1. To the uninitiated listener, atonal music can sound like chaotic, random noise.
2. Atonality is a condition of music in which the constructs of the music do not ‘live’ within the confines of a particular key signature, scale, or mode.
3. After you realize the amount of knowledge, skill, and technical expertise required to compose or perform it, your tune may change, so to speak.
4. However, atonality is one of the most important movements in 20th century music.

After reading all the sentences , it can be inferred that though atonal music can sometimes sound random and chaotic, there is a lot of knowledge and skill that is required to perform atonal music. 

Sentence 2 talks about what exactly atonal music is. Hence, this sentence must be the first sentence of the paragraph. Sentence 1 talks about the misconceptions of atonal music that the uninitiated make. This sentence must be the second sentence of the passage. Sentence 4, now clears the misconception about atonality and states that it is one of the most important movements in music. Sentence 3 gives the reason why atonality is music is so difficult to attain and says that the untrained listener would change his mind when he understands the amount of knowledge and skill required to produce atonality. Therefore, sentences 4 and 3 form a block. 

Therefore the correct sequence of sentences is 2-1-4-3.