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Western music before Berg's time was "tonal," which means that music was composed of established pitches and tone hierarchies. To clarify, let's assume that a piece of music is in the key of A-major. The key defines which tone holds the greatest importance (in this case, "A") and also to a large extent the way in which tones are used in relation to one another. For example, the A-major chord is always formed with the pitches A, C#, and E. In contrast, "atonal" music shows a blatant disregard for these traditional hierarchies. No pitch in atonal music holds a greater importance than other pitches, and no pitches are "more related" to one another simply because of existing hierarchies like the A-major chord.
Serialism takes the concept of atonality one step further. According to serialism, no pitch can be repeated within a piece until all of the other 11 pitches have been used. The word "serial" is used to describe this use of a series of pitches without internal repetition, and a series is also often referred to as a "row." Atonality and serialism represent the two revolutionary concepts for which the Second Viennese School (Schoenberg, Berg, and Webern) was responsible.
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