Approximately how many songs have been produced in the US and UK since the music industry was born?

This question is too generalized. Even a guess is unlikely to come close because of the sheer number of songs that have actually been produced, let alone published. The Library of Congress or the US Copyright Office might be able to provide some info regarding the number of songs that have been submitted for copyright protection, however you would have to be able to weed out the songs submitted but never actually produced - this will most likely be an astounding number in and of itself.

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A date for the birth of the music industry would need to be determined first. Even with that, one would be trying to count sand grains in a sand castle.

Let use a little math, some averages, and a bit of fun, okay?

On Average, there are 50 albums released every week in the United States of America and the United Kingdom. Thomas Edison invented the phonograph in 1878 but it was always a very poor seller. The first artist to sell serious numbers of records was Frank Sinatra in the 1940 (250,000,000 records in his lifetime), so lets start there!

Lets also assume that there are 12 songs per album.

50 albums per week * 52 weeks = 2500 per year

2500 per year * 69 years = 179,400 unique albums (since 1940)

12 songs * 179,400 albums = 2,152,800 songs

So the average points to about 2,100,000 songs being released in the United States of America and the United Kingdom (and nowhere else) in musical history, give or take.

Further, the industry tended, unlike today, to release singles - with a flip side as well, of course. Some were EP's - with 4 tracks. Albums were not the chief seller: people bought the song. There may have been more "singles" [2 tracks really] released than 50 per week: that I wouldn't know. Working out any possible answer is really quite unviable.

A visit to Gracenote's media database shows 97,206,484 songs in the database. This includes international music, different edits of the same song, and recordings of classical music, but indicates that the 2.1 milllion above may actually be a low estimate.