Billroth was a talented pianist and violinist who seriously considered becoming a professional musician before he became a surgeon. 

"In 1865 he [Billroth] met Brahms for the first time when the rising composer and pianist played Robert Schumann's piano concerto and his own works in Zurich. After Billroth had moved to Vienna in 1867 they became close friends and shared many musical insights. Brahms frequently sent Billroth his original manuscripts in order to get his opinion before publication, and Billroth participated as a musician in trial rehearsals of many of Brahms' chamber works before their first performances. Brahms dedicated his first two string quartets, Opus 51, to Billroth.

"Billroth and Brahms, together with the acerbic and influential Viennese music critic Eduard Hanslick, formed the core of the musical conservatives who opposed the innovations of Richard Wagner and Franz Liszt. In the conflict, known as the War of the Romantics, Billroth supported Brahms, but was always fair and measured in his comments. "Wagner was indeed a very considerable talent in many directions," he wrote in 1888.^[11]

"Billroth started an essay called "Wer ist musikalisch?" ("Who is musical?"), which was published posthumously by Hanslick. It was one of the earliest attempts to apply scientific methods to musicality. In the essay, Billroth identifies different types of amusicality (tone deafness, rhythm-deafness and harmony-deafness) that suggest some of the different cognitive skills involved in the perception of music. Billroth died in Opatija, Austria-Hungary, before he could complete the research" (Wikipedia article on Theodor Billroth, accessed 3-2020).

This English translation is the best edition, translated from Fischer's Briefe von Theodor Billroth (1895). Digital facsimile of the 1895 edition from the Internet Archive at this link.