Sure, absolutely, a song can be composed that has no key. There are songs that are "kind of" in a key, others that are "absolutely not" in a key. This is all in reference to European classical music from about 1880 to 1950. Look at Arnold Schoenberg, Alban Berg, Hugo Wolf. Folk music and popular music is always in a key.
Is it possible to write a song without a key?
2 Answers By Expert Tutors
Marcio P. answered 06/24/19
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Of course there are songs that modulate so often it would almost be silly to relate them to a single key. But a good rule of thumb would be to use the first couple of changes in the song to pinpoint the key. Let's say you have a song that starts with the progression "F-Dm-Gm-C7" , but after only four bars it modulates to a different key, you can still consider that it's in the key of F.
Sometimes it's also useful to write it in the key of C, just because of the key signature, so it makes it easier to read and you have to add less accidentals to the score.
Best!
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