Bifurcation behavior and underblowing on the bass crumhorn

Abstract

The crumhorn is a double reed musical wind instrument with a narrow cylindrical bore and a characteristic hook-shaped curve near its open end. It is played by blowing air through a narrow slit into a windcap which surrounds the reed. Crumhorns were made in several sizes, from soprano to contrabass, and in the sixteenth and early seventeenth centuries were frequently employed in wind ensembles in Germany, Italy and the Netherlands. Since no lip control of the reed is possible, the instruments cannot be overblown, and the playing range of a standard crumhorn is limited to a major ninth. On the bass crumhorn, however, a sixteenth century source mentions a technique for extending the lower range of the instrument by up to a perfect fifth by reducing the blowing pressure below its normal level. In 2000, Gibiat and Castellengo investigated these underblown notes experimentally and associated them with period doubling cascades. In the present work, the bifurcation behavior of an artificially blown bass crumhorn has been studied experimentally, and the results are compared with bifurcation diagrams calculated using a continuation method.