@tylermunns, it’s too great a change in pitch for the note to note relationship of a given instrument to remain accurate. When a wind instrument is tuned, say in preparation for a performance, the player (as I explained previously) can essentially alter the length of the tubing of the instrument by, in the case of a saxophone, pulling the mouthpiece out on the neck (lowers the pitch), or pushing it in further unto the neck (raises the pitch). The change in pitch that is required in any playing situation is normally on the order of only a couple of hertz at most. Often, it is a much finer change that is required, even less than one hertz. This could be because of a particularly cold or particularly warm room, or the fact that the reference pitch is not exactly A=440 (or, whatever), or the player is playing on a very soft reed (lowers the pitch), or……Tuning pitch flexibility is absolutely necessary, but there is only so much that is available or practical.
Say a player plays with an orchestra (or band) that tunes to A=440 one night and then has to play with an orchestra that tunes to A=442 the following day. In order to achieve this change in tuning the mouthpiece is pushed in unto the neck a few millimeters. Perfectly acceptable. In order to achieve a downward change of 8 hertz (A=432) the player would have to pull the mouthpiece out on the neck 4X that length. There would most likely not be enough length to the tubing on the neck to accomplish this. Even if there were, the mouthpiece would be barely grabbing the end of the neck. Even more importantly, mouthpieces are designed in such a way that they only respond correctly and tune correctly with a reasonable amount of the saxophone neck inside them. Otherwise, acoustic mayhem ensues and the resulting note to note relationship would be all over the place. A simple major scale would be almost unrecognizable. The same idea applies to all winds including brass. In the case of a clarinet, the player pulls out or pushes in the “barrel” (the piece of tubing between the mouthpiece and the main body of the instrument). If you pull this out too far this creates a space inside the bore of the instrument which throws the pitch of a certain register very flat and unworkable. Brass instruments do this by different means, but same principle. There is only so much flexibility possible with tuning. Instruments have to be designed for normal, high, or low pitch and are designated as such. Also keep in mind that existing mallet instruments are not tunable on the spot and would be completely useless in a A=432 situation.