Intonation and stability of clarinet tones are influenced by the resonance frequencies of the instrument that are influenced in turn by the placement and size of its tone holes. Dimensions of an instrument of moderate quality were measured and served as the starting point for the optimization procedure. Input impedances were calculated for 47 different fingerings of the instrument. Minimization of the frequency differences between four resonance frequencies—modes 1 and 2 in the chalumeau register, mode 2 in the clarion register, and mode 3 in the altissimo register—and four reference frequencies served as the optimization criteria. The reference frequencies were arbitrarily chosen from an equal tempered chromatic scale tuned to A4 = 440 Hz. Tone‐hole position, diameter, and height were the optimization parameters. In one method, these parameters were modified one at a time, while in a second method all three were modified together. Both methods produced similar results with average reductions in “frequency error” of 9 cents for chalumeau mode 1, 28 cents for chalumeau mode 2, and 16 cents for modes 2 and 3 of the combined clarion and altissimo registers. Optimization procedures and results will be discussed.