Having just played six shows in three nights in Melbourne, followed by four in two days in Sydney, Bill Callahan may just be the hardest-working man in showbiz.

Perhaps then it’s not surprising his guitarist Matt Kinsey stayed seated for the entire second show on Friday night, while the American singer-songwriter limited his movements to an occasional shuffle.

But with only two people on stage and not a lot to look at, the music is all that matters (even if there were so many red curtains it seemed certain Twin Peaks’ Kyle MacLachlan would emerge from them at some point).

The duo opened with Jim Cain from 2009 album Sometimes I Wish We Were an Eagle, and it’s immediately obvious – if any such confirmation was required – why many compare Callahan’s rich baritone to Leonard Cohen’s.

In his previous recording persona as Smog, Callahan was known for his sense of humour (an album called Dongs of Sevotion; a track called Dress Sexy at My Funeral; an album cover featuring a cat being stuck by lightning, just after he’d split with Cat Power’s Chan Marshall), but the gag rate dropped considerably when he dropped the band name to use his own.

The Sydney Opera House audience seemed unsure which Callahan to expect. They were respectful, almost standoffish, as if expecting him to come out with reams of zingers. He didn’t.

But who needs laughs when the atmospheric desert blues – an intense, sometimes ferocious sound, considering it’s being made by two guitars (one electric, one acoustic) – is soundtracking a winter’s night just metres from Sydney harbour?

Playing so many shows over a few days, it’s not surprising there were a few empty seats, but it was surprising Callahan commented on it, with a spiel that took in Iggy Pop, cocaine and rich people in fancy cars. His manner is so deadpan, though, no one seems quite sure if he was genuinely annoyed or not.

If the gaps in the crowd were caused by poshos doing coke in 4WDs, it was their loss. They missed a spellbinding version of Lonesome Valley, a traditional gospel folk song, with Callahan’s take inspired by the Carter Family.

They also missed an epic, beautiful version of his 2011 classic America, which did its title proud as it journeyed through blues, folk and country, with lyrics about US television, modern wars, the bible belt and hogs. As with many of Callahan’s latter-day lyrics, the words are more often about how they sound than what they say. Maybe there’s a case to be made for him being less the Leonard Cohen of rock’n’roll, more the James Joyce.

A cover of Red Steagall’s I Gave Up Good Morning Darling was another highlight on a night of highlights, before Callahan finally showed some humour by comparing his thanking of the audience to reading a ransom note. Which, given its tone of Johnny Depp apologising to Australia for breaking our quarantine laws, it was.

Callahan is some kind of genius. Introduce yourself.

• Bill Callahan plays two more shows at the Drama Theatre, Sydney Opera House on 3 June at 4.30 and 8.30