Modern Classical Music
In the 20th century, composers began to experiment more and more with new compositional techniques. Before the 20th century, Western music was almost entirely diatonic: pieces were built using a set of notes known as the major and minor scales. Starting in the 20th century, composers began to make use of other scales, such as the pentatonic and whole-tone scales. Some composers went a step further, and removed the concept of "tonality" altogether: atonal music lacks a tonal centre, and is extremely dissonant as a result.
Examples
Prélude à l'après-midi d'un faune is a symphonic poem by Claude Debussy (1862 - 1918). A symphonic poem is type of program music that is written for orchestra. You can listen to a recording of the piece below. Notice the use of ambiguous tonality throughout the work.
Below is a recording of "Pentatonic Tune", a keyboard piece by Béla Bartók (1881 - 1945). As the name suggests, the piece is built on the pentatonic scale.
Our final example is "Variations for Orchestra", by Arnold Schoenberg (1874 - 1951). Schoenberg uses complete atonality in this piece: the music has no tonal centre, meaning that there is an approximately even distribution of pitches.