Rhythm is at the heart of all music. It is the variation of the duration of sound over time. A rhythm has two components: one is the striking of an instrument – called the "onset" – and the other is silence. Historically, musical forms and works were preferred and became popular by their rhythmic properties. Therefore, to study rhythm is to study the underpinnings of all of music. In this thesis, we explore basic rhythmic preferences in traditional music and, using this as a point of reference, methods are implemented to generate similar types of rhythms. Finally, a software platform to facilitate such an analysis is developed – it is the first of its kind available to our best knowledge as this research field has only recently emerged.

This thesis studies the problem of measuring freedom of choice. It analyzes the concept of freedom of choice, discusses conditions that a measure should satisfy, and introduces a new class of measures that uniquely satisfy ten proposed conditions. The study uses a decision-theoretical model to represent situations of choice and a metric space model to represent differences between options. The first part of the thesis analyzes the concept of freedom of choice. Different conceptions of freedom of choice are categorized into evaluative and non-evaluative, as well as preference-dependent and preference-independent kinds. The main focus is on the three conceptions of freedom of choice as cardinality of choice sets, representativeness of the universal set, and diversity of options, as well as the three conceptions of freedom of rational choice, freedom of eligible choice, and freedom of evaluated choice. The second part discusses the conceptions, together with conditions for a measure and a variety of measures proposed in the literature. The discussion mostly focuses on preference-independent conceptions of freedom of choice, in particular the diversity conception. Different conceptions of diversity are discussed, as well as properties that could affect diversity, such as the cardinality of options, the differences between the options, and the distribution of differences between the options. As a result, the diversity conception is accepted as the proper explication of the concept of freedom of choice. In addition, eight conditions for a measure are accepted. The conditions concern domain-insensitivity, strict monotonicity, no-choice situations, dominance of differences, evenness, symmetry, spread of options, and limited function growth. None of the previously proposed measures satisfy all of these conditions. The third part concerns the construction of a ratio-scale measure that satisfies the accepted conditions. Two conditions are added regarding scale-independence and function growth proportional to cardinality. Lastly, it is shown that only one class of measures satisfy all ten conditions, given an additional assumption that the measures should be analytic functions with non-zero partial derivatives with respect to some function of the differences. These measures are introduced as the Ratio root measures.

This thesis studies the problem of measuring freedom of choice. It analyzes the concept of freedom of choice, discusses conditions that a measure should satisfy, and introduces a new class of measures that uniquely satisfy ten proposed conditions. The study uses a decision-theoretical model to represent situations of choice and a metric space model to represent differences between options. The first part of the thesis analyzes the concept of freedom of choice. Different conceptions of freedom of choice are categorized into evaluative and non-evaluative, as well as preference-dependent and preference-independent kinds. The main focus is on the three conceptions of freedom of choice as cardinality of choice sets, representativeness of the universal set, and diversity of options, as well as the three conceptions of freedom of rational choice, freedom of eligible choice, and freedom of evaluated choice. The second part discusses the conceptions, together with conditions for a measure and a variety of measures proposed in the literature. The discussion mostly focuses on preference-independent conceptions of freedom of choice, in particular the diversity conception. Different conceptions of diversity are discussed, as well as properties that could affect diversity, such as the cardinality of options, the differences between the options, and the distribution of differences between the options. As a result, the diversity conception is accepted as the proper explication of the concept of freedom of choice. In addition, eight conditions for a measure are accepted. The conditions concern domain-insensitivity, strict monotonicity, no-choice situations, dominance of differences, evenness, symmetry, spread of options, and limited function growth. None of the previously proposed measures satisfy all of these conditions. The third part concerns the construction of a ratio-scale measure that satisfies the accepted conditions. Two conditions are added regarding scale-independence and function growth proportional to cardinality. Lastly, it is shown that only one class of measures satisfy all ten conditions, given an additional assumption that the measures should be analytic functions with non-zero partial derivatives with respect to some function of the differences. These measures are introduced as the Ratio root measures.

Maximal evenness was first introduced in the music theory domain by John Clough and Jack Douthett. Later, the concept was explored by others such as Dmitri Tymoczko and Richard Cohn. Although maximal evenness was first explored with respect to pitch-classes, the concept can be understood in the rhythmic domain. An explanation of voice-leading space can be found here to create a conceptual foundation before departing to the implications of maximal evenness on rhythm. This thesis will then explore the concept further by exploring music from Steve Reich and György Ligeti to demonstrate the applicability and deeper understanding of the concept.

