Despite the often mesmerising connectivity between both talents involved, and a sense of wary excitement as to what might lay ahead, it takes less than a song to figure out which shared influence appears to have given flight to this project. The title track of the record, it glides upon a softly repeated piano figure from Canadian virtuoso and former electro producer Chilly Gonzales, and a rumbling, baritone, almost spoken-word invocation from Sheffield's premier wry pop miserablist Jarvis Cocker. 'Don't open the curtains, I'm allergic to sun,' he purrs, inviting us for a 'front row seat for a psychic shakedown … is there anything sadder than a hotel that hasn't been fucked in?' It very quickly reminds of – and makes the listener sad for the loss of – Leonard Cohen.

This album isn't as good as any of Leonard Cohen's, unsurprisingly, yet it passably captures his spirit for most of its duration; in fact, in paying tribute to Room 29 of Los Angeles' infamous Chateau Marmont Hotel (previous occupants: Jean Harlow, Howard Hughes), it's something like a West Coast analogue of Cohen's New York-set 'Chelsea Hotel No.2'. The romance, mystery and worn-velvet sexual frisson of a hotel with history is essayed throughout by Gonzales' smooth lounge style and the arch, detached wisdom of Cocker's eternally well-judged persona. Yet amid interludes, overtures and vocal samples, the minimal musical setting emphasises Cocker's tendency to rest on the wry quip over the emotional sledgehammer.

Buried behind a gorgeous melody and one of the finest vocals here, 'Tearjerker' essays a deeply weird psychoanalysis of a man conducting an affair (or possibly masturbating lonelily) in his hotel room while his girlfriend waits at the airport, admiring the wipe-clean surfaces and hurrying to catch the all-inclusive breakfast; 'Belle Boy' steps up to a rare sense of urgency thanks to the Kaiser Quartet's scything repeated chords, updating the hectic drudgery of The Who's 'Bellboy' with the couplet of the record, 'life could be a bed of roses / if it wasn't filled with so many pricks'; 'Ice Cream as Main Course' laments the loss of classical Hollywood hipsterdom in favour of 'tattoos and sports bars / you can't hear yourself think', a classic Cocker curl of the lip at modern life's most pronounced stupidities.

Yet these are highlights of a record which is only engaging from track to isolated track, with two disparate talents coming together in effective fashion. For its full 16-track duration, however, the tone is too similar, the lyrical observation often decidedly tame by Cocker's standards, the sense of Hollywood classicism almost twee and chintzy in comparison which the dramatic evocations of old Los Angeles out there, not least in the music of Lana Del Rey. In future it's sadly unlikely to enter the pantheon of great works about the city.

Room 29 by Jarvis Cocker and Chilly Gonzales is out on Deutsch Grammophon on Fri 17 Mar. The pair play the King's Theatre Edinburgh, Tue 22 to Thu 24 Aug as part of the Edinburgh International Festival.