Abstract:

Given that a nearly harmonic alignment is a desirable condition, to what extent is it achieved in a particular brass instrument, and how do the bell and the input segment cooperate to bring it about? Answers to these questions that are easily read by human beings are not to be found in a plot of |Z|, or any aspect of the plane-wave reflection coefficient R at the input end of the air column. Instead, the bell and the input segment are each examined from inside the central segment and represented in terms of the effective length to a closed end, which has a simple relationship to the phase of the (internal) reflection coefficient. The sum of those two lengths should be essentially independent of frequency for harmonic alignment. This criterion is very easy to evaluate on a graph, and it applies simultaneously to all lengths of the central segment, hence all fingerings or slide positions. Minor perturbations on this relationship due to processing by the input segment and viscothermal effects on the speed of sound in the central segment will be discussed.