With Tüür's Requiem (1994) his reputation was made, and soon he became one of the most frequently performed composers in Estonia. Tüür was able to quit teaching and go into music composition on a full-time basis. From this time, increasingly more diatonic elements begin to appear in the works of Tüür, and in addition to this there is a shift of focus from chamber music to orchestral and large choral works. In 2002 he developed a method of composition he called "vectoral writing," a technique that yields harmonic variety through voice leading and the use of a numerical code. Tüür has written a Mass, an oratorio Ante Finum Saeculi, symphonies, concerti, several pieces for orchestra, and a wide variety of chamber works. Tüür's music has been performed by Isabelle van Keulen
, Anu Tali
, Tönu Kaljuste
, David Geringas
, Evelyn Glennie
, Paavo Järvi
, and the California EAR Unit
; and has been recorded to a significant extent, particularly on the ECM
label. The recording of his Piano Concerto and Symphony No. 7 was nominated for Gramophone magazine's 2014 awards.
Tüür is a co-director of the International Contemporary Music Festival NYYD held in Tallinn, and has been honored several times by organizations for his contributions to Estonian culture.