In the mid-1980s her career really started to take off outside the Soviet Union. In 1985 the West-Deutscher Rundfunk produced a studio recording of Perception that was broadcast in January 1986. Also in 1985 the Berliner Festwochen commissioned a new orchestral piece. The result was Stimmen ... verstummen, a symphony in 12 movements based on numerical proportions and silence--one movement is a silent solo for conductor. Here is a performance by the Royal Stockholm Philharmonic Orchestra conducted by Gennady Rozhdestvensky, the dedicatee:
In July of 1986 Gubaidulina made her second trip to the West to attend the Lockenhaus Festival near Vienna in Austria. The two composers featured in the festival were Schubert and Gubaidulina whose Perception was given its concert premiere. In September 1986 Stimmen ... verstummen was premiered in Berlin. On this occasion Gubaidulina met and received praise from a number of Western composers including especially Luigi Nono who was very impressed with her music. In 1988 Stimmen ... verstummen received premieres in London and Denmark. The big year of 1986 also saw Gubaidulina attending the big contemporary festival in Huddersfield, UK. On this occasion she met some English composers for the first time including Peter Maxwell Davies and Oliver Knussen.
1987 saw Gubaidulina visit Cologne where her Hommage à T. S. Eliot was premiered. This is a work for soprano and octet in seven movements inspired by the Four Quartets of T. S. Eliot, one of the greatest poetic works in English of the 20th century. Here is a performance of the first four movements, credits in the YouTube description: