Felix Adrian Norman Salmond was born into a family of professional musicians on November 18, 1888 at St George's, Hanover Square, an Anglican church in central London. His father was David Norman Salmond (a baritone) and his mother was Adelaide Cecilia Salmond (a pianist who had been a student of Clara Schumann).

He began his formal music training under the tutelage of William Whitehouse at age 12. At age 16, he received a scholarship to study with Whitehouse in London at the Royal Academy of Music. At age 19, Salmond went to the Brussels Conservatoire where he spent two years with Édouard Jacobs.

Salmond appeared with many orchestras, including the London Symphony Orchestra, Queen's Hall Orchestra, and the Hallé Orchestra. Salmond played Frank Bridge's Fantasy Trio in C minor and Johannes Brahms's Piano Quartet No. 1 in G minor at his concert debut in 1908 at Wigmore Hall (known at the time of this writing as Bechstein Hall) where he was joined by Bridge (the composer of the Fantasy Trio) on viola, his mother on the piano, and Maurice Sons on the violin.

Salmond premiered Edward Elgar's String Quartet in E minor and Piano Quintet in A minor at the Wigmore Hall on May 21, 1919. Five months later, on October 26, 1919, he premiered Elgar's Cello Conerto in E minor with the London Symphony at the Queen's Hall.

Salmond made his U.S. solo debut on March 29, 1922 in New York City at the Aeolian Hall. Among many notable performances, he performed a piano trio in 1924 with violinist Efrem Zimbalist and pianist Ignacy Jan Paderewski at Carnegie Hall.

He moved to the United States and was appointed to the Juilliard School of Music's faculty in 1924. He also played in a piano quartet with Harold Bauer, Bronisław Huberman and Lionel Tertis during tours around the country. He was appointed director of the cello faculty at the Curtis Institute of Music in 1925, serving in that capacity until 1942. He was still employed at Juilliard at the time of his registration for the United States draft in 1942 during World War II.

A highly respected teacher in the United States, Salmond's pupils included Orlando Cole, Bernard Greenhouse, Suzette Forgues Halasz, Channing Robbins, Leonard Rose, Daniel Saidenberg, and Alan Shulman among others. Cole, Rose, and Robbins became highly influential teachers in their own rights, going on to teach Yo-Yo Ma and Lynn Harrell among others.

The obituary of cellist Eleanor Aller in The Independent (London, England) states that, at age 16, she was awarded a scholarship to Juilliard to study with Salmond. The Independent quoted her as saying that the experience was "'the most exhilarating experience' of her musical life. She regarded Salmond as one of the greatest musicians she had ever met, and of his teaching she said: 'My father had given me a wonderful basic training so when I went to him I was already a cellist, but what Salmond did was to teach me to play musically.'"

Joseph Stevenson's Artist Biography of Salmond ends with the following four paragraphs of fascinating remarks:

"Salmond was an emotional teacher. He ordinarily taught with patience and kindness, but was subject, when the student seemed not to be working to his potential, of castigating his pupil angrily. Cole said that at those times 'you had to go through hell...He would say, "What makes you think you can play cello? You're wasting my time and your time. You have no talent!"'

"At the time Salmond began teaching, cello playing was undergoing a revolution in fingering, mostly a result of the innovations of Pablo Casals. Salmond developed a different bowing technique. Instead of spreading the fingers over the bow, with a rigid thumb, Salmond bent the thumb and placed the middle fingers together, more like a violinist. He stressed use of the arm rather than the wrist in crossing strings, again, a violin-like technique. He used the thumb, not pressure from the arm, as the source of power in the bow-stroke. This resulted in a less nasal, much more beautiful tone, and he consistently urged the student to strive for a beautiful tone.

"His recording [sic] do show a lovely, singing tone. Not surprisingly, as the son of a professional baritone, he used reference to singing as his ideal. He called the cello the 'singer par excellence of the [piano] trio, more able to sing than the violin or piano, and unequaled by them in its range of tone color. The violoncello can sing soprano, contralto, tenor, and bass, and it is capable of equal beauty of tone in all of these registers.'

"He was also innovative in the literature he taught his students. He de-emphasized show-off bon-bons such as the Popper pieces, and stressed building programs around sonatas. (Strange as it seems today, cellist up to his time regarded these as recreational pieces for home playing rather than concert items.) He also urged young artists to know the great masterpieces in other fields or art, like sculpture, painting, and literature, and even the great movies."
∼Felix was a cellist and teacher at the Julliard School of Music in New York.