CTLR WORKING 2 SECTORS ISSUED DESCENT CLRNC TO ACFT ACKNOWLEDGED BY ANOTHER AND DESCENT BEGUN.

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WE WERE GIVEN A FREQ CHANGE FROM ATL TO ZME WHILE CRUISING AT 16000' MSL ENRTE TO BNA. THE ATC CTLR WAS VERY BUSY AND I HAD TO CALL TWICE BEFORE I RECEIVED A RESPONSE. UPON ACKNOWLEDGING OUR CHK-IN A CLRNC WAS ISSUED FOR A DSCNT TO 11000' MSL TO ANOTHER COMPANY ACFT ON ANOTHER FREQ. I THOUGHT THAT IT WAS ISSUED TO US. I ACKNOWLEDGED THE DSCNT TO READING BACK 11000'. AT 14500' THE CTLR ASKED FOR OUR ALT; INFORMED ME THAT THE CLRNC WAS FOR ANOTHER ACFT; AND ISSUED A DSCNT TO 14000' MSL FOR US. I BELIEVE THIS IS WHAT HAPPENED: THE CTLR WAS WORKING 2 FREQS AND VERY BUSY. HE ACKNOWLEDGED MY CHK-IN AFTER 2 CALLS; ISSUED A DSCNT TO A COMPANY ON ANOTHER FREQ W/O INDICATING A BREAK IN THE XMISSION. I ACKNOWLEDGED THE CLRNC; BUT RECEIVED NO CONFIRMATION FROM CENTER. I DIDN'T HEAR THE READBACK BY COMPANY AND HE DIDN'T HEAR MINE BECAUSE OF DIFFERENT FREQS. THE DSCNT CLRNC WAS EXPECTED AT ABOUT THAT TIME AS WE WERE NEARING OUR DEST. FORTUNATELY; NO CONFLICT DEVELOPED. SOLUTION: LISTEN UP AND SINGLE FREQ OPERATION.