Dear Phil Harmonic,
I am afraid that 4:40 is not a good time to tune your A string. In fact if you do you may well experience the cracking noise from within the guitar described by one of the readers above. If this has already happened, of course I can carry out remedial work for a reasonable consideration.
In fact, the correct time to tune your A string is at 1:10am. The correct times to tune each of the strings are as follows:
Low E: 0:01:22am
A: 1:10am
D: 1:47am
G: 2:36am
B: 2:47am
High E: 3:30am
However, remember that the guitar is an "ill-tempered" instrument and these timings may not result in an exact tuning and therefore an unhappy guitar. Depending on the temperament of your instrument, it is quite permissible to experiment a few seconds either side of these timings to achieve mutual satisfaction.
Most professional guitarists are well-known night people and therefore stay up late to ensure correct tuning.
Yours sincerely,
Dr. Guitar