An improved scaling method for wooden flue organ pipes

The process of selecting the geometrical dimensions of the pipes in a pipe organ is referred to as scaling. Wooden pipes with rectangular cross-section are usually designed so that their cross-sectional area equals that of the corresponding cylindrical pipe. It often occurs, especially in case of lower registers, that the wooden pipe rank does not fit into the available width, and the pipes are necessarily made narrower. In this case, maintaining the cross-sectional area the same may result in a significant change of timbre due to the increased amount of wall losses. This paper proposes and examines a scaling method that enables designing narrower wooden pipes with avoiding unwanted changes of the timbre. The approach relies on keeping the wall losses the same as that of the reference cylindrical pipe. The theory of the scaling technique is presented, it is analysed using simplified one-dimensional as well as 3D numerical models. Experimental pipes designed for this study are measured and modelled, proving the applicability of the proposed scaling method.