The most common and most likely answer to this crossword clue is the 6 letter word SIXTHS
I've seen this crossword clue in The Guardian
S
I
X
T
H
S
Buddy explains!

The straight part
We know that "Intervals" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case intervals = sixths.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 SIXTHS mean?
SIXTHS noun- (not used in the plural) The person or thing in the sixth position.
- One of six equal parts of a whole.
- The interval between one note and another, five notes higher in the scale, for example C to A, a major sixth, or C to A flat, a minor sixth. (Note that the interval covers six notes counting inclusively, for example C-D-E-F-G-A.)