Alright, I’ll give this one a go, this is my first real attempt at answering one of these questions on this sub, so bear with me folks! :)

Though there have been earlier pieces of music found (such as the Sumerian hymn mentioned below in the comments) the earliest known piece in Western tradition (and usually taught in Music History classes at least) is from a Greek gravestone, which scholars today call the “Epitaph of Seikilos”. (Spellings differ, depending on the translation. In general, we do know what these early pieces sound like, though the system of rhythmic notation we use today didn’t pop up until about the 12th or 13th centuries I believe, with the Notre Dame school in Paris. Before this, only pitch was notated by composers, and many learned simply through oral tradition.

Because we can’t know exactly how some of these pieces sounded due to the fact that notation simply didn’t exist to put all the details together, and the fact that we simply don’t know some of the tuning systems that were used, there aren’t a lot of recordings of these pieces being performed. However, some musicologists do try to put together a “best guess” of what the pieces may have sounded like. (Sorry guys, I know I’m oversimplifying quite a bit!) HERE is one example of the Epitaph of Seikilos being performed.

Now, moving on to my field of “expertise” - I have a Bachelor’s in Music/Music Technology, so I’m using that term loosely - for what we CAN hear:

Early recordings started in the 19th century, with a device developed by Edouard-Leon Scott de Martinville that he referred to as the “phonautograph” that basically cut some patterns into soot on paper by a needle. Apparently, some scientists actually were able to convert the patterns back into sound by scanning the soot stained paper into a computer, and digitally decoded it back into sound. (The recordings were simply of Martinville humming “Au clair de la Lune”.)

Skip forward a little bit, we get Thomas Edison who develops the phonograph in the late 1870s, this leads to what we would consider “modern recording”. (Note that these were on wax cylinder, not vinyl disc.)

SO that brings us to the evening of June 29, 1888 at the Crystal Palace Handel Festival. This is the earliest known real commercial recording of a piece of music that you can hear. The piece was called “Israel in Egypt” and was performed by several thousand singers (yes, thousand) singers conducted by August Manns. You can still easily find this recording floating YouTube and what not.

Hope that kind of answers your question, sorry if I went off on a bit of a tangent!

A sumerian hymn written 3400 years ago - the notes were deciphered by Prof. Anne Draffkorn Kilmer from cuneiform tablets.

http://www.openculture.com/2014/07/the-oldest-song-in-the-world.html

Listen on youtube:

https://www.youtube.com/watch?v=Brvy4BbK2ZQ

Werner Herzog's delightfully quirky documentary Cave of Forgotten Dreams has a researcher using a replica of a bone flute found in the Chauvet caves (about 30-40000 years old). https://www.youtube.com/watch?v=yUCBBDV2Tzk