I am very interested in your motor sound. The original one that was talked about most on this thread, in which I probably started and may have used the word "mismatch ", which was not actually a good word, that sound comes from a partial or incomplete engagement of the Sprague clutches which occurs come as acknowledged by TQ, when there's only 10 or 15% output by the motor. This low output by the motor occurs when there's low torque applied by the writer to the crank. When you apply more torque the motor puts out more power and more torque itself and that goes ahead and engages fully the Fraud clutches.. I don't think it relates to the peddling cadence except that coincidentally after you shifted into a lower gear you may be peddling at a higher cadence in order to catch up to that Geer and also applying minimal torque on the riders part until the bike slows down enough to offer some back resistance therefore the writer applies more torque therefore the motor goes ahead and puts out more torque itself and engages it's sprague gears fully.
This typically happens when you downshift approaching a hill And you're paddling faster but haven't yet felt the resistance of the hill. In that circumstance The motor only puts out a little power in torque. You can reproduce this phenomenon even on level ground by downshifting from seventh gear to fifth gear and peddling a little faster but not applying any torque on your part. I can keep the sound going indefinitely by fine-tuning minimal torque. I can also make it happen on any TQ bike, at least the three different ones that I've tried, and fellow riders who had not appreciated this phenomenon at all. ( but I did not tell them about it because I didn't want them to start noticing it or feel bad about it) it's harder to do when some TQ motorbikes than others. I would be interested in hearing if you can do this on your bike, in order to know if yours is a different phenomenon.