Jazz improvisation in the context of "Billie Holiday"

Jazz is a music genre that originated in the African-American communities of New Orleans, Louisiana, in the late 19th and early 20th centuries. Its roots are in blues, ragtime, European harmony, African rhythmic rituals, spirituals, hymns, marches, vaudeville song, and dance music. Since the 1920s Jazz Age, it has been recognized as a major form of musical expression in traditional and popular music. Jazz is characterized by swing and blue notes, complex chords, call and response vocals, polyrhythms and improvisation.

As jazz spread around the world, it drew on national, regional, and local musical cultures, which gave rise to different styles. New Orleans jazz began in the early 1910s, combining earlier brass band marches, French quadrilles, biguine, ragtime and blues with collective polyphonic improvisation. However, jazz did not begin as a single musical tradition in New Orleans or elsewhere. In the 1930s, arranged dance-oriented swing big bands, Kansas City jazz (a hard-swinging, bluesy, improvisational style), and gypsy jazz (a style that emphasized musette waltzes) were the prominent styles. Bebop emerged in the 1940s, shifting jazz from danceable popular music toward a more challenging "musician's music" which was played at faster tempos and used more chord-based improvisation. Cool jazz developed near the end of the 1940s, introducing calmer, smoother sounds and long, linear melodic lines.

Jazz fusion (also known as jazz rock, jazz-rock fusion, or simply fusion) is a popular music genre that developed in the late 1960s when musicians combined jazz harmony and improvisation with rock music, funk, and rhythm and blues. Electric guitars and basses, amplifiers, and keyboard instruments (including electric pianos and organs) that were popular in rock began to be used by jazz musicians, particularly those who had grown up listening to rock and roll.

Jazz fusion arrangements vary in complexity. Some employ groove-based vamps fixed to a single key or a single chord with a simple, repeated melody. Others use elaborate chord progressions, unconventional time signatures, or melodies with counter-melodies, in a similar fashion to progressive rock. These arrangements, whether simple or complex, typically include improvised sections that can vary in length, much like in other forms of jazz.

Bebop or bop is a style of jazz developed in the early to mid-1940s in the United States. It is characterized by a fast tempo, complex chord progressions—with rapid chord changes, changes of key, and substitute chords—along with virtuosic improvisation based on a combination of harmonic structure, scales, and occasional references to the melody.

Bebop developed as the younger generation of jazz musicians expanded the creative possibilities of jazz beyond the popular, dance-oriented swing music-style to a new "musician's music" that was not as danceable and demanded close listening. As bebop was not intended for dancing, it enabled the musicians to play at faster tempos. Bebop musicians explored advanced harmonies, complex syncopation, altered chords, extended chords, chord substitutions, asymmetrical phrasing, and intricate melodies. Bebop groups used rhythm sections in a way that expanded their role. Whereas the key ensemble of the swing music era was the big band of 16–18 musicians playing in an ensemble-based style, the classic bebop group was a small combo that consisted of saxophone (alto or tenor), trumpet, piano, guitar, double bass, and drums playing music in which the ensemble played a supportive role for soloists. Rather than play heavily arranged music, bebop musicians typically played the melody of a composition (called the "head") with the accompaniment of the rhythm section, followed by a section in which each of the performers improvised a solo, then returned to the melody at the end of the composition.

A transposing instrument is a musical instrument for which music notation is not written at concert pitch (concert pitch is the pitch on a non-transposing instrument such as the piano). For example, playing a written middle C on a transposing instrument produces a pitch other than middle C; that sounding pitch identifies the interval of transposition when describing the instrument. Playing a written C on clarinet or soprano saxophone produces a concert B♭ (i.e. B♭ at concert pitch), so these are referred to as B♭ instruments. Providing transposed music for these instruments is a convention of musical notation. The instruments do not transpose the music; rather, their music is written at a transposed pitch. Where chords are indicated for improvisation they are also written in the appropriate transposed form.

For some instruments, a written C sounds as a C but is in a different octave; these instruments are said to transpose "at the octave". Pitches on the double bass sound an octave lower than written, while those on the piccolo and celesta sound an octave higher, and those on the glockenspiel sound two octaves higher.

In music and jazz improvisation, a melodic pattern (or motive) is a cell or germ serving as the basis for repetitive pattern. It is a figure that can be used with any scale. It is used primarily for solos because, when practiced enough, it can be extremely useful when improvising. "Sequence" refers to the repetition of a part at a higher or lower pitch, and melodic sequence is differentiated from harmonic sequence. One example of melodic motive and sequence are the pitches of the first line, "Send her victorious," repeated, a step lower, in the second line, "Happy and glorious," from "God Save the Queen".

"A melodic pattern is just what the name implies: a melody with some sort of fixed pattern to it." "The strong theme or motive is stated. It is repeated more or less exactly, but at a different pitch level."

Free jazz (also known as free form jazz) is a style of avant-garde jazz or an experimental approach to jazz improvisation that developed in the late 1950s and early 1960s, when musicians attempted to change or break down jazz conventions, such as regular tempos, tones, and chord changes. Musicians during this period believed that the bebop and modal jazz that had been played before them was too limiting, and became preoccupied with creating something new. The term "free jazz" was drawn from the 1960 Ornette Coleman recording Free Jazz: A Collective Improvisation. Europeans tend to favor the term "free improvisation". Others have used "modern jazz", "creative music", and "art music".

The ambiguity of free jazz presents problems of definition. Although it is usually played by small groups or individuals, free jazz big bands have existed. Although musicians and critics claim it is innovative and forward-looking, it draws on early styles of jazz and has been described as an attempt to return to primitive, often religious, roots. Although jazz is an American invention, free jazz musicians drew heavily from world music and ethnic music traditions from around the world. Sometimes they played African or Asian instruments, unusual instruments, or invented their own. They emphasized emotional intensity and sound for its own sake, exploring timbre.