Abstract: A teaching system for increasing understanding of music through expansion of a compositional technique known as contrary motion and methods for creating and utilizing the same contrary motion and/or understanding. Contrary motion can comprise two or more lines of music that proceed in opposite directions from each other. As a first line of music ascends in pitch, for example, a second line of music descends in pitch. In selected embodiments, the teaching system can employ one or more senses, such as an auditory sense, a visual sense, a tactile sense and a kinesthetic sense, of a listener to enable the listener to further understand and enjoy the music. Accordingly, the teaching system advantageously can enhance understanding of music with a focus on contrary motion by incorporating the use of the other senses of the listener in addition to use of the auditory sense.

Abstract: A diagnostic method and system comprising writing to a tape location of a tape medium using a first tape head as the tape medium is transported in a first direction, reading from the tape location using a second tape head as the tape medium is transported in the first direction, detecting an occurrence of a tape system failure, performing a diagnostic tape operation selected from a group consisting of writing to the tape location using the second tape head as the tape medium is transported in the first direction and reading from the tape location using the first tape head as the tape medium is transported in the first direction, differentially diagnosing a tape medium failure or a tape head failure depending on whether the tape operation failure is observed in response to performing the diagnostic tape operation, and posting a corresponding error code.

Abstract: A diagnostic method and system comprising writing to a tape location of a tape medium using a first tape head as the tape medium is transported in a first direction, reading from the tape location using a second tape head as the tape medium is transported in the first direction, detecting an occurrence of a tape system failure, performing a diagnostic tape operation selected from a group consisting of writing to the tape location using the second tape head as the tape medium is transported in the first direction and reading from the tape location using the first tape head as the tape medium is transported in the first direction, differentially diagnosing a tape medium failure or a tape head failure depending on whether the tape operation failure is observed in response to performing the diagnostic tape operation, and posting a corresponding error code.

Abstract: A diagnostic method and system comprising writing to a tape location of a tape medium using a first tape head as the tape medium is transported in a first direction, reading from the tape location using a second tape head as the tape medium is transported in the first direction, detecting an occurrence of a tape system failure, performing a diagnostic tape operation selected from a group consisting of writing to the tape location using the second tape head as the tape medium is transported in the first direction and reading from the tape location using the first tape head as the tape medium is transported in the first direction, differentially diagnosing a tape medium failure or a tape head failure depending on whether the tape operation failure is observed in response to performing the diagnostic tape operation, and posting a corresponding error code.

Abstract: A system and method is provided for modeling a world database that is a spheroid in a computer graphics simulation system. The method includes the operation of modeling the world database using a plurality of geodetic terrain gridposts. A further operation is creating a triangulated network mesh based on the geodetic terrain gridposts in real-time as a function of eye position. In addition, the triangulated network mesh is stored in geodetic coordinates. The triangulated network mesh is then rendered using geometry formed by the triangulated network mesh.

Abstract: A system and method is provided for combining independent scene layers to form computer generated environments. The method includes the operation of constructing a terrain layer using stored terrain data. Another operation is generating a feature layer using feature layer data that is stored separately from the stored terrain data. The feature layer and the terrain layer can then be combined to form a composite scene.

Abstract: A system and method is provided for modeling a world database that is a spheroid in a computer graphics simulation system. The method includes the operation of modeling the world database using a plurality of geodetic terrain gridposts. A further operation is creating a triangulated network mesh based on the geodetic terrain gridposts in real-time as a function of eye position. In addition, the triangulated network mesh is stored in geodetic coordinates. The triangulated network mesh is then rendered using geometry formed by the triangulated network mesh.

Abstract: A system and method is provided for combining independent scene layers to form computer generated environments. The method includes the operation of constructing a terrain layer using stored terrain data. Another operation is generating a feature layer using feature layer data that is stored separately from the stored terrain data. The feature layer and the terrain layer can then be combined to form a composite scene.