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String gauge, pickup height, & volume

Glimmer

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On a recent string change, I switched from GHS Boomer 12s to Thomastik-Infeld Jazz Bebop 12s, just for the hell of it. I've used T-I flat wounds before and wanted to give the round wound Bebops a try. To my surprise strings 5 and 6 were significantly quieter than those of the preceding set and the G string a bit louder, as the gauges of those strings possibly suggest:

Boomers
012    016    019    DY28    DY38    DY52

Bebops
P12    P16    P20    BB28    BB36    BB50

I'm wondering, does lighter string gauge = lower volume, or is it possibly due to the materials used, or a combination of the two, or ... ? Chords, in particular extended chords, played with the Bebops sound really balanced – the lows don't dominate and you seem to hear each note equally well, which is odd, because the low E and A strings are definitely not as loud. On melodies however I find that I have to adjust my picking so that higher and lower register notes have a roughly equivalent volume.

Might I attenuate this by raising the pickup height a bit on the E-A-D side? Don't know if I'm going to like the Bebops well enough to want to use them in the future (they're pretty expensive as well) but would like to give them a chance.

One final question: I tend to experiment with a lot of different strings before settling on one or two that I like best. I know that changing gauges can necessitate adjustments to the guitar. Should I expect to have to adjust pickup height with each string change as well?
 
There are several widely accepted myths regarding guitars in general that are actually truths about acoustics, but not about electrics. Wood species and finish thickness are probably the most widely circulated and are considered dogma, but another one is the effect of string gauge on the tonal character. When you consider that Billy GIbbons played spiderwebs (7-9-11-20-30-38) and SRV played guy wires (.013 – .015 – .019p – .028 – .038 – .058), you have to wonder how such a myths is propagated. Nobody with even marginally functional ears could ever say Billy's guitar had a testosterone deficiency.

In other words, change wood species, finish weight or string gauge set on an acoustic and the whole world changes because it's basically a mechanical device. A lot of its performance depends heavily on such physics as inertia and resonance. On an electric. not so much, if at all. Changing wood species on an electric's neck is probably as much as you can do and actually notice a substantial change. What will make a huge difference on an electric is the pickup(s). With the pickup, you have a number of variables. But, to narrow it down to output level, you're mainly concerned with the velocity (pitch) of the individual strings, the string alloy, the distance of the strings from the pole pieces, and the gauss rating. You can't really change the gauss rating without changing the pickup's materials and construction, so with a given device you may as well say that's not a variable. With a given tuning, say open "E", you're not going to change the velocity of the strings, so that's not really a variable. But, you sometimes you can change the string alloy and you can usually change the distance of the strings from the pole pieces, if not individually then at least as a group by raising/lowering one, the other, or both sides of the pickup.

Some pickups will come constructed with different pole heights built in, some will have adjustable poles, and some with none of the above. In any case, you can usually do the 'group' adjust with the pickup mounting screws on either side. Some pickups also allow individual pole height adjustment. The general rule of thumb is the farther away the pole is from the string, the less output you will get from that string, and vice-versa. Reason being is that the farther away you get from the string, the more the pickup is only seeing peaks on the string travel, which means the pickup sees less velocity change. At the peak of the vibration, the string isn't moving as much as when it's headed in the opposite direction. Distances from side-to-side of the pole pieces vs. the string don't matter so much for the same reason. With the height set optimally, the pickup sees the maximum velocity it ever will for a given distance.

Also, keep in mind that string gauge will affect the tension a string needs to be under to produce a certain pitch. The tighter a string is, the smaller the peak-to-peak movement is going to be as it's vibrating, so the more sensitive pickup height gets to be.

Given all that, In your case, I'd look at pole heights and string alloy to explain the differences you're hearing. More often than not, the differences in gauge sets will affect how the instrument feels more than anything else, due to the different tensions involved in getting the pitch you need for a given length. 
 
Thanks for your very thorough reply, Cagey.

I wound up adjusting the height on the string 4–6 side of the neck pup, bumping it up a couple of 32nds of an inch. I measured beforehand and found that that side was lower than the other and than both sides of the bridge pup. The Boomers must've sounded a bit boomy in the bass and the gentleman who set the guitar up lowered the pup accordingly. It sounds better now, but the relative volume balance between strings is still rather different than the preceding set. Interesting.
 
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