That's Beat slang for bass fiddle. I went looking for the genesis of "cat" as a term for "cool guy", and stumbled upon the Beatitude: Dictionary of Jive, in which I learned that Cat (n.) -- musician in swing band. Also Hep cat (n.) -- a guy who knows all the answers, understands jive.
There's a fair amount of pet types in your true blue Beat speak:
Mouse (n.) -- pocket. Ex., "I've got a meter in the mouse."
Yarddog (n.) -- uncouth, badly attired, unattractive male or female
Canary (n.) -- girl vocalist
And some are just funny, frankly.
Mash me a fin (command.) -- Give me $5
Sadder than a map (adj.) -- terrible. Ex., "That man is sadder than a map."
I should ask my dad if he used some of these when he was a teenager in a beret in San Fran with a beret* and a goatee -- for all of six months. He said he did it for the chicks.
* I see I have the word "beret" in here twice. I guess the thought of my dad in one made an indelible impression.