Born in Rome, to an Italian father and an English mother, Sgambati, who lost his father early, received his early education at Trevi, in Umbria, where he wrote some church music and obtained experience as a singer and conductor. In 1860 he settled in Rome, and took up the work of winning acceptance for the best German music, then little known in Italy. The influence and support of Franz Liszt, who was in Rome from 1861, was naturally of the greatest advantage to him, and concerts were given in which Sgambati conducted as well as played the piano.
His compositions at this period (1864–1865) included a quartet, two piano quintets, an octet, and an overture. He conducted Liszt's Dante Symphony on 26 February 1866 at the opening of the Sala di Dante at the Palazzo Poli, with 27 of Filippo Bigioli's paintings exhibited nearby. He made the acquaintance of Richard Wagner's music for the first time at Munich, whither he travelled in Liszt's company. His first album of songs appeared in 1870 (Schott Music), and his first symphony was played at the Palazzo del Quirinale in 1881; this, as well as a piano concerto, was performed in the course of his first visit to England in 1882; and at his second visit, in 1891, his Sinfonia epitalamio was given at the Philharmonic.
Notable students include pianist and composer Lucia Contini Anselmi.
- Cola di Rienzo Overture (1866)
- Piano Concerto in G minor, Op. 15 (1878–1880)
- Symphony No. 1 in D major, Op. 16 (1880–1881)
- Symphony No. 2 in E flat (1883–1885)
- Piano Quintet No. 1 in F minor, Op. 4 (1866)
- Piano Quintet No. 2 in B-flat, Op. 5
- String Quartet in C-sharp minor, Op. 17 (1882)
- Two Pieces for violin and piano, Op. 24 (1890)
- Gondoliera for violin and piano, Op. 29 (1894)
- Prélude et Fugue, Op. 6
- Deux Études de concert, Op. 10
- Fogli Volanti, Op. 12
- Quatro Pezzi di Swguito, Op. 18
- Suite in B minor, Op. 21
- Pièces Lyriques, Op. 23
- Mélodies poétiques, Op. 36
- Trois morceaux, Op. 42
- Melody from "Orfeo ed Euridice" (Transcription for solo piano of "Dance of the Blessed Spirits" from Gluck's opera)
- Messa da Requiem, Op. 38 (1895–1901)
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