"As the two men conferred, they were greeted by a familiar sight: American troops in full flight before the enemy. As Knowlton’s men scampered across the Hollow Way, British light infantry followed close on their heels and, wrote Reed, “in the most insulting manner sounded their bugle horns as is usual after a fox chase. I never felt such a sensation before – it seemed to crown our disgrace.”...The light infantry’s ill-advised use of a fox-hunter’s call was clearly an insulting gesture that demanded a response. By nature an inherently aggressive field commander, Washington accommodated and quickly decided to pounce on the redcoats, who had clearly rendered themselves vulnerable by advancing so far beyond their own lines."

https://allthingsliberty.com/2014/04/cursedly-thrashed-the-battle-of-harlem-heights/

"British troops made a tactical error by having their light infantry buglers sound a fox hunting call, “gone away,” while in pursuit. This was intended to insult Washington, himself a keen fox hunter, who learned the sport from his neighbor and mentor near Alexandria, Virginia, the Sixth Lord Fairfax (Thomas Fairfax) during the French and Indian War. “Gone away” means that a fox is in full flight from the hounds on its trail. The Continentals, who were in orderly retreat, were infuriated by this and galvanized to hold their ground."

https://www.harlemworldmagazine.com/the-battle-of-harlem-heights/

Yes, but Tom, that's the folklore.

From Reed's subjective impression that the bugle calls were intended to be insulting, these two writers, like many others, evidently with little knowledge of the hunting field have woven a fiction that these were specific fox-hunting calls (there might be various sounded at the end of a chase. 'Gone Away' is not one of them), that Washington heard them, interpreted them as did reed and acted accordingly; ditto his men. There is nothing in the sources to suggest any of this. In any case, Reed heard the bugles while he was still making his way back to report to Washington, not while the two men were conferring.

While Reed, the small town lawyer who may never have been in the hunting field, heard insults while officers commanding Washington's forward troops believed, variously, the bugles were sounding to rally to the dispersed Light Infantry, or possibly calling for support; both of which are inherently more likely conclusions. THey do not however supply the sense of hubris that the traditional narrative requires.

As I said, that is the old story. It would be most interesting to learn that at least the possibility of confusion resided in the choice of calls, even if their purpose was misinterpreted.