Looks like The Tetrarch's sire was a horse named Roi Herode. Here is Roi Herode's peedigree.

Roi Herode was bred in France in 1904 by Maurice Caillaut and the Comte de Pourtales. He was a grey son of the grey Le Samaritain (1895), a very good stakes winner in France (winner of the Grand Prix de Deauville, Grand St. Leger de France, Prix Daru), and himself a son of the grey Le Sancy. Le Sancy was the dominant sire in France in his time, although his male line back through Atlantic, Thormanby, Windhound, and Pantaloon, was one of the last surviving remnants of the once mighty Herod male line (Pantaloon was by Castrel, by Buzzard, by Woodpecker, by Herod).

Roi Herode, out of the mare Roxelane, by War Dance (the French War Dance, by Galliard - War Paint, not to be confused with the American one, by Lexington - Reel). This gave Roi Herode an interesting pedigree background, because not only was he inbred 4x4 to his tail-male ancestor Thormanby, but his second dam, Rose of York, was a half-sister to the great Derby winner and sire Bend Or, both out of Thormanby's daughter Rouge Rose. Roxelane had been an outstanding racemare in her own right, winner of the Poule d'Essai des Pouliches (French 1,000 Guineas) and Prix de Diane (French Oaks), and she was a full sister to the Poule d'Essai des Poulains (French 2,000 Guineas) winner Rodilard.