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BEAD/EADG

Is there a guage of strings that will work for both BEAD and EADG tuning on the same bass? I realize that the change in tension from one tuning to the other would require adjustments to the set up but I am still curious.

NO. The difference both in tension and tonal quality would be too drastic for it to be practical.

The simple solution would be two basses, one for EADG and one for BEAD. Or, even simpler, one 5-string bass for BEADG.
 
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Yes. Any set of strings designed for BEAD tuning and a capo for the fifth fret when you want EADG. No string light enough to tune up to E will sound good tuned down to B.

Or a Bass Whammy pedal to pitch shift up a fourth to EADG.

The difference in tension will require a lot of truss rod adjustments each time you tune up or down. Plus, you might end up needing to adjust intonation. Sounds like an enormous PITA that isn't worth your time because of how crappy it will be to play on either super floppy BEAD or super taut EADG.
 
Is there a guage of strings that will work for both BEAD and EADG tuning on the same bass? I realize that the change in tension from one tuning to the other would require adjustments to the set up but I am still curious.
You seem to be already aware but let me restate what follows: going from one tuning to the other would be impossible (to do well) on the fly, because of setup reasons. If going back and forth is required, a capo on the 5th fret would be a much more sensible option.
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Now for the academic question:

in this interview,
Rob Lauritsen — 12-String Bass Encyclopedia
dUg Pinnick's technician Rob Lauritsen says
- that the King's X frontman uses a 100 string as the lowest on his 12-string bass
- that said 12-string bass is tuned ccCggGccCffF (Rob also, confusingly, calls the top-course main string a "G")
- that 100 is also the lowest gauge for dUg's 4-string basses
- that one of said 4-stringers is tuned to CDCF as well; the other to BEAD, and sometimes to drop-A (AEAD).
It would seem to follow that Pinnick sometimes uses a 100 tuned to 27.5Hz A, i.e. a perfect fifth below the Leo-given usual. Certainly, he uses that gauge tuned to at least C, which is one semitone above B, and is able to make it work for him.

Conversely, there are string sets out there that have a 055 highest string and a 075 for its second-highest, and some people use them tuned to standard. Even flatwound sets. Typically, the A and E of those sets don't come larger than 095 and 110, respectively. However, it would stand to reason that the same users may be able to play an A and an E with the same tension as those treble strings: in practice, use a 100 A and a 130 E.

In other words, there is certainly overlap between BEAD and EADG gauges, because there are folks out there who play very thin BEAD sets and very fat EADG ones. However, I believe they wouldn't object to being described as outliers.

If I were to choose the least ineffective compromise in gauges for those two tunings (say, if only one set could exist in nature, with both groups of players of either tuning having to make do with it and nothing else), it might be something like 115 - 090 - 070 - 055.
 
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I recently got a bass specifically for BEAD, and when I first tested it, I just tuned down the standard tuning strings. I was fine with them - low tension, but playable for me. A friend tried it, and he hated it, as he hits harder, so it was alll buzz and rattle. I always intended to put slightly heavier strings on, and when I got a BEAD set it was better, but I could have lived with both.

However there's really no gain. Tuning down required a major setup to get it playable, and was more work than putting the new heavier strings on (which required another setup). Having strings which can do both isn't going to save you any time, as the bass can't be set up for both. If you're going to set ir up for a tuning, you might was well put the best strings on for that tuning.
 
I tune regular light chromes down to dgcf, and find I run into problems with tuning and intonation, but love the way they feel. Ha, I also currently have a two saddle bridge, so that adds to the problem. Like everything, there are compromises that can be tolerated, and only you can decide what is tolerable. Try it out.
 
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