Here is a part of a letter written by Pliny the Younger to his wife's aunt, in which he praises his wife:
"She even sets my poems to music and sings them, to the accompaniment of a lyre. No musician has taught her, but love itself, the best of instructors."
Martial describes what a dinner at his house would be like, down to the music:
"I will provide entertainment which is neither serious nor frivolous: you will hear the music of a small flute."
Another view of dinner music comes from Petronius in his novel the Satyricon. Here, however, the music is used as a way to illustrate the ostentatious behavior of the host:
"We were about halfway through some very elegant hors d'oeuvres when Trimalchio himself was carried in to the sound of orchestra music and placed on a pile of pillows. This spectacle surprised us and made us laugh."
In addition to dinner entertainment, music was also performed at special programs. There were musical concerts that included lyre playing as well as singing. These were not as popular as mimes and plays, however. The oriental music of foreigners could be criticized, as it was here by Juvenal, who cries out against the Greeks and Syrians for a list of reasons, into which he lumps their musical instruments:
"For a long time Syrian Orontes has poured its sewage into our Tiber -
Its language, its customs, its flutes, its string instruments, its foreign
Tambourines, and the prostitutes who are sent to hang out at the race track."
Music was also used at times in initiations and rites of which some Romans disapproved. For instance, Livy speaks about the initiates of Bacchus committing evil deeds which were obscured by music:
"Many outrages were attempted through fraud, more through violence.
The violence was concealed, however, because the shrieks of those
Tortured by deviant sex or murder could not be heard over the loud
Wails and the crash of drums and cymbals."
Here, the poet Lucretius describes a procession in honor of Cybele, Magna Mater:
"In processions, tightly stretched drums thunder out as they are struck by
The hands of her attendants. Curved cymbals clash, and horns threaten
With their harsh wailing. And the hollow flute stirs the heart with
Finally, here is a description of an initiation into the cult of Isis, an Egyptian goddess who came to be worshiped in Rome. This account was written by Apuleius, and is found in his novel The Golden Ass:
"…Flutes and pipes and piccolos sounded a very soothing harmony.
An attractive choir of carefully chosen boys, radiant in their white
Vestments, followed, singing a hymn which had been composed by
a skillful poet, inspired by the Muses, and which explained the
processional rites of this important ceremony. Then came the pipe
players dedicated to the cult of mighty Serapis. Holding their pipes
out to the side, toward their right ears, they played a tune usually
heard in a temple, by the god."
All of the above are words of the ancient Romans themselves, describing how and when music was used.
If you are interested in ancient Roman music, also see this post about a new classics doctorate that encompasses ancient Greek and Roman music as part of the degree.