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Quartet pre-recorded Obama music
Cellist Yo-Yo Ma, violinist Itzhak Perlman, pianist Gabriella Montero and clarinettist Anthony McGill did play along - but without being amplified.
Organisers said a late decision to use a recording was made over fears frozen weather could damage instruments.
The version heard around the world was recorded two days earlier, they said.
The musicians, playing John Williams' Air and Simple Gifts, "were very insistent on playing live until it became clear that it would be too cold", said Carole Florman, a spokeswoman for the Joint Congressional Committee on Inaugural Ceremonies.
She said the cold weather could have caused strings to snap, and instruments to crack or go out of tune.
"No-one's trying to fool anybody," she told the New York Times newspaper. "It's not something we would announce, but it's not something we would try to hide," she said.
"This isn't a matter of Milli Vanilli," she added, referring to a pop band that was stripped of a Grammy music award in 1989 because the duo did not sing on their album and lip-synched in concerts.
Ms Florman said that the NBC network, which was handling the television pool of the inauguration ceremony, were told of the likely use of a recording the day before.
Violinist Itzhak Perlman said "it would have been a disaster if we had done it any other way".
"This occasion's got to be perfect. You can't have any slip-ups," he told the New York Times.
Yo-Yo Ma added: "A broken string was not an option. It was wicked cold."
All the other musical performances during the ceremony were live, although Aretha Franklin was accompanied by taped music and additional voices.
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