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She was the daughter of Josef Geyer, a police doctor who played the violin himself. When she was 3 years old she started playing the violin, with remarkable results for someone who had not practiced at all. She subsequently studied under Jenő Hubay.
Béla Bartók and Othmar Schoeck, who were both in love with her, wrote violin concertos for her. Bartók's first violin concerto was only published after he and Geyer had both died. Willy Burkhard dedicated his 1943 violin concerto jointly to Geyer and Paul Sacher.
Her first marriage was to Vienna lawyer Erwin Jung. He died during the flu epidemic of the First World War. In 1920 she married Swiss composer Walter Schulthess. She moved to Zurich, where she gave concerts, and taught at the Zurich Conservatory (merged in 1999 into the School of Music, Drama, and Dance (HMT), itself merged in 2007 into the Zurich University of the Arts (ZHdK)) from 1934 to 1953. She schooled numerous musicians, among them composer Klaus Huber.