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The purpose of this research work is to investigate the relationship between humidity and tone in musical instruments. A basic hypothesis that motivates this work is that normal seasonal variations in relative humidity are thought to alter the tone of instruments constructed from wood. These changes in tone are believed to be due to changes in the dimensions and material properties of an instrument that are a result of wooden components absorbing and adsorbing water in equilibrium with their ambient environmental conditions. To investigate this hypothesis an experiment was conducted with a guitar acclimatized at different relative humidity levels. Sample sounds recorded at each humidity level were then evaluated by the test subjects using a three alternative forced choice listening test paradigm. Subjects were readily able to distinguish sounds recorded at different humidity levels, supporting the claim that changes in ambient humidity can create perceptible differences in instrument tone. A finite difference model was then developed to produce simulated sounds as a function of moisture content (MC being the weight percentage of a piece of wood that is water). The model was validated and further listening tests were conducted to determine the perceptual limit of MC differences. The just-noticeable difference value for MC change was established to be 0.7% MC difference. To be considered imperceptibly stable with respect to tone, materials used to replace traditional soundboard woods would need to have less variability than the equivalent material property changes due to this 0.7% MC difference. Testing of an acetylated plate in terms of its vibration and material properties followed. An increase in both stiffness and density was noted, yet even after modification the vibration properties of the plate were observed to remain within an acceptable range of material properties typical of soundboard grade woods. Instrument builders would likely welcome this new material, as long as its properties can be shown to not vary significantly from traditional choices. A second component of this thesis concerns the application of wavelets in musical analysis. Psychoacoustical signal parameters (PSPs) are a tool used to quantify aspects of sounds, such as brightness or percussiveness. These PSPs are often calculated using the Fast Fourier Transform (FFT), an algorithm that has certain limitations. To address the deficiencies of the FFT a wavelet transform was em- ployed and conventional PSPs were reformulated in the wavelet domain to improve their accuracy. Tonal differences due to changes in MC were shown to be well suited to analysis by wavelet PSPs where improved sensitivity was observed in comparison to the conventional methods. Finally, an acoustical study of the development of the piano from the clavichord to the modern grand piano was conducted. An improved bass response and the presence of more energy in the upper partials, particularly in these bass notes, were concluded to be due to an increase in soundboard area, the introduction of longer string scale lengths, and the use of wound strings for bass notes.

Within the past decades, wavelets and associated wavelet transforms have been intensively investigated in both applied and pure mathematics. They and the related multi-scale analysis provide essential tools to describe, analyse and modify signals, images or, in rather abstract concepts, functions, function spaces and associated operators. We introduce the concept of diffusive wavelets where the dilation operator is provided by an evolution like process that comes from an approximate identity. The translation operator is naturally defined by a regular representation of the Lie group where we want to construct wavelets. For compact Lie groups the theory can be formulated in a very elegant way and also for homogeneous spaces of those groups we formulate the theory in the theory of non-commutative harmonic analysis. Explicit realisation are given for the Rotation group SO(3), the k-Torus, the Spin group and the n-sphere as homogeneous space. As non compact example we discuss diffusive wavelets on the Heisenberg group, where the construction succeeds thanks to existence of the Plancherel measure for this group. The last chapter is devoted to the Radon transform on SO(3), where the application on diffusive wavelets can be used for its inversion. The discussion of a variational spline approach provides criteria for the choice of points for measurements in concrete applications.

Thesis (Ph.D.)--McMaster University, 2005. / Supervisor: Jean-Pierre Gabardo. Includes bibliographical references (leaves 138-145).

Thesis (Ph. D.)--Ohio University, June, 2001. / Title from PDF t.p.

Thesis (Ph. D.)--Ohio University, August, 1994. / Title from PDF t.p.

Thesis (Ph.D.) -- University of Adelaide, Dept. of Electrical and Electronic Engineering, 2003. / "August, 2003" Bibliography: p. 261-268.

Thesis (Ph.D.)--George Mason University, 2008. / Vita: p. 160. Thesis director: Edward J. Wegman. Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Information Technology. Title from PDF t.p. (viewed Mar. 9, 2009). Includes bibliographical references (p. 151-159). Also issued in print.

Thesis (M.S.)--Ohio University, November, 1995. / Title from PDF t.p.

Thesis (Ph. D.)--University of Washington, 1998. / Vita. Includes bibliographical references (p. [85]-88).