If you want to start a fast and heated debate in a gathering of clarinetists, just mention the word vibrato.
Vibrato, by definition, is a tool of musical expression utilizing controlled pitch wavering of the tone. These undulations of pitch rapidly alternate between rising slightly above and falling slightly below any given note. How far the pitch deviates (width) and the rapidity of the vibrato undulations (speed) are at the discretion of each player.
Vocalists regularly incorporate vibrato, achieving this effect by manipulating their air, throat, and oral cavity. String players make controlled up and down movements of their left hand on the fingerboard. Brass players can achieve vibrato through pulsating their air and/or using their physical equipment, such as slightly and rapidly moving the slide in and out on trombone, and moving the fingers laterally back and forth on the valves of the trumpet, French horn, and tuba.
Vibrato on flute and saxophone is achieved through a combination of pulsating air and controlled undulating lip and jaw movements. Oboe and bassoon vibrato can also be achieved in this manner, but most double reed players utilize a diaphragm vibrato, where the diaphragm muscle is consciously moved rapidly up and down while sustaining the tone.
These methods of vibrati have been standard performance practice on these instruments for well over a hundred years. Teachers of these instruments spend many hours teaching and cultivating vibrato with their students. So where is the clarinet in this discussion?
Vibrato is a controversial subject with clarinetists. There are those who believe that the clarinet's tone is pure and should be "straight", achieved without using any vibrato. They argue that because the unique overtone series of the clarinet (overblowing at the interval of the 12th) eliminates the first note in the harmonic series, that vibrato should be avoided. Others argue that using vibrato as a tool to make the musical line more expressive is not only acceptable, but preferable.
Most of the vibrato I have heard with clarinetists is unique and has developed naturally over time by the individual player. I have not heard of a specific and/or documented pedagogical approach to clarinet vibrato.
In the early to mid-twentieth century, the omnipresence of jazz music certainly had an influence on clarinet vibrato. Many jazz clarinetists were multi-instrumentalists and most played saxophone. So, oftentimes, saxophone vibrato was carried over on to the clarinet. Therefore, the use of vibrato for jazz clarinet became the norm and remains so to this day.
Ethnic and folk music of that time, especially from Eastern Europe, Turkey, and Greece, often featured the clarinet. Many of these players had no formal training and vibrato came naturally to them as they were imitating the human voice.
In the classical world, it is documented that Richard Mühlfeld (1856-1907), the great German clarinetist for whom Brahms composed his clarinet compositions, used vibrato. Mühlfeld began as a violinist, so it was quite natural for him to carry this tool of expression over to the clarinet. Unfortunately, there are no known recordings of Mühlfeld; so much is left to the imagination.
The great English clarinetist, Reginald Kell (1906-1981) was the true pioneer of clarinet vibrato in classical music. Kell, like Mühlfeld, began as a violinist and his use of vibrato stirred controversy amongst classical clarinetists, many of whom openly criticized him for his free use of vibrato. After serving as principal clarinet in the London Philharmonic, Philharmonia Orchestra, and Royal Philharmonic, Kell became an internationally acclaimed soloist. Some of the greatest conductors of the time praised Kell for his tasteful use of vibrato and encouraged him to continue his personal approach to playing.
In more recent years, leading American classical clarinetists like Harold Wright, Stanley Drucker, and Richard Stoltzman have freely used vibrato, each in an individual and unique way. This has also been the case in a number of players and schools of clarinet teaching from around the world, perhaps most notably in the leading players from the French school of the twentieth century.
The controversy continues today. It is up to posterity to continue or settle this great debate - vibrato or no vibrato? Personally, I enjoy great musicianship, which can be enjoyed with or without vibrato.