The most common and most likely answer to this crossword clue is the 8 letter word SEVENTHS
I've seen this crossword clue in The Guardian
S
E
V
E
N
T
H
S
Buddy explains!

The straight part
We know that "Intervals /Intervals" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case intervals /intervals = sevenths.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 SEVENTHS mean?
SEVENTHS noun- The person or thing in the seventh position.
- One of seven equal parts of a whole.
- A tone of the seventh degree from a given tone, the interval between two such tones, or the two tones sounding in unison.