Quaternion Representation of Crystal Point Groups

Quaternion Representation of Crystal Point Groups

Date: August 1959
Creator: West, Richard Harrison
Description: The physical behavior of crystalline solids is very closely related to the internal symmetry of the crystal structure. For this reason it is desirable to represent mathematically this symmetry in such a way that the actual physical problems can be handled as they arise. In the case of this thesis the research has been guided by a list of desired properties for such a representation. No claim is made that the list is complete.
Contributing Partner: UNT Libraries
Accent and Grouping Structures in the String Quartets of Béla Bartók

Accent and Grouping Structures in the String Quartets of Béla Bartók

Date: May 2001
Creator: Bocanegra, Cheryl D.
Description: The music of Béla Bartók is defined in part by its unique blend of rhythmic vitality and inventiveness, and his string quartets offer a glimpse into a consistency of technique evident throughout his compositional career. Bartók's rhythmic environments are primarily metrical, but many of his rhythmic configurations are placed in such a way as to potentially override established meter. It is necessary, therefore, to institute an analytical means by which the delineation and comparison of rhythmic structures both within and without the metrical context may be accomplished. An analytical method using Timepoint Accent Structures (TAS) allows for the comparison of rhythms resulting from patterns of accent produced by pitch onset, dynamic stress, articulation or any other accentual factors. Timepoint Grouping Structures (TGS) delineate the number of timepoints present in alternating groups/blocks in a texture, thereby allowing for the recognition of patterning created by these larger groups. By applying TAS and TGS analysis, relationships of rhythmic equivalency, rotation, retrograde, complementation, augmentation, diminution, subset, superset, exchange, compression and expansion are clearly confirmed in the string quartets. In addition, symmetrical structures and arithmetic progressions are discovered. In many ways, Bartók's rhythmic organization mimics his procedures of pitch structuring.
Contributing Partner: UNT Libraries
Deconstructing Webern's Op 25, Drei Lieder: a Multidimensional Assessment

Deconstructing Webern's Op 25, Drei Lieder: a Multidimensional Assessment

Date: August 2013
Creator: Morgeson, Paul Taylor
Description: Webern scholarship has not comprehensively examined op. 25, drei lieder. If the selection of text for op. 25 is viewed as one work in three movements they create a ternary form (A-B-A1). To show how this form is developed in the music the author creates a new analytical system based on Schoenberg's Grundgestalt which is defined by three basic ideas: symmetry, liquidation, and variation. The relationship between the voice and accompaniment and Webern's deliberate manipulation of the text is used to reveal the use of a program which is then tied to the numerical symbolism of 2 and 3.
Contributing Partner: UNT Libraries