You raise an interesting point. I'll have to dig out my original article on this and post it.
The sequence of the middle letter is actually quite logical.
It took me a while, but I worked all the sequences out back around 1996 when I was doing a book on Irish Banknotes, with the help of a friend who had been recording notes before I started. Basically it is as follows below.
The progression of a sequence is alphabetical, usually skipping one or two letters before using the next letter. When the sequence reaches L, it recommences at A again until all of the letters are used. Letters are not reused, and an extra letter will be skipped until the sequence falls on unused letter. Some of the sequences run backwards.
BASE LETTER: Third letter.
Generally remains the same until all sequences are complete, i.e, all letters A to L in the sequence are used up.
SEQUENCE LETTER: Second, middle, letter.
This changes almost always with each date of issue.
SUB-SEQUENCE LETTER: First letter.
Generally runs A to L for a sequence, giving up to 12,000,000 notes for each sequence.
Sometimes a sequence will adjust by skipping one or no letters so that the letter A may be used next.
The base letter is also generally used to decide the replacement note identifier.
There are anomalies, where bits of sequences are missing, and where left over prefixes are used on other denominations.
Example: £1 NOTES
First Sequence: (10.06.77 – 15.06.79)
Base letter µµB. Replacement BBB.
Sequence runs backwards.
(Letters in brackets are skipped)
L (JK) I (GH) F (DE) C (LAB) K (IJ) H (FG) E (CD) B (KLA) J (HI) G (EF) D (BC) A
Thus, we have: ALB-LLB (first date, 10.06.77); AIB-LIB (second date, 27.06.77); AFB-LFB (third date, 20.09.77) etc.
Thus, the 07.05.93 fiver is quite logical, when you run the sequence backwards, it is (letters in brackets are those that are skipped):
E (FG) H (IJ) K, backwards gives you K, H, G for the middle letters.
So you have AKG, AHG, AEG.