TL;DR: In this article, the natural frequencies of the coupled horn and resonator were analyzed and it was shown that hand stopping is equivalent to truncating the horn near the position of the hand and terminating it with a lumped resonator.
Abstract: Hand‐stopping is a technique employed in horn playing to obtain a particularly pungent and biting tone quality. To stop a horn, the player blocks its bell as completely as possible with his right hand. With the length of the horn fixed, the notes sounded are not the same with the bell stopped as with the bell open. There has long been controversy over the relation between the stopped and open notes. One group contends that a stopped note is the next lower note that has been raised in pitch by stopping; another group holds that it is the next higher open note that has been lowered. It is the purpose of this paper to show that hand‐stopping is equivalent to truncating the horn near the position of the hand and terminating it with a lumped resonator. The natural frequencies of the coupled horn and resonator are found. Comparison of these with the natural frequencies of the separated horn and resonator reveal the reasons for the confusion and show that both the falling‐pitch and rising‐pitch theories are at least partially justified, depending on whether or not the resonator is considered an integral part of the horn. Experimental data confirm these conclusions.