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Turning up an amp is no biggie, but the hum of a Mustang American Performer is due to pickup design and how they are externally wired.
Ironically, Fender's most expensive Mustang model wires the halves of the split pickup IN phase with each other, so that the signal of one half does not cancel with the added jazz pickup.
Less expensive Mustangs only have the small split pickup, so they are instead wired out of phase, so no hum - but no extra pickup.
The split pickup of a Precision is built differently, with the magnet polarity and winding direction each reversed
internally in the one half, which makes it unnecessary to change how the pickup is wired externally, so the hum is cancelled like it would be on a P bass.
But in a PJ bass, Mustang or otherwise, the Jazz pickup generally is still a single coil, so when soloed, it can pick up hum if any is available in the room.
Also ironically, there have been some reports [earlier this year in this TalkBass thread or in one other specifically about their pickups] that in lower priced Mustangs, and in the Japanese ones, the small split pickup might be constructed like that of a P bass, which could allow an extra pickup to be added without any problems of signal phase.
From my browser bookmarks, here is a link to one of my previous posts on this issue in the current thread :
Mustang Bass Pickup Wiring, My Summary - Fender Mustang Club, Page 219, Post 4370 - TalkBass
Also, here are some of the other threads where we have discussed it :
Pickup upgrade for American Performer Mustang Bass? | TalkBass.com
Replacement Pickups for Fender Mustang Bass | TalkBass.com
Mustang American Performer Bass, Split Pickup Design - Post #36, KenB, Pickup upgrade for American Performer Mustang Bass - Page 2 - TalkBass
Picked up a jmj and wondering about the AweSome tone control mod | TalkBass.com
There may be other related posts just before or after each of these.
Hopefully, all of this sheds some light, rather than causing further muddying of the waters.
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