Schramm was born to Marie Hofmann and an unknown father, in Vienna. His mother later married Gustav Schramm, who adopted the boy.
He was a musical prodigy, giving his first professional concert aged eight. He taught piano in Austria, including the great pianist Claudio Arrau among his students, and composed and performed. He married in 1916 but was divorced in 1927, and married Bernardina Adriana Soetermeer, a Dutch musician, in 1928. They worked together as teachers and performers for the next 18 years.
The political situation in Germany drove them to emigrate with their young son to the Dutch East Indies (now Indonesia) in 1933, then to New Zealand, in 1938. They became leading lights in Wellington musical circles, continuing to teach and give concerts. But when World War II broke out, as aliens their activities were severely restricted, and Schramm was reduced to working in a comb factory. His application for citizenship was rejected, and he became increasingly bitter.
In 1946 he went to Australia on tour and never returned to New Zealand. He died in 1953, while selling underwear and hosiery from the back a trailer.