The ensemble carries on a tradition established in the 1930's by the pioneer of the classical saxophone and founding member of the quartet Sigurd Raschèr, who animated many composers to write music especially for him. In a similar fashion, the quartet has inspired over 350 composers to dedicate music to them, including, Aho, Berio, Bergman, Bialas, Dean, Denhoff, Donatoni, Firsowa, Franke, Glass, Gubaidulina, Halffter, Kagel, Kaipainen, Kancheli, Keuris, de Raaff, Maros, Moe, Nilsson, Nordgren, Nørgard, Rosenblum, Raskatov, Sandström, Stucky, Terzakis, Tüür, Wuorinen, Xenakis, and Chen Yi. All of these composers have shared an enthusiasm for the four musicians' unique homogeneous tone quality, virtuosity and dynamic interpretation of new and old music. Regarding their interpretation of Bach, the well-known German musicologist Ulrich Dibelius wrote, "When the Raschèr Quartet plays Bach, the music takes on a seraphic aura—as if the organ and the string quartet had come together."
Numerous composers have been fascinated with the combination of the Raschèrs and orchestra, which has resulted in more than 40 new works for that combination as well as invitations from many of the world’s leading orchestras, including the Gewandhaus Leipzig, the Staatskapelle Dresden, the Symphony Orchestra of the Bavarian Radio Orchestra, Bergen Philharmonic, American Composer’s Orchestra, Saint Cecilia National Academy Orchestra Rome, Gulbenkian Orchestra Lisbon, Malaysian National Orchestra, Orchestre de Paris, Pilharmonique Strasbourg, Helsinki Philharmonic Orchestra, Royal Liverpool Philharmonic, Residentie Orchestra of the Hague, Berlin Sinfonie Orchestra, Scottish Chamber Orchestra, Swedish Chamber Orchestra, Philharmonisches Orchester Kiel, Ostrobothnian Chamber Orchestra, Stuttgart Chamber Orchestra, Tapiola Sinfonietta, Camerata Bern, Vienna Symphony, BBC London Symphony, SWR Baden-Baden, MDR Orchestra Leipzig, Radio-Sinfonie-Orchester Stuttgart, Radio-Sinfonie Orchestra Cologne, I Fiamminghi and the Berlin Philharmonic Orchestra under the direction of Sir Simon Rattle.
In addition to the Raschèr Quartet’s numerous solo recitals and collaborations with the world’s leading orchestras, the Quartet has performed with many various instrumental and vocal combinations, including Christain Lindberg, The Kroumata Percussion Ensemble, The London Voices, The West German Radio Choir, The Rias Chamber Choir, The Finnish Radio Choir, The Belgian Radio Choir, The Icelandic National Cathedral Choir, and the Netherlands Chamber Choir. Numerous composers such as Luciano Berio, Erkki-Sven Tüür, Bernd Franke, Stefan Thomas, Giya Kancheli, Maricio Kagel and Sofia Gubaibulina have been inspired to contribute works for the Raschèrs in these combinations. The Raschèr Quartet is a musical democracy. Therefore, in contrast to many other chamber ensembles, the quartet has no leader.