The optimum geometry design of geodesic domes presents difficulty due to the fact that the height of the dome keeps on changing during the design process. This in turn makes it necessary to automate the computation of the coordinates of joints in the dome when the height of crown changes. The algorithm presented in this study carries out the optimum geometry design of single layer geodesic domes. It treats the height of the crown as design variable in addition to the cross-sectional designations of members. A procedure is developed that calculates the joint coordinates automatically for a given height of the crown. The serviceability and strength requirements are considered in the design problem as specified in BS5950-2000. This code makes use of limit state design concept in which structures are designed by considering the limit states beyond which they would become unfit for their intended use. This new addition contains revisions adopting European and international standards for materials, processes and loading. BS 5950 is adopted by many commonwealth countries as their steel design code. The optimum solution of the design problem is obtained using harmony search algorithm. This numerical technique imitates the musical performance process that takes place when a musician searches for a better state of harmony. Jazz improvisation seeks to find musically pleasing harmony similar to the optimum design process which seeks to find the optimum solution. The design examples considered have shown that harmony search algorithm obtains the optimum height and sectional designations for members in relatively less number of searches.