NMAC AT ARPT WITH MULTIPLE RWY OP PARALLEL RWYS.

Narrative

THE ARPT HAS PARALLEL RWYS 16/34. SEPARATE LCL FREQS ARE USED FOR EACH RWY. WE HAD ALREADY DONE 1 TOUCH AND GO ON 16R AND WANTED TO DO A FULL STOP LNDG. THE LCL CTLR WAS WORKING BOTH FREQS. AN SMA TWIN Y WAS DOING AN INST APCH TO 16R AND I COULD HEAR THE CTLR MAKING XMISSIONS TO AN SMT TWIN Z; TO WHICH I HEARD NO RESPONSE. ON DOWNWIND; I TWICE REQUESTED A FULL STOP LNDG TO WHICH I RECEIVED NO RESPONSE. WE HAD RECEIVED NO CLRNC OF ANY TYPE AS WE TURNED R BASE. AT THAT TIME; I HEARD THE CTLR TELL THE SMT Z 'OH; THERE YOU ARE; I THOUGHT YOU WERE COMING FROM THE W. YOU ARE #2 BEHIND THE SMA Y ON FINAL.' AT THE SAME TIME; WE OBSERVED THE SMT Z ON L BASE FOR 16R AT OUR ALT. ALTHOUGH THIS IS NOT STANDARD; I CHOSE TO MAKE A R 360 TO AVOID THE SMT Z AND XMITTED THAT INFO. I HAD NO CLRNC AND; AS THE SMT Z WAS STILL ON THE FREQ FOR THE E RWY (16L); I DID NOT KNOW WHETHER OR NOT THEY HAD SEEN US. WE THEN RE-ENTERED ON BASE TO FINAL AND RECEIVED LNDG CLRNC. IN LATER CONVERSATION WITH THE TWR; CTLR STATED THEY COULD HAVE INSTRUCTED US TO GAR; RATHER THAN SENDING THE SMT Z TO THE W TO RE-ENTER L BASE. I BELIEVE THIS COULD HAVE BEEN AVOIDED HAD THE SMT Z BEEN ON THE W FREQ.