
Hayley H. answered 03/30/19
Teacher Specializing in Music, Special Education, and Math
Yes, this would likely then be considered atonal music, which is music written without a tonal center. In fact, there is much music outside of the Western realm, that does not follow any of our written rules and structures for music. There are often different scales and intervals than we are used to.
As much as we have rules that are followed in Western music, there are just as many songs that break all of those rules so there are certainly songs written without keys, or without the intention of a key, though many theorists are likely to analyze the music and try to make it fit a key even if that is not what the composer intended.