Ok, I reassembled my M37C (but just the air chamber, not the case) and got some interesting results.
If I blow hard without pressing any keys, the bladder inflates, as expected.
If I blow hard and then press a key, the key fails to sound. Too much pressure? As long as I continue to blow hard, I get no sound. And it’s not just the low notes.
If I ease up a bit, I get sound. And while I blow, the bladder remains somewhat inflated, which is a bit of a surprise, but it just means that I have more to learn.
I’m not sure if the bladder inflation does anything useful at this point. I suspect if may just be acting as a pressure gauge: it tells me the pressure in the air chamber is slightly higher than the atmospheric pressure, but that would probably also be true without the bladder. As long as the bladder remains inflated, it can’t contribute to the airflow.
Actually, it’s hard to tell that it does anything at any point. I can’t hear much difference when I block the bladder than when I don’t. I did try pressing on the bladder as I played low notes. Oddly, the low D was the only one that produced any sort of bend-y effect.
One other thought: when one stops blowing, the bladder should keep the air pressure up for a bit. If you keep a key depressed, the decay should be slower.
Could the bladder be used to balance the notes? (My current definition of “balanced” is that two notes played simultaneously have the same volume.) Nope. If I play a low note and a high note together and release the low note, the high note gets a lot louder. If I release the high note, the volume of the low note doesn’t change significantly. If the notes were balanced, both would get equally louder when the other note was released. Of course, it could be worse without the bladder.
Bottom line: I don’t know why there’s a bladder on the M37C. It does seem to affect the low D, but that could be re-tuned to work without the bladder.