Clarinet mode‐alignment measurement under playing conditions

Abstract

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.]