Technically, we wouldn't be celebrating the New Year this week if we lived in most ancient and Medieval societies. Most cultures celebrated the changing of the calendar year around the vernal equinox, March 25th, or another astrologically-important day. But hey, let's get anachronistic and sentimental anyway.
Agrarian societies, like that of Medieval Europe and earlier cultures, usually turned their calendars over during the spring as a way to celebrate the fertility of their land and the end of another winter. Here are a few traditions from around the world with examples of the music that accompanied their celebrations through the millennia.
Babylonia
The Babylonians of ancient Mesopotamia began their annual celebration of the new year around 2,000 B.C. Their tradition was called Akitu. Oddly enough, the Babylonians incorporated a ritual humiliation of their own king during the Akitu festival which included stripping their leader of his royal garments and slapping him around a bit.
The Babylonians believed this pleased their gods and would bring prosperity to their land in the coming year... It sort of sounds like some news channel political comment sections gone awry to me.
Here is some music that these folks may have enjoys while they, um, slapped their monarch around.
https://www.youtube.com/watch?v=DKDFxEcLWi8
Ancient Rome
The Romans can be credited with today's observation of the New Year on January 1st. Their celebration of New Years was originally also on the vernal equinox (March 25th), but their festivities soon took a more religious bent and they chose January 1st to worship their god Janus.
Janus, from which we get the name 'January', was their god of two faces. His persona was said to be an idol for endings and beginnings since he was thought to look both to the past and the future at once, making him an obvious choice for the sentiment of this holiday. Here is a bit of ancient Roman and Etruscan music so you can hear what these ancient people heard as they worked and partied.
(To me, the close intervals and discord seem to suggest that liminal state of past and future.)
https://www.youtube.com/watch?v=SB9ZZ5V1DX8
Ancient Egypt
The ancient Egyptians looked to changes in the stars for the elements of their yearly celebrations. In particular the bright star, known as Sirius today and known to the ancient Egyptians as Sopdet (trans: "She who is"), was anticipated during their New Year since it reappeared after a 70-day absence every year in mid-July. This time coincided with the annual flooding of the Nile, so it seemed like an obvious choice to the Egyptians for celebrating the renewal of their land and calendar.
The ancient art an tradition of the Egyptian ney flute is still popular today. Here is a bit of that musical legacy:
https://www.youtube.com/watch?v=Ac2g5NW9RhU
Chinese New Year
Beginning around 3,000 years ago with the Shang Dynasty, the Chinese New Year is one of the oldest traditions still celebrated today. The 15-day festival occurs in confluence with the bamboo-planting season. Unlike the other traditions mentioned above, the Chinese New Year follows the lunar calendar, thus occurring in late January or early February each year.
Of course, what would the New Years celebration be without fireworks? Following the invention of gunpowder in the 10th Century, the people of China began ringing in the new year with massive displays that continue today around the world.
Here is one of my favorite videos of traditional Chinese music, GuanShanYue 中国古乐---关山月 (trans: "The Moon at the Fortified Pass"):
https://www.youtube.com/watch?v=tuNiVPg_q2I
Medieval Europe
Most of Medieval Europe celebrated New Years on March 25th until the 16th Century. They got away with this admission to their pagan roots by co-opting the equinox with the Feast of the Annunciation of Mary. Typically, if the church could add some officially recognized date to an existing holiday, it sort of saved everyone the trouble of abolishing parties and changing the calendar. And who could blame them? Nobody likes a party pooper.
PS: Check out this guide to Medieval cookery from the British Library!
Additionally, the Feast of the Annunciation was also the biggest holiday on the Medieval calendar. Where we place a great significance on Christmas and New Years today, the people of this time rolled these two major holidays into one giant festivity as the most important Christian holiday of the entire year.
During the later Middle Ages, however, January 1st did make a comeback with the Feast of Fools. This seems to have been some hybrid of our typical New Year celebration with the informality of Mardi Gras or Carnivale. Slaves and servants openly mocked their masters, people publicly cross-dressed, and everyone drank... extensively.
(Want to read a great scholarly work about this banned feast day? Check out: "Carnival in Religion: The Feast of Fools in France," by Ingvild Salid Gilhus in the journal Numen, Vol. 37, Fasc. 1 (Jun., 1990), pp. 24-52. You can access it most easily on JSTOR at jstor.org.)
Of course, this was not tolerated for very long by the Roman Catholic Church. By the 15th Century, the Feast of Fools had been abolished, but in its place in 1582, Pope Gregory XIII established the Gregorian Calendar which placed New Years on January 1st as the Feast of the Circumcision of Christ.
... That's one way to celebrate, I guess.
Today, many European towns still celebrate Medieval traditions such as Epiphany and the Feast of the Annunciation with full parades in anachronistic dress. Here is a taste of how New Year's Day may have looked, and sounded, in Medieval times:
https://www.youtube.com/watch?v=NNXKsUgv3Vg
https://www.youtube.com/watch?v=Rs1Sbwtn14U
https://www.youtube.com/watch?v=doIvP4B1IE4
Happy New Year, Columbus! Here's to making 2016 as fantastic as 2015 with Classical 101.