Leonard Cohen has described his new collaboration with Philip Glass, “The Book of Longing,” as being “like a bumblebee: from what we know, it shouldn’t fly.” After all, the worlds of popular and classical music have been steadily distancing themselves from each other for the entire 20th century. And, on the face of it, a partnership between the detachedly romantic Cohen and the insistently cerebral Glass is not an easy fit. But fly the piece does — stunningly and movingly.

On Tuesday, Oct. 9, Stanford Lively Arts co-commissioned the West Coast premiere of “Book of Longing,” which was performed at Memorial Auditorium to a packed audience. “Book” is difficult to classify in traditional terms — it is, in essence, a chamber concert piece, with a small instrumental ensemble backing four voices. The performance, however, includes theatrical elements, as well: the singers enter and exit, move and gesture, as do some of the instrumentalists, who will occasionally stand up and take center stage, or turn their backs to the audience.

Leonard Cohen’s book of the same name provides not only the poems that constitute the libretto but also the sketches and line drawings that are projected onto the stage’s Zen-like black-and-white backdrop — solemnly unflattering self-portraits and naïve, sacred erotica changing with the music’s shifting mood.

Still, at the center of this work of art is Glass’s superb intertwining of text with music. It is an initially jarring experience to hear Cohen’s subtle humor and intensely personal musings belted out as if in an opera house, or worse, on Broadway. Something in Cohen’s quiet irony seems lost in the vibrato and the hand gestures of a classical vocalist, and this problem remains evident in certain later passages.

But, generally, as the audience acclimates itself to the idea, the music and poetry — and the “classical” and the “popular” — begin to seem inseparable. The quiet “1-2-3-4” of the conductor — uncommon in the classical tradition — the melodic, almost catchy lyricism of the vocal parts and Cohen’s celebrations of everyday sexuality meld seamlessly with Glass’s complex polyrhythms and repetitious, constantly modulating chord progressions, as well as Cohen’s tragically elegant turns of phrase.

Of the 150 or so poems in Cohen’s book, Glass has scored 22, arranging them in cycles. Cohen’s smoky chocolate recorded voice, for instance, opens “Book,” speaking over a ceremonial dirge (the excellent “I Can’t Make the Hills”) and returns frequently to recite short, often dryly humorous poems unaccompanied by the ensemble (a favorite being “You go your way/ I’ll go your way too”).

The longer romantic poems Glass characterizes as the “ballads,” ascribing to them beautiful, simple choral melodies over his constantly shifting rhythms, also make frequent appearances, forming the slow crescendo that carries “Book” steadily upwards. Standouts include the Lorca homage “The Night of Santiago” and the climactic but sparsely arranged, “You Came to Me This Morning.”

Even more impressive musically are the periodic instrumental solos Glass hands out like jazz breaks. Through these occasionally virtuosic (go, if only to see Timothy Fain’s impassioned attack on the violin), dazzlingly constructed sections, swinging between a Baroque cadenza and modern polytonality, run clear motifs that repeatedly pop up elsewhere, as if Glass were briefly revealing the bones of his work.

This is not to say the piece is utterly without flaw. As mentioned before, the vocalists’ interpretations are occasionally frustrating. Oddly, the women (Dominique Plaisant and Tara Hugo) often seem more effective as interpreters, perhaps because their voices, unlike the men’s, evoke no memories of Cohen’s.

Along similar lines, the depth of Cohen’s style — his ability to express simultaneous misery and serenity, or triumph and self-effacement — are sometimes drowned, not only in the operatic vocals, but in one of Glass’s more heavy-handed passages. “Puppet Time” and “How Much I Love You” — which uses the somewhat cheesy touch of a Middle Eastern-sounding introduction in reference to Cohen’s “Arabian Sea/ and its perverse repetitions of white and grey” — both could have used lighter touches. Still, these are the exceptions to the rule. Much more common are triumphs of text-music interplay, like the marvelously nuanced “Mother Mother” or “The Light Came Through the Window.”

In an Aurora Forum the night before the performance, Glass revealed that he had originally thought that “The Book of Longing” was too beautiful. “I don’t know what course he would have taken to correct that aberration,” explained Cohen. Perhaps Glass was worried about “Book” being simply pretty — of not doing justice to the obscene sanctity of Cohen’s work. But he doesn’t need to. For two men who, for their entire lives, have been concerned with making art popular, and vice versa, “Book” is not, as Cohen puts it in his epilogue, “merely a song/ merely a prayer.” Rather, it is a great step toward what these two men have been searching for.