After the political and cultural seclusion of the 1950s young Hungarian composers turned to Western European new music. While learning contemporary compositional techniques they were searching for a new Hungarian identity in music. The musicological discourse about new Hungarian music concentrated on the ‘Hungarianness’ of their music too. Composers used Hungarian literary texts, and referred to Hungarian music culture with musical allusions. They inherited the idea of the combination of the up-to-date Western European compositional techniques with the old Hungarian tradition from Kodály and Bartók, i.e. they were aware of the primacy of tradition. György Kurtág’s (1926) concerto for soprano and piano, The Sayings of Péter Bornemisza (1963–1968) represented for Hungarian musicians the paradigmatic example of new Hungarian music, modern and traditional at the same time. It was based on an old Hungarian text from the 16th-century, like Kodály’s Psalmus Hungaricus (1923). The vocal part, however, refers to Webern’s melodic concept, the piano part follows Stockhausen’s piano writing, and Kurtág quotes neither Hungarian folk music nor old Hungarian art music. The paper investigates by means of musical analysis the question why contemporaries felt that Kurtág’s piece represents unambiguously a Hungarian identity. Kurtág — as well as his contemporaries — uses symbols, allusions connected to certain words and word-paintings while concentrating on the picturesque elements of music. The source of this compositional attitude is Kodály’s oeuvre, foremost the Psalmus Hungaricus. From this angle Kurtág’s The Sayings stands for the new-old Hungarian musical tradition.