NMAC BTWN A SIGHTSEEING FLT C207 TURNING ABOUT A PROMINENT SCENIC MONUMENT AND A PILATUS PC12 CIRCLING IN THE OPPOSITE DIRECTION NEAR THE SAME ALT.

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I FLY FOR A SCENIC TOUR OPERATOR; AND WAS FLYING A TOUR THAT ORIGINATED IN MONUMENT VALLEY AND ALSO ENDED IN MONUMENT VALLEY. THE TOUR INCLUDED FLYING OVER PART OF LAKE POWELL AND RAINBOW BRIDGE. I AND 3 OTHER ACFT WERE AT RAINBOW BRIDGE WHEN ONE OF OUR ACFT VISUALLY SPOTTED A PILATUS PC12 ACFT IN THE AREA AND ADVISED US TO BE ON THE LOOKOUT. WE ALWAYS COMMUNICATE ON FREQ 122.75 THROUGHOUT THE TOURS AND MAKE ALL POS RPTS ON THAT SAME FREQ. THE PC12 WAS MONITORING 122.75 AND AFTER HE HEARD US TALKING ABOUT HIM HE RPTED THAT HE HAD ALL 4 OF US IN SIGHT. WE CONTINUED AND ANNOUNCED THAT WE WOULD BE DOING R-HAND TURNS AROUND RAINBOW BRIDGE AND WE ALSO ANNOUNCED THE ALTS WE WERE AT AND THOSE WE WOULD BE CLBING TO AS WE CIRCLED THE BRIDGE. I ANNOUNCED I WAS STARTING MY R TURN ON THE BRIDGE LEAVING 5400 FT FOR 6000 FT. WHEN I WAS APCHING 6000 FT AND STILL IN A TURN; THE PC12 ACFT FLEW FROM MY L TO MY R ABOUT 20 FT IN FRONT OF ME. HE WAS MAKING A L TURN AROUND THE BRIDGE AT THE SAME ALT THAT WE WERE CLBING TO. I THEN ASKED HIM IF HE HAD SEEN ME. HE APOLOGIZED AND ANNOUNCED THAT HE WAS BUGGING OUT. I THEN CALLED OUR OPS IN TO INFORM THEM AND TO ASK THEM TO GET THE ACFT REGISTRATION NUMBER AND PLT NAME IF POSSIBLE. THEY WERE ONLY ABLE TO GET ME THE N-NUMBER. I THINK THE PLT OF THE PC12 ONLY HAD A COUPLE OF US IN SIGHT AND WASN'T LISTENING TO THE SPECIFICS LIKE DIRECTION OF TURNS AND ALTS. I DON'T BELIEVE ANY REASONABLE PLT WOULD CHOOSE TO MAKE TURNS IN THE OPPOSITE DIRECTION AND AT THE SAME ALT AS 4 OTHER ACFT AROUND RAINBOW BRIDGE.