Code and ciphers: Julius Caesar, the Enigma and the internet

RHAPSODY and SYMPHONY agree in positions 4, 6 and 8;
SYMPHONY and SCHUBERT agree only in position 1;
RHAPSODY and SCHUBERT have no identical letters in the same
position.
The encipherments of the message using the three keywords when
written in three lines under each other in blocks of 8 letters are as
follows:
EVWMAGAR YLXIAAHV WVRMSZOV XVOSPAHL
FMIMPGKR ZCJIPARV XMDMHZYV YMASEARL
FQDRJWOM ZGENJQVQ XQYRBPCQ YQVXYQVG
OAOMUCPC OAOMLVHV RPDMGTAR YLXESFWW
PRAMJCZC PRAMAVRV SGPMVTKR ZCJEHFGW
PVVRDSDX PVVRULVQ SKKRPJOM ZGEJBVKR
Messages (1) and (2), and (2) and (3) are in ‘partial depth’.
Such an observation ought to quickly lead to a solution.
Solutions to problems 219
3.2 (Vigenère decryption)
Studying the cipher text reveals several digraphs which occur four times
or more and among these are some which extend to repeats of three or
four letters, including: ZMUI which occurs at positions 15 and 135; ZMUE
at positions 67 and 163; and KRD at positions 9, 8, 172 and 176. All the
intervals between these repeats are multiples of 4 so we conclude that the
key is of length 4.
Looking at the four cipher letter frequency distributions we find that
the cipher letter for ‘space’ is almost certainly M in the first alphabet, Z in
the third and S in the fourth; the second alphabet is slightly less informative
but D is the best bet and so we are led to the key as probably being 13-
4-0-19 which is equivalent to the keyword NEAT.
Decryption of a few words confirms this and, with ‘space’ replacing Z,
the decrypt is
THERE ARE SOME THEOREMS WITH A PROOF WHICH IS
SO SHORT AND ELEGANT THAT IT SEEMS UNLIKELY
THAT A BETTER ONE WILL EVER BE FOUND SUCH IS
THE CASE WITH EUCLIDS PROOF THAT THERE ARE AN
INFINITE NUMBER OF PRIMES THE PROOF IS IN THE
APPENDIX IN THIS BOOK. (M4)