Cryptic crossword clue
Possible allusion to Fitzgerald’s work about dynasty: “A major 20th-century contribution to culture” 3,5,8,8

The most common and most likely answer to this crossword clue is the 3 plus 5 plus 8 plus 8 letter word THE GREAT AMERICAN SONGBOOK

I've seen this crossword clue in The Guardian
T
H
E
G
R
E
A
T
A
M
E
R
I
C
A
N
S
O
N
G
B
O
O
K

Buddy explains!

The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.
This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.

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