Optimization of valve tube lengths for brass instruments.

Abstract

The intonation deviations from the well-tempered scale are presented for valve brass wind instruments. Compensating and full double instruments are considered. Systems including descending valves and less popular ascending valves are studied. The lengths of the valve tubes are optimized by minimizing the overall root mean squared (rms) intonation error using the method established in 1967 [R. Young, J. Acoust. Soc. Am. 42, 224–235 (1967)]. Open note detuning is considered in each case and improves the overall intonation. The worst three valve instrument without open note detuning has an rms deviation 24 cents The best of the three and four valve instruments is a three valve compensating euphonium tuned 3 cents sharp on the open notes and flat on valves 2, 1, and 3 by 3, 3, 10 cents, respectively. It exhibits only 2 cents rms deviation on single valves and less than 3 cents on combinations of valves. The comparisons also include several new three, four, and five valve systems. Included is a double horn with only two double valves and a switch valve.