In the beginning of 19th century, the development of the clarinet was characterized by slow technical progress. The breakthrough came with the construction of Ivan Müller (1786-1854), a German instrument maker and clarinet player who presented his innovations to the Paris Conservatory in 1812. These were:
Although Müller's changes were initially rejected by the Paris Conservatory, Parisian instrument makers eventually adopted the innovations. Two years later, these instruments were already being used at the Conservatory. Müller's innovations quickly spread as the basis of the later clarinet with the German system.
Belgian instrument maker and musician Adolphe Sax (1814-1894) invented the saxophone around 1840, which was an important step for the further development of the clarinet. His student, Eugene Albert (1816-1890), transferred the ring mechanism he had invented to Müller's design. He added two rings to the lower joint of the instrument, and two years later, he added two more rings to the upper joint. The resulting instrument, with over 13 keys and 4 rings, spread under the name of Albert system, also called Simple System. The instrument already had significantly better sound and intonation. Its popularity continued until the mid-20th century. Many famous jazz clarinetists, such as Woody Allen, Raymond Burke, and George Lewis, used this type. Most of them did not switch to the Boehm clarinet, which had already become popular. Jazz clarinetist Edmond Hall expressed his opinion on the Albert system as follows:
"…The tone of an Albert is different for a band. Playin’ with a combination (a six piece dixieland band), I don’t think a Boehm clarinet fits as there. The tone is beautiful and rich and everything, but it hasn’t got the Albert big tone, especially when you get in the low register. You get a bigger tone out of the Albert than you do a Boehm.” ”…It’s agood [sic] instrument. I’ve used it ever since." #1
Munich clarinet virtuoso Carl Baermann (1810-1885) further developed the clarinet. The instrument he envisioned was much more complex than its German predecessors in technical terms. Baermann became familiar with the work of Boehm (see below), which also had a great impact on the instrument he developed. To implement his ideas, Baermann worked with Munich instrument makers, most notably Georg Ottensteiner (1815-1879). Their collaboration led to the Baermann system clarinet in 1860. The term "German clarinet" is also used after Baermann's innovations. Compared to the earlier Müller clarinet, it has the following changes:
Also associated with his name is the publication of the Baermann clarinet school (Vollständige Clarinett-Schule). This work, written between 1864 and 1875, contains the most versatile knowledge and instructions of that time for clarinetists. Since the material goes into detail and is of great use, it is still an important part of clarinet education today.
Robert Stark (1847-1922) played a decisive role in the development of the German clarinet in the 19th century. He wanted to merge the advantages of the Boehm clarinet with the model previously built by Müller. #4
The Berlin instrument maker and musician Oskar Oehler (1858-1936) also rethought the structure of the German clarinet. He made numerous changes to the instrument's bore, mouthpiece construction, and mechanics. #5
The variant he created spread under the name Oehler system and is still used in German-speaking areas today.
 I consider it more likely that the source mistakenly indicated the notes b/f, because according to the fingering chart in Baermann's published work "Vollständige Clarinett-Schule" the c/f key is located on the left side of the clarinet.
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