Neoclassicism as it relates to music refers to a period of time in the 20th century, specifically between 1920 and 1950, or roughly between the first and second World Wars. During this period, composers sought to revisit earlier musical principles. Composers were primarily concerned with the principles of music common in the classical period, but also reexamined ideals from other musical periods such as the Baroque and Renaissance.
Music of the Classical period was founded largely on aesthetic concepts such as emotional restraint, balance and order. These principals contrasted the concepts of the Romantic period, in which composers sought to use music to the emotional extreme. They also differed from the concepts within the music of the early 1900s, which was largely experimental. Neoclassical composers did not want to completely eliminate non-classical principles because they felt those concepts were in fact still worthwhile, but they did want to show a respect for old styles and put some basic boundaries on music to make it approachable and understandable. Thus, neoclassical composers combined classical concepts with the musical advances that had occurred to create an entirely distinct compositional philosophy.
Three elements emphasized in musical neoclassicism were rhythm, counterpoint and tonality. With jazz as a major influence, neoclassical composers frequently incorporated additive rhythm and syncopation. Additive rhythm is where the rhythmic feel contrasts with how the music is barred or measured, while syncopation is the placement of emphasis on a subdivision of a beat. Counterpoint, an element common in the Baroque period and perfected in the music of J.S. Bach, refers to two or more voices that complement each other but which are rhythmically and melodically independent. Tonality is the formation of pitch relationships based on a single key or tonal center.
Neoclassicism developed along two major lines in Europe, French and German. Supporters of French neoclassicism included composers such as Erik Satie and Igor Stravinsky. On the German side were composers such as Paul Hindemith and Ferruccio Busoni. In the United States, major composers such as Nadia Boulanger and even "atonal" Arnold Schoenberg passed on neoclassical ideas from these leaders to musicians such as Aaron Copland and Alban Berg.
Neoclassicism is truly a musical philosophy involving the desire to return to what composers have done before. This means that a composer born after World War II still can be categorized as neoclassical, and that composers cannot be pigeon-holed based on dates alone. Furthermore, composers often change their compositional approach as they learn and are exposed to new ideas, meaning that some composers went or may go through neoclassical phases in their composition.