The ensemble was founded in Utrecht (hence Latin trajectina; of Utrecht) in 1974 by Jos van Veldhoven and Jan Nuchelmans. Following the departure of Veldhoven in 1976 to lead the Utrechts Barok Consort, leadership of the ensemble passed to the current director, the musicologist Louis Peter Grijp (b. 1954).
The ensemble has specialised in recovering and sometimes reconstructing Dutch vocal music from the Dutch Golden Age, and much of its discography are of Dutch-language songs which have not been recorded. The ensemble has particularly concentrated on domestic, middle-class, and Dutch-language church music which—unlike the Latin language church music of the Spanish Netherlands—is little known and little researched. The lyrics of the recovered songs often illustrate cultural history, as in the case of the ensemble’s two recordings of Dutch sea shanties.
They have cooperated twice with the poet Gerrit Komrij; the first time in reconstruction of Jacob Obrecht‘s secular works. The original texts to Obrecht’s Dutch songs had been lost, leaving only Dutch incipits as titles of instrumental versions. Komrij wrote new texts in the style of lyrics of Obrecht’s time. A second project based on The Seven Deadly Sins and the Four Last Things of Hieronymus Bosch set new Dutch texts to 16th Century melodies.