Date: 201406
Local time of day: 0601-1200
Location: DWH.Airport, TX
Flight conditions: VMC
Light: Daylight
Aircraft: Embraer Legacy 450/500
Operator: Corporate
Operating under: Part 91
Mission: Ferry / Re-Positioning
Flight phase: Taxi
ATC / advisory: Tower DWH
Second aircraft: Military
Reporter organization: Corporate
Reporter function: First Officer; Pilot Not Flying
Reporter qualification: Flight Crew Flight Instructor; Flight Crew Multiengine; Flight Crew Air Transport Pilot (ATP)
Human factors: Situational Awareness; Communication Breakdown; Confusion
Second reporter function: Pilot Flying; Captain
Anomaly: ATC Issue All Types; Conflict Ground Conflict; Less Severe; Deviation / Discrepancy - Procedural Published Material / Policy
Detector: Person Air Traffic Control
When detected: Taxi
Result: Air Traffic Control Issued Advisory / Alert; Air Traffic Control Issued New Clearance
Contributing factors: Chart Or Publication; Airport; Human Factors; Procedure
Primary problem: Ambiguous

Narrative: Upon contacting DWH Ground; we were instructed to taxi behind a Cherokee to runway 17R via Charlie. Ground advised us that we should; 'expect to be number one as the Cherokee would most likely need to conduct a run-up.'Approaching 17R; Tower advised us by call sign '...cleared for takeoff Runway 17R' on East Tower frequency 127.4 and the clearance was read back. At this time; the pilot flying and I noticed a restored World War II war bird back taxing northbound on the displaced threshold of Runway 17R appearing to be heading towards the hangars.We crossed the hold short line to depart southbound on Runway 17R and were immediately told to 'Stop' by Tower. The 'Stop' clearance was read back at which time Tower informed us we had not been cleared for departure.Tower stated that the back taxing war bird had been cleared for takeoff and asked us to 'switch to 118.4 to avoid any further confusion' and cleared us to make a 'one eighty degree turn to taxi back on to taxiway Charlie.'The war bird finished its back taxi; turned around and completed an uneventful takeoff as we were holding short of Runway 17R at Charlie. We were then subsequently cleared for an uneventful takeoff.Both crew members recall hearing Tower clear us for takeoff and there was no correction from Tower following our cleared for takeoff read back. It is apparent the war bird was using the 'East' Tower frequency and we were on the 'West' Tower frequency. Neither of the runways had a Tower designation as noted on most other airport diagrams with multiple Tower frequencies. Having taxied from the east side of the airport complex that is the Tower frequency we were communicating on and acknowledged by Tower.Fortunately; this was an innocent mistake that was corrected with alert air traffic control and crew members. It would be my recommendation to either designate 17R and 17L with specific Tower frequencies or to combine the two Tower frequencies in to one Tower frequency to avoid any future confusion.


Second narrative: [Report narrative contained no additional information]


Synopsis: Confusion as to which aircraft received a takeoff clearance at DWH resulted in the reporters' Embraer Phenom coming nose to nose with a military war bird back taxiing on 17R/35L at DWH. The existence of 'east' and 'west' Tower frequencies with no clear designation as to which to use was a contributing factor.