The year 1678 in music involved some significant events.

• January 2 – Public opera in Hamburg begins when the Oper am Gänsemarkt is inaugurated with a performance of Johann Theile's biblical Singspiel Adam und Eva.
• May 4 – André Campra begins ecclesiastical studies at the age of 17.^[1]
• June 19 – Guillaume-Gabriel Nivers is appointed to join Nicolas Lebègue, Jacques Thomelin and Jean Buterne as an organists of the Chapelle Royale at the French court.
• John Blow becomes a doctor of music.
• Seventeen-year-old Giacomo Antonio Perti composes his first opera.
• The Teatro Grimani is constructed, the grandest opera house in Venice.

• Albertus Bryne – 5 dance movements^{[clarification needed]}
• Henry Purcell – 3 Parts upon a Ground, Z.731^{[2][failed verification]}
• Giovanni Buonaventura Viviani – Capricci armonici da chiesa e da camera, Op.4
• Bernardo Pasquini – Sant'Agnese
• Giovanni Paolo Colonna – Il transito di S. Giuseppe

• Jean-Baptiste Lully
  • Psyche
  • Bellérophon, LWV 57
• Johann Theile – Der erschaffene, gefallene und aufgerichtete Mensch.
• Carlo Pallavicino – Il Vespasiano
• Giovanni Maria Bononcini – Astianatte
• La Despina, Agnelli, Milano 1678, performed in Milan.

• March 4 – Antonio Vivaldi, composer (died 1741)
• July 6 – Nicola Francesco Haym, opera librettist and composer (died 1727)
• December 30 – William Croft, organist and composer (died 1727)
• probable – Manuel de Zumaya, composer (died 1755)

• March – Jacques Hardel, harpsichordist and composer
• August 5 – Juan García de Zéspedes, composer (born 1619)
• September 28 – Maurizio Cazzati, Italian composer (born 1616)
• November 18 – Giovanni Maria Bononcini, violinist and composer
• date unknown
  • Leonora Duarte, composer
  • John Jenkins, composer (born 1592)
• probable – Chiara Margarita Cozzolani, Benedictine nun and composer (born 1602)