Consider the most common example of difference in tone: 'and' and 'but'. 'And' and 'but' are both truth-functionally conjunctions -- 'but' doesn't handle true and false any differently than 'and' does -- and thus the difference between them is only a matter of tone. But it is clear that this is not always true of 'but'; sometimes 'but' is not truth-functionally equivalent to 'and'. For instance, sometimes if I say, A but B, whatever the letters stand for, I am saying that B is actually a defeater of some sort for A. In this case 'but' is not a logical conjunction (by definition). Thus the example really boils down to saying that a logical conjunction maintains its properties regardless of whatever the rest of the meaning is. This is undeniably true, and is important. But it doesn't tell us much about conjunction and it doesn't tell us anything about the tone or rest of the meaning. It is entirely consistent with the possibility that 'tone' and 'sense' are unstable, so that the very same thing that is sometimes 'sense' will at other times be 'tone', and vice versa.
Consider another example, which is sometimes used: 'cur' and 'dog'. Suppose I were to say, "There's a cur at the back door." You go out and find a well-behaved, well-groomed, pure-bred spaniel. There are only two ways of taking my claim, assuming that I knew what I was talking about. In one way, my claim is simply false: what is at the back door is not a cur. But I could just be the sort of crotchety person who hates dogs and so can't talk about them without insulting them, in which case we can say that my claim is true, although insultingly expressed. But this appears to depend entirely on what parts of the meaning I take to be 'sense' (i.e., to be relevant to the actual truth and falsehood) and which I take to be 'tone' (i.e., independent of actual truth and falsehood).
This is all a consequence of the way 'tone' is characterized: it's just the residue, whatever happens to be left when you've taken everything you need in order to determine truth values. But there's no reason thus far to think that there's anything that counts as tone that always counts as tone. Fregean examples are very disparate. So, for instance, Frege takes the difference between active and passive voice to be one of tone. This is unsurprising, since his logical system can't distinguish the two, but it's unclear that active and passive voice are consistently irrelevant to whether a claim is true or false. Active and passive voice do at least two things: indicate the complementary aspects of one action and indicate attempt and success in an action. The former guarantees that active and passive voice stand or fall together, but the latter splits their fortunes. Roxane loves Christian, but it does not follow immediately that Christian is loved by Roxane or vice versa, and much of the story of Cyrano de Bergerac builds on the tension between the complementarity of loving and being loved and its disparity with attempt-success understandings of how love works. Even in the former case, there are cases in which the complementarity between the active and passive might break down -- God, on some theological views, for instance, or spontaneous uncaused actions, on other views. If these can even be formulated coherently, there is no way to hold that the active/passive distinction is always a matter of tone.
In any case, I was thinking about tone today, and considering the question of how one might analyze this residue of meaning. Analytic philosophers are next door to useless for getting any idea about it. But I had an idea for how one might have something like Laban Effort graphs (typically used to represent the force and control of movements in dance) to represent tonal differences. The graphic results would not be easy to put here, but a textual proxy certainly can. Suppose we have a (nonexhaustive) list of common (alleged examples of) tonal contrasts, and give them symbols. For instance:
^ light
| serious
x contrastive
~ conformal
< passive/nonactive
> active
, unordered
; ordered
! sure/certain
? unsure/uncertain
+ positive-valued/good
- negative-valued/bad
We could then represent different kinds of conjunction. & [|~<,!] would be something like our usual 'and', whereas & [|x<,!] would be more like 'but', and & [|~>;!] would indicate that we are taking 'and' to mean adding something to something already there.
Likewise, we can get subtle variations. Take the sentence, "He believes in a bearded man in the sky." In ordinary conversation this could have many subtleties. The following would indicate a plain statement of (at least supposed) fact:
He believes in a {bearded man in the sky [|!]}.
But this would be contrasted with the non-literal and more derisive:
He believes in a {bearded man in the sky [^!-]}.
Which in turn would be contrasted with the more baffled (but still non-literal):
He believes in a {bearded man in the sky [^?-]}.
Which in turn is different from the mere puzzled literal statement:
He believes in a {bearded man in the sky [|?]}.
These sorts of things do make a difference. (I do not claim, however, that the 'tone' here necessarily does not affect truth-values; rather, these are just things that are often not taken into account when analyzing statements even though they are analyzable in some sense -- by contrast, if nothing else.)