Set in 1930s America, our hero, a poor musician / hobo, finds a (unexplained, but simple) way to duplicate anything. He first duplicates his trombone, then himself, to form a full jazz band. Some of his duplicates are a little "off", and further duplicate themselves. This goes on until there are thousands, then millions. There's a huge war, but eventually the dupes die out and things go back to normal.
The story could have been written anywhere from the 50s-80s, and is American.
It's "Double Double Toil and Trouble" by Holley Cantine, first published in The Magazine of Fantasy and Science Fiction, January 1960.
To fill the void in my life left by the cessation of political activity, I began to revive my old interest in magic. I had acquired, over the years, a fair collection of books on magical lore — like all radicals I was an inveterate browser of secondhand bookstores — which I had not previously found time to look into seriously.
My only other hobby was early New Orleans jazz, an interest I had shared with several of my younger comrades in the city. I had a number of worn, but still playable phonograph records — chiefly marching band music of the Bunk Johnson-George Lewis school — and with part of my legacy I had bought a beat-up old slide trombone. When I wasn’t poring over my books on magic, I spent my free time listening to records and teaching myself to play the horn.
....
At some point in my investigations, I worked the formula for doubling correctly, and while I was never able to get any other formula to go right, it convinced me that with sufficient perseverance I could accomplish almost anything
....
Then one night I woke up after dreaming of being a member of a band — a perennial wish-fulfillment dream of mine — and it suddenly dawned on me that I could employ my gift to satisfy that desire. I got right out of bed — I knew if I waited for morning, I’d probably lack the nerve to try it; I was scared enough half-asleep — and doubled myself. I hadn’t tried to double anything more complicated than a salt herring until then, and while I had never failed at anything I had attempted, I had no way of knowing if I’d come out of the experience alive. I was just desperate enough to take the chance, though, and the result was, or seemed to be, perfect. The two of us looked at each other, laughed, sort of hysterically, then we shook hands, and both of us doubled and redoubled. We all decided that eight was plenty for a start, and set about doubling enough food and drink to feed us. We had a feast, with plenty of beer, after which we doubled the mattress and bedclothes into enough for all — they pretty nearly filled the cabin — and tried to get back to sleep. But we were too excited and overstimulated; we kept giggling and skylarking like a bunch of schoolboys in a dormitory when the proctor was away.
