J. S. Bach's Air on a G-string, from his 3rd orchestral suite in D major, BWV 1068.
FAQ

Q: Where can I get free sheet music for this piece?
A: The score in the video can be downloaded from here:
musanim.com/pdf/air.pdf
And here's a piano arrangement of it
musanim.com/pdf/AirOnAShoeString.pdf
musanim.com/pdf/AirOnAShoeString_5thdown.pdf

Q: Who is performing?
A: I licensed this recording from Premium Beat; it is performed by the "Apollo Symphony Orchestra" which is just a catch-all name for "various European music orchestras with professional classical musicians and singers." In other words, I don't know, and the people who licensed the recording to me won't tell me.

Q: What does this have to do with a g-string?
A: The short answer is that many people know it by the name "Air on the G-string," so I put it in the title to help people find it. You can read more about this here:
en.wikipedia.org/wiki/Air_on_the_g_string

Q: What is the real name of this piece?
A: It is the second movement of Bach's Orchestral Suite No. 3 in D major, titled "Aria" ("Air" is the English word for "aria").

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