Balther of Säckingen, Bishop of Speyer, Composer of Chants for St Fridolin ca. 970

Balther of Säckingen was a remarkable scholar, writer and composer, who was born about 930, made bishop of Speyer in 970, and died in 986 or 987. Educated at the famous monastery in St. Gallen, he went as a wandering student in search of learning as far as North Spain. He had a special veneration for St Fridolin, founder of a convent in Säckingen. On his travels Balther found a copy of a Life of St Fridolin, memorized it, wrote it down on his return home, composed chants to be sung on the feast day of the saint, and sent both the Life (vita) and the chants (historia) to one of his former teachers at St. Gallen for approval. Balther says he composed them “per musicam artem”, “according to the art of music”. This paper tells how Balther’s chants came to be composed and compares them with others in order to understand what was considered to be “musical art” around 970

Estimation of reaction forces in high bar swinging

Reaction forces experienced by gymnasts swinging on the high bar may be determined indirectly using inverse dynamics analysis or may be measured using strain gauges. The accuracy of inverse dynamics analysis may be poor because of errors in the estimated inertia parameters and in the accelerations obtained from digitized data. On the other hand the use of strain gauges is not always possible in elite competition. This paper presents a method for estimating the reaction forces based on the linear displacements of the bar. The bar was modelled as a point mass attached to horizontal and vertical linear springs (obeying Hooke’s law) with stiffness coefficients determined from static loading. The stiffness coefficients of the bar were determined with three different tensions in the stabilizing cables of the high bar. A force and video analysis of backward giant circles was performed. Estimates for the reaction forces were obtained by multiplying the bar displacements from the video analysis by the stiffness coefficients determined from the static loadings. Comparisons were made between the estimated reaction forces and the reaction forces recorded using strain gauges attached to the high bar. Varying the tension in the stabilizing cables of the high bar did not effect the stiffness of the bar. Root mean squared differences between estimated and recorded reaction forces were on average within 99 N for three ‘regular’ and three ‘accelerated’ giant circles. This was less than 3.5% of the range of forces recorded. The bar displacement method was able to estimate the peak reaction forces to within 7% on average, which compares favourably with 24% reported by Gervais (1993) using inverse dynamics