Date: 201703
Local time of day: 0001-0600
Location: ZLA.ARTCC, CA
Flight conditions: VMC
Light: Daylight
Aircraft: Gulfstream V / G500 / G550
Operator: Corporate
Operating under: Part 91
Flight plan: IFR
Mission: Passenger
Flight phase: Descent
Airspace: Class A ZLA
ATC / advisory: Center ZLA
Reporter organization: Corporate
Reporter function: Pilot Not Flying; Captain
Reporter qualification: Flight Crew Air Transport Pilot (ATP); Flight Crew Multiengine
Human factors: Situational Awareness; Communication Breakdown
Second reporter function: First Officer; Pilot Flying
Anomaly: ATC Issue All Types; Conflict Airborne Conflict; Deviation - Altitude Excursion From Assigned Altitude; Deviation / Discrepancy - Procedural Clearance
Detector: Person Air Traffic Control
When detected: In-flight
Result: Air Traffic Control Issued New Clearance; Flight Crew Became Reoriented; Flight Crew Returned To Clearance
Contributing factors: Human Factors; Procedure
Primary problem: Human Factors

Narrative: Upon flying the JANNY3 STAR arrival into BUR airport; we were given a clearance to cross KREME waypoint at FL240. Upon arriving at that intersection; we were then given a clearance to descend via the JANNY3 arrival and an altitude of FL210. After looking at the arrival again; there were other waypoints above FL210 ahead on the arrival so I asked the controller to verify that we are cleared to descend to FL210 at this time in which the answer was yes.After we discussed in the cockpit what to do next; we agreed that we were cleared to descend via the JANNY3 arrival; so we began a slow descent from FL210 to meet the next crossing restriction at CHKNZ at or below FL190.Upon passing through at 20;700 feet; we were told to maintain FL210 by ATC. We then returned to FL210 without any issue or conflict indications from the cockpit.ATC then instructed us to write down a contact phone number for us to call when able on the ground. I complied with the request and called the number to clarify the misunderstanding.He explained that there was a loss of separation by us initiating the descent and I explained that we were given the descend via the JANNY3 arrival with initial altitude of FL210. He further explained that he had listened to the tapes and that when I asked for clarification of the FL210 altitude and the controller agreed; then that became a hard altitude and that the descend via the JANNY3 was no longer valid. He also explained that there are new ATC procedures for arrivals and departures in the LA area.After the phone call was made to ATC; the First Officer; who was the flying pilot; and I spoke at length to try and figure out where the communication breakdown occurred and how could we both have maybe missed an altitude assignment and we both agreed that we were given the cleared to descend via the JANNY3 arrival along with initial altitude of FL210. We then agreed that what we were supposed to abide by the descend via Janny3 arrival initially given.We were operating in a high workload environment and are wondering if the descend via the JANNY3 arrival verbiage should be used if we are expected to just go to a hard altitude?A clearance for a descent to FL210 would've worked initially; and then a clearance for the JANNY3 arrival after that would lead to less confusion I believe.LA Center then apologized for any misunderstanding or miscommunication before handing us off to Joshua approach.


Second narrative: [Report narrative contained no additional information].


Synopsis: Gulfstream V flight crew reported an altitude deviation occurred on the JANNY3 STAR into BUR. Crew cited an ATC communication breakdown as contributing.