Stephin Merritt, the wonderfully glum songwriter behind the indie rock band the Magnetic Fields and Chen Shi-Zheng’s new play “My Life as a Fairy Tale,” is among the most celebrated musical talents of his generation.

The praise, typically, comes in two varieties. The first is to hail him as a modern pop genius. The New York Times called “69 Love Songs,” the three-part 1999 Magnetic Fields album which established his reputation, “a tour de force of deadpan pop ventriloquism” and praised Mr. Merritt’s “prose of jaded romanticism a la Lou Reed, David Bowie, Bryan Ferry and Cole Porter.” The Guardian of London called it “an essential guide for loving music.” A critic writing for this paper – okay, me – called it a “three-disc pop master class full of sparkling wit and bitterness.” Mr. Merritt is not someone who inspires moderation – or much criticism – in critics.

The second variety of praise is to cast Mr. Merritt as an heir, and sometimes equal, to the greats of musical theater: Irving Berlin, Lorenz Hart, Bertolt Brecht, and, most commonly, Cole Porter. “I’m so sick of being compared to Cole Porter,” he told the New York Times in 2003, “now I hate Cole Porter.” But to really understand Mr. Merritt’s music – and what makes it so captivating for some and unapproachable for others – both claims need be examined.

Mr. Merritt’s art took shape in the indie-rock underground of the early 1990s, first in Boston, then in New York. Even in this context, his music was an alternative. What set him apart was a fascination with, and encyclopedic knowledge of, the past. I stand by my claim that “69 Love Songs” is a pop master class: Mr. Merritt uses it to take on virtually every 20th-century pop style he can think of: country, torch songs, bluegrass, cabaret, new wave, beatnik a capella.

But though he works in once-popular modes, Mr. Merritt’s songs actually have an anti-pop quality about them. The historicism makes you hear them at a remove; it turns pop songs into art songs. What’s more, there’s little of the pep or eagerness that characterizes modern, Billboard-topping pop music. If Mr. Merritt’s sleepy baritone were any more disinterested, it would be a snore. And he buries many a potential pop hit beneath limp electronic arrangements – music for which he has an inexplicable weakness.

Neither are the songs “pop” in the evergreen sense of Paul McCartney’s, John Lennon’s, or Brian Wilson’s work. Mr. Merritt’s music lacks the grand harmonies and swooping dynamics for which these others are rightly idolized. His songs – especially on “69 Love Songs” – are often single ideas, riffs really, sometimes no longer than a minute. If he were Brian Wilson, he’d paste six of them together and make it work as a single song. So if he’s none of these things, on what is his pop reputation based? First, his melodies are terrific. “Absolutely Cuckoo,” the song that opens Disc 1 of “69 Love Songs,” is a great example: simple, charming, hummable. He matches that feat on the album a couple of dozen times without repeating himself. But it’s as a lyricist, Mr. Merritt shines. He’s witty, bitter, mournful, droll, and playfully sappy. It’s hard to represent all of these things in a single example, but the first few verses of “A Pretty Girl Is Like … ,” Mr. Merritt’s homage to the Irving Berlin song, does a fair job:

A pretty girl is like a minstrel show:
It makes you laugh, it makes you cry, you go.
It just isn’t the same on radio.
It’s all about the makeup and the dancing and the ohhhh.
A pretty girl is like a violent crime:
If you do it wrong you could do time,
But if you do it right it is sublime.
I’m so in love with you girl,
It’s like I’m on the moon.
I can’t really breathe,
But I feel lighter.

Which brings us to the second category of praise: comparisons to the musical-theater greats. These stem mostly from the fact that Mr. Merritt approaches albums the way a theater songwriter might a play. Much of his work doesn’t sound explicitly biographical. Rather, it starts with an idea, a situation, or a challenge posed to himself. He has written entire albums about topics such as road trips and vacations, and likes to set arbitrary rules for himself (like beginning every song of the last Magnetic Fields album with the letter “I”). The strictures are necessary, you sense, to focus his creativity and keep him amused.

“69 Love Songs” is, in many respects, more like a musical’s cast recording than a conventional album; the songs seem to further a through-narrative that doesn’t exist. “The Night You Can’t Remember,” about a tryst between an army officer and a Rockette (unremembered by the former), is a good example.

No rose conveyed your sentiments not even a petunia.
But you’ve got vague presentiments and I’ve got little junior.
You said “nobody loves me” and I said “wanna bet.”
The night you can’t remember the night I can’t forget.

You wonder what happens to the characters, but never find out, as they’re abandoned after the song.

Mr. Merritt has been approached about turning the collection into a musical revue of some sort. And you can imagine some of the songs treated that way: a full-chorus version of “The Sun Goes Down and the World Goes Dancing”; a slow-motion choreographed “Busby Berkeley Dreams.” But it’s hard to imagine that it wouldn’t lose something in translation – namely, Mr. Merritt’s own theatricality.

In this, Mr. Merritt really is like a traditional pop singer-songwriter, and not a Tin Pin Alley lyricist and composer. You have to see him sing to get the full force of the songs. Only his deadpan delivery and Eeyore-like air of perpetual gloom can mine lines like “nobody wants you when you’re a circus clown / I should know, I’ve looked all over town” for their full comic effect. It’s the musical equivalent of a Buster Keaton gag: Mr. Merritt’s the only one who isn’t laughing.

Mr. Merritt’s most recent work for the stage, “My Life as a Fairy Tale,” shows the problem. The music – played by a typically unconventional quartet of bassoon, accordion, Stroh violin, and trilling electric pipa – was eerie and often lovely, but the sound was uniformly awful, and many of the lyrics were swallowed by Gerald W. Lynch Theater before they reached my ears.

There were some quintessential Merritt moments: the use of the word “autovivisect” to describe “The Little Mermaid” chainsawing her tail into legs; lines like “he kept his braggadocio / through years of haul and squalor / he toasts the maid that loved him so / the caller and the garter.” But the play is a bad fit – too abstract, surrealistic, and lacking in clear narrative to make use of Mr. Merritt’s talents. The fragile, whimpering Hans Christian Anderson – as portrayed by Fiona Shaw – would have been a poor vehicle for the caustic wit and ironic distance that characterize Mr. Merritt’s best work anyway.

Still, there’s little doubt that Mr. Merritt’s songwriting is far better than most heard in the theater. Here’s hoping his next project is a more conventionally structured love story dealing with the things that populate Mr. Merritt’s albums: jealousy, boredom, dancing. Then, perhaps, we’d hear something truly exceptional.