In the summer of 1983, John Adams was hit by a nasty bout of composer's block.

"I was gradually drifting into a first-class funk," he writes in his autobiography Hallelujah Junction. "Day after day, with what I deemed Yankee rectitude and Protestant work ethic, I would lock myself in my studio and try any and all tricks to unravel the thread of what had become a perfect tangle of reasons as to why everything I was doing was wrong, 'aesthetically unethical', or in bad taste, or not sophisticated enough."

Part of the problem was one Arnold Schoenberg. The father of atonalism (and, moreover, the stylistic asceticism that he inspired in others) cast a suffocating shadow over many 20th-century composers –– a shadow long enough to reach even the sunny shores of California, where Adams was composer-in-residence at the San Francisco Symphony. At the depths of his funk Adams dreamt that Schoenberg, dressed in a swarthy fedora, attacked him in the night and stole his infant babies. The meaning of the dream was not lost on him: if he was to regain his creative voice he needed to work through this particular father-son relationship.

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Then Adams had another dream. "At what seemed like the absolute nadir of my creative block I'd had a vivid dream in which I was crossing the San Francisco Bay Bridge. I looked out to see a huge oil tanker sitting in the water. As I watched, it slowly rose up like a Saturn rocket and blasted out of the bay and into the sky." The next morning he sat down at his desk, mind overflowing with music. He wrote the pounding Eb major chords that launch the megalithic orchestral force of Harmonielehre.

This weekend the Royal Scottish National Orchestra and their music director Peter Oundjian give the first of two all-American concerts (the second is in late April). Alongside the usual suspects of Bernstein, Barber, Gershwin and Copland, the 40-minute Harmonielehre should make quite an impression. The name is a kind of brazen catharsis in itself, lifted from Schoenberg's treatise on tonal theory – Adams describes Harmonielehre as "a statement of belief in tonality at a time when I was uncertain about its future". The score fuses minimalist insistency and post-Wagnerian grandeur; "a one-of-a-kind, once-only essay in the wedding of fin-de-siècle chromatic harmony with the rhythmic and formal procedures of minimalism."

There are quotations aplenty, from Wagner and Mahler to Reich and Glass, but don't be fooled into calling it ironic or postmodern. Adams's art is like a mixtape of musical heritage, a humble tribute and a ballsy appropriation. "I felt as if I were channelling the sensibilities of composers I loved and finding a contemporary form for their special harmonic worlds, treating them as if they had been conjured in a séance," he writes.

Harmonielehre rocketed Adams out of his first-class funk and into the limelight as the leading American orchestral composer of his generation. Talking last week about programming the RSNO's so-called American Festival, Oundjian told me that "this [Harmonielehre] is my favourite of all the American masterpieces I could have chosen". He once conducted the piece in front of Adams ("pretty intimidating") and later became friends with the composer. He remembers asking Adams when it was that he understood that he had a powerful voice: "He pointed to this score."

In the second programme Oundjian will showcase Adams's theatrical side. As with most of his stage works (Nixon In China, The Death Of Klinghoffer), the 2005 opera Dr Atomic treats a toxic political subject: the story of J Robert Oppenheimer and the Manhattan Project developing atomic bombs in the New Mexico desert. In 2007 Adams created the Dr Atomic Symphony out of instrumental chunks and transcribed vocal lines from the opera, and it's this symphony that we'll hear from the RSNO in April. "It's a powerful work," says Oundjian, "a real emotional synopsis of the opera".

The American Festival is not, though, the start of a "complete orchestral works of John Adams" – not like the complete works of Debussy that the RSNO recorded under their previous music director, Stéphane Denève. And where Denève's sensibilities were unequivocally French, Oundjian sits somewhere mid-Atlantic: between the UK, where he was schooled, Canada, where he was born and is music director of the Toronto Symphony, and America, where he has lived since the 1970s.

A violinist before he became a conductor, Oundjian's first professional gig was in Times Square. "It was New York, New York for daytime TV," he remembers. "The conductor was Leonard Bernstein, and though there were about 20 of us kids playing, Bernstein sent each and every one of us a thank you letter afterwards. He was a real gent that way."

When it came to choosing which Bernstein piece to include in the American Festival, "the problem was that he was good at too many things," says Oundjian. In the end he went with the overture to Candide, a fizzy flash of a thing with show tunes ringing out at full pelt. He pairs it with Gershwin's Piano Concerto in F, likewise incubated on Broadway and brimming with jazz licks and brash gestures. The second programme continues the piano theme with concertos by Barber and Copland, and opens with Copland's wistful, vibrant folk-ballet Appalachian Spring.

Oundjian's aim is "to represent the fusion between jazz and high art in American music". He describes Adams as "a fascinating compilation of European and American: he came out of what some people consider narrow [minimalism] but doesn't sound like he's obsessed with rules. He kept his ears and eyes open to allow many influences to come into his music while honing in on his own voice. He's a real juxtaposition of what his previous generation established, and of late 20th and early 21st-century preoccupations."

Denève's propensity for French music left the RSNO with a palpable Gallic panache to their sound. Will Oundjian's programming have the same effect with American repertoire? "First and foremost the orchestra will need a fantastic sense of swing," he says. "Then there's the special quality to the longing in American music. A particular tinge of sadness –a longing for homeland and belonging. There's also a sense of awe at the expanse of the landscape. But mostly it's the swing."

As for how to get a symphony orchestra to swing- "That I cannot put a finger on. Hopefully they just will. It has to be very spontaneous. Let's see what happens."

Peter Oundjian conducts the RSNO's American Festival this Friday (Usher Hall, Edinburgh) and Saturday (Glasgow Royal Concert Hall) and April 26-27.