The earliest theoretical atonal writing was called twelve-tone music.
The meaning of atonal music has undergone some changes. Generally speaking, it now refers to the writing method of abandoning tonal vocabulary in avant-garde classical music. The characteristic of atonality is that tonality must be strictly avoided, so there are many restrictions. In contrast, the looser concept is pan-tonality, that is, it is not bound by tonality vocabulary, but it is also free from atonality vocabulary.
Polyphony means not only tonality, but also that different parts are in different tones (the actual auditory effect may be atonal or overtone). The earliest theoretical atonal writing is called twelve-tone music. Its basic idea is to arrange twelve tones in a regular order and then compose music in this order. This idea was later developed into the rhythm, intensity, expression, range and so on of music.
The parameters should be designed in order in advance, and then written into music in order. This is called sequenceism, or whole sequenceism. Jazz has nothing to do with these, and there is no communication or influence between them. Jazz gradually develops its own style on the basis of traditional classical music and popular music. Even if jazz is atonal sometimes, its thinking is totally different from atonal music.