Crossword Genius

Singular pet runs both ways, old and disjointed (8)

Ross

I believe the answer is:

staccato

I'm a little stuck... Click here to teach me more about this clue!

'disjointed' is the definition.
Both the definition and answer are adjectives. Perhaps you can see a link between them that I don't see?

'singular pet runs both ways old' is the wordplay.
I cannot really see how this works, but
'singular' could be 's' (abbreviation sometimes used in dictionaries) and 's' is present in the answer.
'pet' could be 'cat' (I've seen this in other clues) and 'cat' is present in the answer.
'old' could be 'o' (common abbreviation eg in OE for Old English) and 'o' is present in the answer.
This explanation may well be incorrect...

'and' is the link.

Can you help me to learn more?

(Other definitions for staccato that I've seen before include "Disconnected, like musical notes say" , "With each note detached, musically" , "With sharply detached sounds (music)" , "Separating the notes, in music" , "with clipped notes" .)

I've seen this clue in The Telegraph.
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