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Ignazio Cirri or Giacomo Matteo Ignazio Cirri (20 September 1711 – 13 July 1787) was an Italian organist and composer in the 18th century. He was born and died in Forlì (current Emilia-Romagna). He was a friend of Giovanni Battista Martini, who had a portrait of Ignazio Cirri among his valuable men's portraits. In 1759, he became Maestro di cappella in the Cathedral of Forlì and he was admitted in the Philharmonic Academy of Bologna.
- Dodici Sonate per l'organo, Op. 1, published in London
- Six Sonatas for the Harpsichord with an accompanyment for a Violin, Op. 2, also published in London.
- A lot of works are unpublished: the manuscripts are kept in the archive of the Cathedral of Forlì.
- Ignazio Cirri, Dodici Sonate per l'Organo, played by Andrea Macinanti and Francesco Tasini; organs by Gaetano Callido in the Cathedral of Forlì, La Bottega Discantica, 26.