Optimal valve slide lengths for double and triple horns.

Abstract

The optimal valve slide lengths for three valve double and triple brass instruments are investigated to ensure that the errors in intonation never exceed five cents sharp or flat over the range of playing. Using the method of least squares to minimize the intonation errors caused by various common valve combinations, it is shown that tuning the open tone 3.2 cents sharp and making suitable valve slide adjustments yield an overall root mean square error of about 2.6 cents. This calculation does not count the errors resulting with the 13 and 123 valve combinations encountered in the low register of the F side of the horn. At the risk of stuffiness, these notes are often corrected by alteration of the right hand position. The best overall intonation is shown to exist for the triple horn in F, Bb, and high Eb, exhibiting the overall root mean square error of about 2.6 cents. In this case the pedal notes on the high Eb side of the horn are used. They are fingered 12 and 23 for said low G and F#. The more common triple horn in F, Bb, and high F requires the use of the 13 and 123 combinations.