetation. From PCA, it could be observed that soil characteristics and slope explained 26% of the total variability, and, out of these, 72% was explained in the main component 1, showing a strong correlation between soil characteristics and the presence of phytosociological groups in different slopes. This relationship is stronger for the presence of the two groups in the ranges of medium and high slope, on the other hand, in terms of low slope, the two groups showed no positive correlation with soil characteristics. For G1 in high slope and G2 in medium and high slope, correlation is positive concerning the whole characteristics of cationic exchange. However, G1 in medium slope was strongly correlated to the complex of exchangeable acidity. G2 at higher slopes also shows high correlation with clay, the finer texture may confer a greater degree of aggregation and reactivity, allowing the development of large species such as Luehea divaricata and Cordia americana. In general, due to restrictions of soil and slope, maintaining of the remnants is prior, aiming at important environmental services for the region. / O estudo objetivou avaliar a vegetação arbórea e arbustiva em relação à formação de agrupamentos, declividade do terreno e influência do solo nos agrupamentos em Floresta Estacional Decidual. A avaliação da vegetação foi realizada em 14 parcelas distribuídas sistematicamente na floresta e divididas em subparcelas de 10 x 10 m, onde foram observados os indivíduos com CAP (circunferência a 1,3 m do solo) ≥ 30 cm, os quais representaram a classe I, e indivíduos com 15 ≤ CAP < 30 cm, representando a classe II. Na análise da vegetação utilizou-se o método TWINSPAN (Two-way Indicator Species Analysis) para classificação de grupos, dentro dos quais foi estudada a estrutura horizontal da floresta. Em 36 subparcelas foi realizada a descrição morfológica do perfil do solo, coletada amostra para análise química e determinação de argila em três profundidades (0-10, 10-20 e 20-30 cm), além da declividade, que foi classificada em baixa (1 ≥ 15º), média (15 ≥ 35º) e alta (≥ 35º). A relação com os grupos e características do solo foi estudada por meio de Análise de Componente Principal (PCA). No G1 as espécies indicadoras foram Trichilia claussenii, Cupania vernalis e Crysophyllum marginatum e no grupo G2 Luehea divaricata e Sebastiania commersoniania. Na estrutura horizontal essas espécies estiveram entre as três melhores representadas. Ambos os agrupamentos ocorreram em áreas com variáveis declividades, entretanto, o G2 ocorreu em ambiente mais susceptível às interferências na vegetação. A partir do PCA observou-se que as características do solo e declividade explicaram 26% da variabilidade total, sendo que desses 72% foi explicado no componente principal 1, demonstrando forte correlação entre as características dos solos e a presença dos grupos fitossociológicos em diferentes declividades. Essa relação foi mais expressiva para a presença dos dois grupos nos intervalos de média e alta declividade, por outro lado, em declividade baixa os dois grupos não apresentaram correlação positiva com as características do solo. Para G1 em alta e G2 em média e alta declividade, a correlação é positiva em relação ao conjunto de características de troca catiônica. Entretanto, o G1 em declividade média teve forte correlação com o complexo de acidez trocável. O G2 em maior declividade também apresenta alta correlação com a argila, essa textura mais fina talvez confira um maior poder de agregação e reatividade, permitindo o desenvolvimento de espécies de grande porte como Luehea divaricata e Cordia americana. De forma geral, devido às restrições de solo e declividade, a manutenção do remanescente é prioritária visando importantes serviços ambientais à região.