His was a towering account of the great 32, full of insight and unfussy intellect. The recording established Goode as his nation's leading pianist. Now 70, he is generally referred to as the elder statesman of American pianism.
Goode himself seems typically level-headed about the whole business. "Was it a big deal that I was the first American to record the complete Beethoven?" he says, sounding bemused. "To be honest, I didn't think about it until somebody pointed it out. 'American pianist' is a label that's been attached to my name ever since. It's technically true, of course, but mostly I reckon that these kind of labels don't really matter."
He points out his training was in fact entirely European: his teachers included the German-born Claude Frank, Polish-born Mieczslaw Horszowski and Russian-Jewish Rudolf Serkin. Growing up in the East Bronx in the 1950s, the cultural hodgepodge around him was anything but American born-and-bred. His first teacher, the Hungarian Elvira Szigeti, lived a couple of blocks down the road.
"Of course nationality has mattered in some ways," Goode continues. "When I think about the upbringing of somebody like Serkin: he had to go to Vienna without his parents when he was young and he had a very difficult time. I've had it all so easy in comparison, and that has surely effected the person I've become."
The person he has become is a disarmingly open and affable gentleman with a friendly Bronx twang and a soft, grandfatherly face. He's as committed a teacher as he is an iconic recitalist: he knows the value of artistic lineage and of encouraging young talent. And if his concert schedule is busy, he doesn't seem weary of the routine.
"Sure, long flights aren't so much fun," he concedes, "but I have plenty of friends in far-flung places who I like to visit when I'm travelling. And I love getting to know cities around the world."
He even has a favourite restaurant in Glasgow (the Italian Kitchen, near City Halls). It was first recommended to him by none other than Alfred Brendel.
This month Goode is back in Scotland to perform with the Royal Scottish National Orchestra - he's soloist in Mozart's G Major Concerto, K453 - and the same week gives a solo recital at Perth Concert Hall. Both will be highlights of Scotland's spring classical calendar.
What is it that makes Goode's concerts unmissable? For me, his mastery lies in the quiet certainty of his interpretations. He isn't dogmatic or rigid, but clear, focused, uncluttered, wonderfully matter-of-fact. His performances trade whimsy and showmanship for an unflappable intellectual grounding.
When asked whether this steadfast clarity is a deliberate thing, Goode ponders a moment before replying. "I guess the way you play is a bit like the way you look," he says carefully. "It is something that other people can judge much better than you can judge yourself. But yeah, that matter-of-factness you're talking about probably came from my training. Especially from Serkin. He put enormous emphasis on examining a score and being faithful to it. I always look at every single one of the composer's markings. I take tempos seriously. I take articulation seriously. I try to figure out exactly what the composer imagined - not necessarily always as the last word, but certainly always as the first word."
He pauses. "And to be honest, what the composer imagined is usually a heck of a lot more daring than anything I could come up with."
After 50 years on the concert platform, Goode says he is still searching. "Always searching for the right expression, and it's maddening. Take the Mozart G Major Concerto. It's one of the first pieces I ever played. The challenge is to find the right balance of humour, grace and vivacity. Every time it's still different, but when I find it - that is, when the conductor and the orchestra and I all manage to get that balance right together - I enter a kind of groove. That's the sweet spot. That's what I'm searching for."
And despite a formidable discography, Goode never listens to recordings of himself. "Nope, that is total no-no: I'm too afraid that I won't agree with my interpretations!" That said, the last time he went to the dentist he found himself lying on the chair, waiting for the filling to go in and listening to a Brahms Intermezzo over the clinic radio. "I sort of enjoyed the performance, and when it finished I said to my dentist, 'I wonder who was playing that'." Of course it turned out to be him. Was he pleased by the discovery? "I guess I was. Mostly I just thought that I should probably go to the dentist more often."
The programme for the Perth recital is a classic Goodean line-up, minus Beethoven. To open he pairs two of Schubert's Impromptus with what he calls the composer's "strange, obsessive" posthumous Klavierstücke. "I like to mix up the Impromptus," he explains "They go together beautifully, but they don't go together inevitably. Hearing them in new contexts can draw attention to aspects of them that we don't always hear."
Then it's on to Chopin: four Mazurkas and the Polonaise Fantasie, Op. 61. "I can't think of any music that depends so much on rhythmic flexibility as the Mazurkas. Here the matter-of-factness that we talked of earlier doesn't apply so much. It's all about freedom - or at least, about the illusion of freedom, which of course relies upon a great deal of discipline under it all."
In the second half he turns to Debussy, and the entire first book Preludes. Now the pleasure comes from completions: from hearing the pieces in their original context. "The juxtapositions are stunning. The Girl with the Flaxen Hair is beautiful in any context, but after What the West Wind Saw it becomes the calm after the storm. I do like to draw connections. The longer you can carry the listener's ear - and your own ear - the less you get lost in the beat. It's about hearing a longer perspective." Hearing a longer perspective: it isn't a bad way of summing up Goode's artistry all together.
Richard Goode plays Mozart with the RSNO in Perth on February 6, Edinburgh on February 7 and Glasgow on February 8; his recital at Perth Concert Hall is on February 9.