FATIGUED FLC FAILED TO SET CORRECT FREQ WHEN CTR CTLR GAVE A FREQ CHANGE. THEY FINALLY REALIZED THE RADIO WAS VERY QUIET AND CAUGHT THE FREQ ERROR. NOTHING WAS SAID BY CTR. RPTR FLC WAS FATIGUED FROM VERY EARLY WAKE UP; 4TH DAY OF MINIMUM REST BTWN FLTS. RPTR'S COMPANY TRIED TO ASSIGN EXTRA LEGS AFTER THEIR SCHEDULE; BUT THEY REFUSED IN SPITE OF POTENTIAL DISCIPLINE THREATS FROM COMPANY.

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IN CRUISE; ZMA GAVE US A FREQ CHANGE TO ANOTHER CTR FREQ 132.2. THE FO (PNF) ACKNOWLEDGED AND CHANGED FREQ. AT THAT TIME; WE WERE DISCUSSING THE DISTANCE TO AN AIRWAY TURN POINT; AND BOTH FAILED TO RECOGNIZE 2 ERRORS: 1) THE RADIO WAS IMPROPERLY SELECTED TO 132.0. 2) WE NEVER CHKED IN AND GOT A RESPONSE. WE MERRILY NAVED ALONG OUR RTE FOR 5 OR SO MINS. WHEN I FINALLY NOTICED HOW QUIET THE RADIO TFC WAS (ZMA IS RARELY QUIET) AND LOOKED IN HORROR AT THE RADIO FREQ SELECTOR; THE FO QUICKLY CHANNELIZED AND CHKED IN! CTR IMMEDIATELY RESPONDED AND HANDED US OVER TO MIA APCH; AND NOTHING ELSE WAS SAID BY ATC (ABOUT OUR ERROR). I BELIEVE THAT THE PRIMARY CAUSE OF THIS ERROR WAS FATIGUE. THE FO AND I BOTH HAD AN XA00 WAKEUP FOR THIS TRIP; AND NEITHER GOT A GOOD NIGHT'S SLEEP. THIS WAS MY 4TH DAY OF 'OUT-AND-BACK' TRIPS WITH SHORT OVERNIGHTS AT HOME. THESE INCLUDE SCHEDULED REDUCED REST OVERNIGHTS WHICH IMPLY 4 HRS SLEEP MAX (BUT IT'S LEGAL!). BOTH CREW MEMBERS WERE AWARE OF OUR MUTUAL FATIGUE; AND HAD DISCUSSED 'WATCHING OUT FOR EACH OTHER.' ON THIS DAY; WE COMPLETED OUR NEXT 2 SCHEDULED LEGS AND WERE THEN SCHEDULED TO DEADHEAD HOME. CREW SCHEDULING CALLED AND 'EXTENDED' US TO FLY 2 MORE LEGS; AND WE REFUSED -- INVOKING THE FATIGUE PROVISION OF OUR UNION CONTRACT. (NEVER AN EASY THING TO DO DUE TO THREATS OF DISCIPLINE.) WE SHOULD HAVE STOPPED FLYING SOONER.