The most common and most likely answer to this crossword clue is the 14 letter word DEMISEMIQUAVER
I've seen this crossword clue in The Times
D
E
M
I
S
E
M
I
Q
U
A
V
E
R
More clues leading to the result DEMISEMIQUAVER
Buddy explains!

The straight part
We know that "Note" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case note = demisemiquaver.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.
What does DEMISEMIQUAVER mean?
DEMISEMIQUAVER noun- A thirty-second note, drawn as a crotchet with three tails.