The case for denying Grieg greatness is easy. He was certainly no Beethoven when it came to ambitious musical forms. At 20, urged by a mentor, he wrote a symphony but soon withdrew it and never completed another. He came under pressure to compose a stirring Norwegian national opera and tried to do it, but got no further than some choral scenes and sketches. He wrote the wonderful, if modest, Lyric Pieces, some chamber works, a few volumes of elegant songs. His incidental music for Ibsen’s play “Peer Gynt” were fashioned into two popular orchestra suites. A nd there is, of course, his justly beloved Piano Concerto.

A great? No. Should that matter? Absolutely not.

Yet I’ve come to accept that I and other lovers of music, like lovers of any art form, can’t help being swept up in the search for, and identification of, greatness. Your first time hearing some exhilarating or mystifying work by a composer of the past — Mozart’s “Jupiter” Symphony, Beethoven’s searching Fourth Piano Concerto, Wagner’s trance-inducing “Tristan und Isolde,” Stravinsky’s shattering “Rite of Spring,” take your pick — can be as formative a moment as anything in your life. These works, and the composers who wrote them, become living presences; it’s natural to acknowledge the place they hold for us, and to seek reassurance that the things we love are important to others, too.

My most brazen venture into grappling with greatness came in 2011, with my Top 10 Composers project, a two-week series of articles I wrote for The New York Times. The goal was to determine a list of the top 10 composers in history. Of course, the whole project was an intellectual game, though one played seriously by me and the more than 1,500 readers whose comments were posted during the two weeks.

Some of the most interesting reactions came from music-lovers who actually found the game harmful. Others, while dismissing the exercise as absurd, sent in their own top 10 lists, often with injunctions like “Don’t you dare leave out Mahler!” For me, the game was also a genuine exercise in trying to be precise about what makes a composer’s music great, about why a composer merits a place. The final list, as I emphasized, was not the point. The analysis involved in determining it was.

As a ground rule I omitted living composers from consideration, arguing that we are just too close to these creators to have enough perspective. I think that one of the most rewarding things about taking in music by living composers, as with new work in any artistic field, is that questions of the greatness of a piece, and predictions of its longevity, are irrelevant. If an exciting new novel comes along, literary-minded people want to read it, talk about it, maybe argue over it. But the question of whether the novelist is another Dickens or Proust is absurd. The same goes for new plays, new films, new pop groups, new television dramas.

In the end, I think of my job as bifurcated. I will always be unapologetically hooked by the reality that there is greatness in music. In my reviews and other stories, I try to explain, for example, why Schubert was absolutely great; why Debussy; why Wagner.