The most common and most likely answer to this crossword clue is the 9 letter word SOLFEGGIO
I've seen this crossword clue in Financial Times
S
O
L
F
E
G
G
I
O
More clues leading to the result SOLFEGGIO
Buddy explains!
The straight part
We know that "singing Do- Re-Mi" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case singing do- re-mi = solfeggio.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 SOLFEGGIO mean?
SOLFEGGIO noun- A method of sight singing music that uses the syllables do (originally ut), re, mi, fa, sol (or so), la, and si (or ti) to represent the pitches of the scale, most commonly the major scale. The fixed-do system uses do for C, and the movable-do system uses do for whatever key the melody uses (thus B is do if the piece is in the key of B).