Clarinet mode-alignment measurement under playing conditions
A. H. Benade · The Journal of the Acoustical Society of America · 1984
The musical advantage of aligned first- and second-mode air column resonance frequencies for all clarinet low-register fingerings has been clear for 15 years. Practical exploitation requires efficient measurement of the f2/f1 modal frequency ratio and systematic air column correction methods. The alignment error ε = 1719(f2/3f1 − 1) cents. Clarinetists must sometimes tolerate 40 > |ε| > 30¢. They accept |ε| in the range 30– 15¢ and consider |ε| < 10¢ excellent. (ε is not the tuning error of normally played twelfths.) Techniques to find frequencies having Im Zin = 0 have long been available, giving ε with accuracies of ± 3¢, but these ignore player, reed, humidity, and temperature effects. Before elucidation of reed-resonance phenomena, existing “players' experiments” for ε were difficult to teach. Adjustment of embouchure tension can align the reed-resonance frequency .f1 relative to the air column mode-2 frequency f2 such that f1/f2 ≃integer. Only then is a second-register note playable sans register key, thereby precisely defining the air column's upper-end active boundary condition at a playing frequency P2. Momentary interruption of the oscillation by tonguing causes a transition to the more favored low-register note playing at P1. The P2/P1 ratio is insensitive to reed structure and ambient temperature, giving ε under playing conditions within ± 5¢ from day to day, player to player. The method is readily taught and cross checks are available. [Work supported by NSF.]