Charles Ives in the context of "Polystylism"

Indeterminacy is a composing approach in which some aspects of a musical work are left open to chance or to the interpreter's free choice. John Cage, a pioneer of indeterminacy, defined it as "the ability of a piece to be performed in substantially different ways".

The earliest significant use of music indeterminacy features is found in many of the compositions of American composer Charles Ives in the early 20th century. Henry Cowell adopted Ives's ideas during the 1930s, in works allowing players to arrange the fragments of music in a number of different possible sequences. Beginning in the early 1950s, the term came to refer to the (mostly American) movement which grew up around Cage. This group included the other members of the New York School. In Europe, following the introduction of the expression "aleatory music" by Werner Meyer-Eppler, the French composer Pierre Boulez was largely responsible for popularizing the term.

The American Academy of Arts and Letters is a 300-member honor society whose goal is to "foster, assist, and sustain excellence" in American literature, music, and art. Its fixed number membership is elected for lifetime appointments. Its headquarters is in the Washington Heights neighborhood of Manhattan in New York City. It shares Audubon Terrace, a Beaux Arts/American Renaissance complex on Broadway between West 155th and 156th Streets, with the Hispanic Society of America and Boricua College.

The academy's galleries are open to the public on a published schedule. Exhibits include an annual exhibition of paintings, sculptures, photographs and works on paper by contemporary artists nominated by its members, and an annual exhibition of works by newly elected members and recipients of honors and awards. A permanent exhibit of the recreated studio of composer Charles Ives was opened in 2014.

David Wallis Reeves (February 14, 1838 – March 8, 1900), also known as D. W. Reeves or Wally Reeves, was an American composer, cornetist, and bandleader. He developed the American march style, later made famous by the likes of John Philip Sousa, and his innovations include adding a countermelody to the American march form in 1876. Sousa called Reeves "The Father of Band Music in America", and stated he wished he himself had written Reeves' "Second Regiment Connecticut National Guard March". Charles Ives also borrowed from the "Second Connecticut" on four occasions.

A tone cluster is a musical chord comprising at least three adjacent tones in a scale. Prototypical tone clusters are based on the chromatic scale and are separated by semitones. For instance, three adjacent piano keys (such as C, C♯, and D) struck simultaneously produce a tone cluster. Variants of the tone cluster include chords comprising adjacent tones separated diatonically, pentatonically, or microtonally. On the piano, such clusters often involve the simultaneous striking of neighboring white or black keys.

The early years of the twentieth century saw tone clusters elevated to central roles in pioneering works by ragtime artists Jelly Roll Morton and Scott Joplin. In the 1910s, two classical avant-gardists, composer-pianists Leo Ornstein and Henry Cowell, were recognized as making the first extensive explorations of the tone cluster. During the same period, Charles Ives employed them in several compositions that were not publicly performed until the late 1920s or 1930s, as did Béla Bartók in the latter decade. Since the mid-20th century, they have prominently featured in the work of composers such as Lou Harrison, Giacinto Scelsi, Alfred Schnittke and Karlheinz Stockhausen, and later Eric Whitacre. Tone clusters also play a significant role in the work of free jazz musicians such as Cecil Taylor, Matthew Shipp, and Kevin Kastning.

In music, a simultaneity is more than one complete musical texture occurring at the same time, rather than in succession. This first appeared in the music of Charles Ives, and is common in the music of Conlon Nancarrow and others.

Elliott Cook Carter Jr. (December 11, 1908 – November 5, 2012) was an American modernist composer who was one of the most respected composers of the second half of the 20th century. He combined elements of European modernism and American "ultra-modernism" into a distinctive style with a personal harmonic and rhythmic language, after an early neoclassical phase. His compositions are performed throughout the world, and include orchestral, chamber music, solo instrumental, and vocal works. Carter was the recipient of many awards – he was twice awarded the Pulitzer Prize for his string quartets. He also wrote the large-scale orchestral triptych Symphonia: sum fluxae pretium spei.

Carter was born in New York City. He developed an interest in modern music in the 1920s. He was later introduced to Charles Ives, and he soon came to appreciate the American ultra-modernists. After studying at Harvard University with Edward Burlingame Hill, Gustav Holst and Walter Piston, he studied with Nadia Boulanger in Paris in the 1930s, then returned to the United States. Carter was productive in his later years, publishing more than 40 works between the ages of 90 and 100, and over 20 more after he turned 100 in 2008. He completed his last work, Epigrams for piano trio, on August 13, 2012.

A quarter tone is a pitch halfway between the usual notes of a chromatic scale or an interval about half as wide (aurally, or logarithmically) as a semitone, which itself is half a whole tone. Quarter tones divide the octave by 50 cents each, and have 24 different pitches.

Quarter tones have their roots in the music of the Middle East and more specifically in Persian traditional music. However, the first evidenced proposal of the equally-tempered quarter tone scale, or 24 equal temperament, was made by 19th-century music theorists Heinrich Richter in 1823 and Mikhail Mishaqa about 1840. Composers who have written music using this scale include: Pierre Boulez, Julián Carrillo, Mildred Couper, George Enescu, Alberto Ginastera, Gérard Grisey, Alois Hába, Thomas Heberer Ljubica Marić, Charles Ives, Tristan Murail, Krzysztof Penderecki, Giacinto Scelsi, Ammar El Sherei, Karlheinz Stockhausen, Tui St. George Tucker, Ivan Wyschnegradsky, Iannis Xenakis, and Seppe Gebruers (See List of quarter tone pieces.)