I'm pretty sure, a lot of people has already asked this question, but after spending a few time with google, I still don't konw the good answer.
The size of common music sheets is a bit larger than A4, but
Q1: what is this size exactly, and
Q2: why is it used instead of A4 or US Letter?
I guess the answer is "because of tradition", but it may has a more interesting reason / story.
If any of You knows something about this, please tell me.
In the past it has been whatever the publisher wished to use. There has never been one standard size to my knowledge. In todays present music market, althoguh you will see lots of 8-1/2 x 11 which is a common readily available size for our computers it is not common for the major publishers. To use A4 or US letter doesn't allow you to put much on the page without scrunching things down. Music writting is an art in itself and needs proper space to be seen.
Paper used for publishing music is not categorized under your common typical paper sizes you find down at the mega market paper store (Staples, Office Depot, etc). It is categorized under book paper sizes. When printing a large number of parts the printing is done on large papers and then folded, and then cut and trimmed. When I was in college music writing class we used a size called "Imperial Folio", folded in half gave you 4 pages of manuscript paper 21"high by 14" wide after trimming. One of my professors used to write everything out on Onion skin manuscript paper. There is nothing like the feel or using the proper ink on a large sheet of onion skin manuscript paper. It's heaven.
Much of the published music I have laying around my house this morning seems to be "Medium Folio" or "Demy Folio".
So the answer is not so much tradition but rather book sizing based on the printing equipment being used and the aesthetics of the publisher.
Thank You very much for Your long and exciting answer!
Now, I have here my sheets, that I'm using at the moment. All of them is roughly 22.8 cm X 30 cm, which is 9" X 11.8". This is like the medium quatro. However, I guess I should count a whole sheet (so the double of it), that is 18" x 11.8" according to my measure, which is the medium folio, that You mentioned.