What criteria might you apply? Would a composer’s influence and popularity factor in? Schoenberg was arguably the most influential composer of the 20th century. That he pushed tonality past the brink and devised a technique to supersede it completely shook up the music of the era. Every composer in his wake had to come to terms with Schoenberg. But on the basis of his actual pieces, many of which excite and move me, does he make the Top 10?

What about a composer whose range was narrow but whose music was astonishing? Chopin, a staggering genius, wrote almost exclusively for the piano. And what do you do with opera? Is that a separate thing entirely?

Do you break music down by the elements and analyze, for example, who was the greatest master of counterpoint? The most inventive rhythmically? And then, of course, there is my personal take on things, which will, of course, factor in strongly but not be determinative.

Anyway, between talking with Mohammed and going through the annual “best of the year” ritual, I have been emboldened. So here begins an open deliberation leading eventually — in later articles, online videos and posts on ArtsBeat (artsbeat.blogs.nytimes.com) — to my answer to this irresistible question: Who are the 10 greatest composers in history? My editors urged that if I went down this path, I should go all the way and rank the Top 10 in order. But first I have to narrow the scope, so here are the ground rules:

I am focusing on Western classical music. There are compelling arguments against honoring this classification. Still, giants like George Gershwin, Duke Ellington and Stephen Sondheim are outside my purview here. And on the assumption that we are too close to living composers to assess their place and their impact, I am eliminating them from consideration.

Finally, I am focusing on the eras since the late Baroque. You could make a good case for Josquin or Monteverdi, but I won’t. The traditions and styles were so different back then as to have been almost another art form. I’m looking roughly at the era an undergraduate survey of Western civilization might define as modern history.

Image Clockwise from top left: Schubert, Haydn, Beethoven, Mozart’s grave marker. Credit... Clockwise from top left: Imagno/Getty Images; Keystone/Getty Images; Hulton Archive/Getty Images; The New York Times Archive

So to get things going, let’s start with an easy one: Bach. He would probably be the consensus choice among thinking musicians for the top spot. But why?