I'm sorry for wasting your time... I really didn't understand the sentence at all. SevenDays helped me understand a part... At first, I didn't know who is Strauss. When I googled "Straussian", it didn't give me any clue; but now I know that Strauss is a German composer. I don't know who is Barber. I know that "triad" and "melody" are components of music, but I can't differentiate between them...Please tell us which part of the phrase is confusing you, so we don't waste time explaining what you already understand. For example, do you know who Strauss and Barber are? Do you know what a musical triad is?
In this case, the group of three is not three beats, but three notes forming a triad chord. The composer named Strauss who characteristically used such triads was Richard Strauss, and not Johann.