Now, here's the thing... "Balanced tension" doesn't always guarantee "balanced tone", especially when it comes to flats as the dreaded TES (Thuddy E Syndrome) shows its ugly face from time to time.
Exactly. That is why early Fender sets had a 50 G string and a tight D string, for tone and volume balance, but had lighter A and especially E strings, to retain flexibility and tonal consistency, than the numbers might indicate. It is a limitation of string technology. Fortunately, companies like GHS and D'Addario are revisiting this issue because we bass players are a picky lot: we want consistency of all three across the fret board: tone, volume and feel. Also, basses are different, with generally flatter fingerboards than historical examples. That is why the D string is particularly tight on "traditional" sets: to get more mass to interact better with the magnetic field of a flat pickup, like a J-pickup, with an instrument that had a 7 1/4 crown radius. When set up, the D string was significantly farther away from the pickup than the others. Since the magnetic output varies as the
square of the distance from the string to the pickup, this made sense in the early 60's. But with basses, especially 5-ers, which have a significantly flatter crown radius, say, 14-16 inches, this is not the issue it used to be. But in spite of that, very few strings manufacturers, like GHS and D'Addario, have actually taken steps to address the issue. Jon Moody of GHS goes on about how they have changed the construction of their E strings to attempt to regain the tonal consistency, and I can tell you from playing both gauges of the new Balanced Pure Nickels that they have succeded, and are applying that technology to my favorite strings for my 4002, the Progressives 2.0, which I am patiently awaiting. Rotosound very quietly did that in the early 2000's with their famous Swingbass strings, especially the E strings, essentially double wrapping them to retain flexibility and the low-end edge. They did this about the time I had a show gig in Branson and talked to the Rotosound rep about sending me some strings to get some TV exposure, and we discussed this very issue: tapings for the shows were over a period of days, with cuts and edits, and I had to have continuity of tone and could not afford an E string to die prematurely. The rep delivered in spades.
The whole discussion of the post about sets that have a flatwound G and rounds on an E is all about the same issue: tonal consistency. The problem is that the wound E string is prone to collect finger gunk, prematurely killing the string, so the experiment does not get a player that far. Thomastik-Infeld, on their jazz flats guitar strings, seem to have weird gauges, until you cut open an E string and see it is double wrapped with a fine gauge round first winding and then the flat narrow ribbon second winding so the E string stays flexible and tonally consistent. That is a significant technology challenge: to have the flat ribbon as the outer wind but still retain consistency of windings and not lose the reason for having the double wrap in the first place. Some companies chamfer the edges of the flat ribbon as it is wound on the string, but that can create a rough feel to the string which is the opposite of why some players play flats, especially something like the mirror smooth finish of D'Addario Chromes.
All these reasons are why Fender 9050's are still my favorite flats, although I don't have a gig right now to use them to advantage, and even if I have to replace the E string every so often with an EB regular steel flat.