Namely this definition of 澄ます:
よけいなことを考えないで、その事一つに注意・意識を集中する。
(under 3, http://dictionary.goo.ne.jp/leaf/jn2/119957/m0u/).
This seems to be used like ある, e.g. あること ("a certain thing"), not like "that thing" そのこと, since the noun which その describes isn't referenced anywhere else. Can this be the case?
Checking definitions of 其の 1 to 4 here http://dictionary.goo.ne.jp/leaf/jn2/131116/m0u/%E3%81%9D%E3%81%AE/, none of them seem to fit.
So what does 其の in the 澄ます definition mean here?
This その is closest to the definition #2, 「聞き手が当面している事柄や場面をさす。今の」. So 'present', 'current', or 'immediate' could be the possible translation.
And here その事 is used instead of この事, because the author of the dictionary is objectively describing 耳を澄ます as if someone else were doing that in front of the author.
Besides, at least in the following idioms, I think その is used to mean 'immediate', and who is facing the problem is not important.
その日暮らし is used without specifying "that particular day" prior to this, and あの日暮らし／この日暮らし is almost always wrong. あの場限り／この場限り is uncommon, and people tend to use その場限り regardless of the mental/physical/temporal distance of the problem.
It is important to distinguish between whether a sentence is grammatical and whether it is meaningful or comprehensible in a given context.
sono otoko is a grammatical phrase, but without any context at all, it tells us little if nothing at all by itself.
Consider the examples given by the dictionary entry (デジタル大辞泉) for sono.
「その男は何者だ」「その服はどこで買いましたか」「その仕事が終わったら、次を頼むよ」「その調子で進めてください」「その日はとても暑かった」「その話はもうやめよう」「その一、その二」「まあ、その、何て言うか」
«Who is that man?» «Where did you buy these clothes?» «When you finish that task/job, please take care of the next too. » «Please continue at that pace/rate.» «It had been really hot on that day.» «Let's not talk about that anymore.» «First [part of that], second [part of that]» «Well, that is, how should I put it...?»
By asking nani mono da?, the first example establishes the necessary context for sono otoko ― that man we saw and as to whose identity or affiliation we are inquiring. Note that we can use that in a smilar way in English ― who is that man?
If you think about it, the different dictionary definitions are pretty similar; sono always refers to something, be it explicitly or implicitly. They only differ as to what it refers to exactly:
- some thing close to the listener
- some circumstances the listener faces
- some thing mentioned recently
- some numbered part of a whole
- some thing you cannot or do not want to talk about
These examples all start with sono. There is no referent mentioned explicitly up to that point, and yet these example sentences are comprehensible and meaningful. Here the sentences are commonplace enough one can easily supply or imagine the context necessary to figure out what sono refers to.
Applying this to your sentence:
よけいなことを考えないで、その事一つに注意・意識を集中する。
This sentence is meaningful; and the referent of sono is indicated implicitly.
よけいなことを考えないで……
First of all the definition starts off by saying what sono koto does not refer to ― yokei na koto. Do not waste your thoughts on superfluous things.
Thus sono koto refers to those things that are important.
その事 → よけいではない事
In other words, the present, current, or immediate (=ima no) circumstances of higher priority one needs to focus his attention to by sharpening his ears or eyes.
