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Taper/Exposed Core

Actually, there is a difference between taper core and exposed core.

Taper core's have a graduated reduction in the windings around the bridge string end. Sadowsky, MTD, and certain Fodera models are good examples of this.

Exposed cores actually have the thin, solid core of the string exposed at the bridge saddle. Examples of these are the DM SR2000's, and the Labella strings that come on the FBass's (I can't remember the name of them).

Having a taper on the B string makes some sense to me, since on some bridges and with fatter B strings (128+) it's hard to get them through the bridge opening.

However, I've never really notices any tonal impact or even intonation impact with taper, exposed or normal strings IME.
 
The thing tht I noticed on the taper/exposed cores is that the low B string is less floppy than the regular core strings.

I wouldn't think that the tapering would have any impact. While I too find that 135 MTD taper core an amazing sounding and tight B string, I would be surprised if you noticed any difference with that same 135 MTD in non taper version. However, it sure makes installing it easier.

Interestingly, my primary set-up guy swears that taper core B's do not intonate properly versus the standard design. I would have though that would not be the case, but it's just an impression he's developed over hundreds of set-ups.. something to do with the different mass or diameter of the string over the saddle versus the diameter of the string that actually vibrates.

That's beyond my expertise though! Who knows!
 
Interestingly, my primary set-up guy swears that taper core B's do not intonate properly versus the standard design. I would have though that would not be the case, but it's just an impression he's developed over hundreds of set-ups.. something to do with the different mass or diameter of the string over the saddle versus the diameter of the string that actually vibrates.

They intonate just fine - more the issue with taper or bare cores is their tendency to have inharmonicity problems. There is more upper harmonic content the thinner the string is across the saddle, and not all of that harmonic content is friendly.

What you want to see in either a taper or bare core is that the full thickness is as close to the break angle point as you can get it. This isn't necessarily something you can adjust, but I suspect that if you string through the body with either of these types of strings that you will have fefwer issues that those who top-load.
 
They intonate just fine - more the issue with taper or bare cores is their tendency to have inharmonicity problems. There is more upper harmonic content the thinner the string is across the saddle, and not all of that harmonic content is friendly.

What you want to see in either a taper or bare core is that the full thickness is as close to the break angle point as you can get it. This isn't necessarily something you can adjust, but I suspect that if you string through the body with either of these types of strings that you will have fefwer issues that those who top-load.

Interestingly. I have a feeling that the 'unfriendly' harmonic content might show up in the upper ranges of the Peterson type tuners, which is maybe where the 'intonation' issue came from. However, your description makes sense to me.