Tuning Winds - edwardkort/WWIDesigner GitHub Wiki

Unlike strings and percussion, wind instruments do not produce an exact frequency when played. Even for a specific musical note, the frequency produced can vary over a non-trivial range (100 cents is not unusual) depending on the playing conditions. The situation is simplest for fipple flutes: the frequency increases as the velocity of air leaving the windway increases, until the pitch jumps to the next register. For other instruments, such as transverse flutes, single-reed winds, and French horns, the player can also use other aspects of technique to control the frequency of the note, and where the jump to the next register occurs.

Thus, it is impossible to design or build a wind instrument guaranteed to play on-pitch or in tune. The best we can do is make it easy for the player to play in tune. Assuming each note has a minimum and maximum frequency that can be comfortably played, the target pitch should fall between the minimum and maximum, and should be achievable under playing conditions that the player is likely to use in practice. Terry McGee discusses his take on the problem here.

For example, on a fipple flute, the target pitch of the lowest note is typically slightly below the frequency where the flute jumps to the next register. For each note, the blowing pressure required to get the note in tune should be similar to that required to get adjacent notes in tune.

I would emphasize that the design choices have an important influence on the playing technique that will be required from the musician. This is particularly important in the higher pitch notes. My experience is mainly with reed instruments but this should also apply to flutes. One may design an instrument with higher or lower notes in the high range which demand a different conception of the embouchure. The preferred design may vary among musicians. I usually deal with those issues by providing an embouchure/mouthpiece semi-empirical frequency-dependent model. I found this to be the trickier part.