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String gauge and volume

I've read some conflicting information this morning and am hoping for clarification. My D string seems quieter than the others with 2 different sets of stings. Pickup height adjustment, EQ adjustment, compression, and plucking the D string with more force all help but don't completely even it out. I prefer balanced volume more than balanced tension - would I want to slightly increase or decrease the guage of the D string to increase the volume (understanding that I may have to pluck the D string with more force with a thicker guage)? Thanks!
 
All other things being equal, there is indeed a direct correlation between the diameter of a string and the volume it is capable of producing. However, even with unbalanced tension sets (like 45-100) I have never encountered a drastic difference from one string to another. And even if that had happened, I'm sure adjusting the pickups height would have solved the problem.

What bass and what brand and gauge of strings do you use?
 
All other things being equal, there is indeed a direct correlation between the diameter of a string and the volume it is capable of producing. However, even with unbalanced tension sets (like 45-100) I have never encountered a drastic difference from one string to another. And even if that had happened, I'm sure adjusting the pickups height would have solved the problem.

What bass and what brand and gauge of strings do you use?

I found it to be so on my SUB Ray4 with stock rounds (I did not adjust pickup height and returned it for other reasons) as well as my Mustang PJ with what I'm guessing were stock rounds as well as D'Addario Regular Light guage half rounds (I did adjust pickup height). I've watched some EQing technique videos and have it dialed in much better now. It is completely possible that I just want more midrange out of the string and the volume is equal - or that it is my hearing.

What is the direct correlation? All things being equal, would a larger or smaller diameter produce more volume?
 
I found it to be so on my SUB Ray4 with stock rounds (I did not adjust pickup height and returned it for other reasons) as well as my Mustang PJ with what I'm guessing were stock rounds as well as D'Addario Regular Light guage half rounds (I did adjust pickup height). I've watched some EQing technique videos and have it dialed in much better now. It is completely possible that I just want more midrange out of the string and the volume is equal - or that it is my hearing.

What is the direct correlation? All things being equal, would a larger or smaller diameter produce more volume?
On paper yes, larger diameter equals more volume, but there are a lot of other factors, like the material and the way the strings are made. And I doubt it's really noticeable to the human ear most of the time, especially with an electric instrument.

In my experience, stock strings are rarely of good quality and they can be old and/or nearly dead when you buy a new bass. This is more likely to be causing volume issues than string gauges, IMHO.

Edit: Here is a good video on how to adjust the pickups height.

 
When tuning my E-String down to D, the amplified sound seems louder to me.

So I made up this theory:
a string under less tension (tuned lower or a thinner string on the same pitch) has more excursion than a string under higher tension.

That would mean, a lighter gauge string creates more volume in the pickup than a heavier one tuned to the same pitch.

Could that be?