To support population growth in Las Vegas, Nevada, large scale increases in groundwater pumping are planned across the state. This pumping could affect riparian areas in Great Basin National Park by lowering groundwater levels, reducing stream flows, and xerifying riparian vegetation. Great Basin National Park (GBNP) is mandated to manage its resources unimpaired for future generations. Loss of biodiversity is unacceptable under this mandate. If groundwater levels are reduced beyond a threshold, aquatic and riparian diversity would be lost, but the effects on small mammal communities are less clear. To provide baseline information and to consider the effects of groundwater withdrawal a priori, we sampled and compared small mammal communities in two watersheds susceptible to groundwater withdrawal and one non-susceptible watershed. We also used to stable isotopes of nitrogen, carbon, deuterium and oxygen to characterize small mammal communities. Evenness was higher in susceptible watersheds, which were distinct in species composition. Riparian and upland habitats in susceptible watersheds supported complementary small mammal communities, while communities in the non-susceptible watershed were more homogenous. Susceptible watersheds are located at the lowest elevations of GBNP where habitat heterogeneity due to the contrast between mesic riparian and xeric upland habitats is important in maintaining small mammal diversity. Partitioning was primarily seen in nitrogen and carbon isotopes which reflect feeding ecology (trophic level and primary production source), but was also seen in oxygen isotopes. Major differences in nitrogen and carbon isotopes were between taxonomic groups, while similarity was highest within these groups. Shrews and ermine were highest in nitrogen reflecting their high trophic positions. Harvest and piñon mice were intermediate in nitrogen suggesting omnivory, while chipmunks, voles, woodrats and pocket mice were apparently herbivorous. Carbon ratios were consistent with C3 based diets but were relatively enriched in Sigmodontinae species. Small mammal deuterium was similar to stream water suggesting that stream water is an important water source of water to small mammals. Oxygen enrichment relative to stream water and precipitation suggested that small mammals are sensitive to body water evaporation. Contrary to a previous study, oxygen isotopes were inversely related to water use efficiency. Increases in the rate of groundwater pumping adjacent to Great Basin National Park could lower water tables, reduce stream flows, and xerify riparian vegetation. We suggest that groundwater levels, streams flow and riparian vegetation, in addition to small mammal species composition will be important response variables in monitoring the effects of groundwater withdrawal. If predictions of groundwater withdrawal are realized, groundwater levels, stream flows, vegetation, microclimate, and invertebrates riparian dependent as well as small mammals will be negatively affected resulting in a decrease in diversity and loss of riparian species from affected areas.

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The present state of forestry post mining land uses has prompted concern among researchers, landowners, and the public. Surface mines reclaimed to forests under the provision of the Surface Mining Control and Reclamation Act (SMCRA) may not achieve site productivity levels required by the law. Anecdotal evidence suggests that many pre-law reforested mined sites are growing productive forests. The purpose of this study was to characterize these forests and the mine soils in which they are growing, and use them to benchmark forest development on mined land. Using 14 mined and 8 non-mined sites in the midwestern and eastern coalfields research to address the following objectives was undertaken: (i) characterize the development, composition, and diversity of woody species on pre-SMCRA, forested surface mined land; (ii) estimate forest and site productivity on surface mined land and determine the soil and site properties most influencing forest growth; (iii) estimate projected rotation-age timber product value; (iv) quantify current carbon sequestration pools associated with the developing woody plant biomass, the forest floor, and developing soil medium; (v) compare the diversity, forest and site productivity, commercial value, and carbon capture of reclaimed mined sites to that of regional non-mined forest systems. Species richness between non-mined and mined sites was about the same within each region with 14 to 15 tree species in the canopy. Canopy richness of eastern mined sites was less than that on midwestern mined sites (12 species compared to 17 species, respectively). Species richness of the understory and woody ground layer were similar between sites planted to pines versus hardwoods. White pine (Pinus strobus) monocultures, planted on many sites in the eastern region, caused species unevenness throughout all forest strata. Midwestern mined sites and eastern sites planted to hardwoods closely approximated non-mined sites in commercial species composition. Planted species represented the majority of canopy layer dominance and abundance (82% relative dominance and 56% relative abundance). Site productivity between non-mined sites and 12 of the 14 mined sites was similar. Regression analysis identified the five most influential soil properties affecting site quality, which included soil profile base saturation, total coarse fragments, total available water, C horizon total porosity, and soil profile electrical conductivity. These five properties explained 52 % of the variation in tree growth. Forest productivity of these mined sites was equal to or greater than that of non-mined forests, ranging between 3.3 m3ha-1yr-1 and 12.1 m3ha-1yr-1. Management activities such as planting pine and valuable hardwood species increased the stumpage value of forests on reclaimed mine sites. Rotation-age stumpage values on mined study sites ranged between $3,064 ha-1 and $19,528 ha-1 and were commonly greater than stumpage values on non-mined reference sites. After 20 to 55 years, total site carbon levels on mined study sites averaged 217 Mg ha-1, while total carbon amounts on natural sites averaged 285 Mg ha-1. The amounts of carbon captured within the plant biomass and litter layer were the same on mined and natural sites. However, the soil carbon content of mined sites averaged 39 % lower than natural soils. The amount of carbon captured across mined sites was largely a function of forest stand age. Pre-SMCRA forests growing on mined sites with productivity levels similar to non-mined sites are capable of developing forest attributes comparable to or greater than those found on non-mined land within a period of 60 years, the length of a commercial hardwood rotation. These mature forests can serve as benchmarks for forest development on mined lands being reclaimed under current state and federal regulations. / Master of Science