Jazz is a musical tradition that was born in North American out of the blues. The blues was a musical genre developed within the African American population in the late 19th and early 20th centuries, deriving from work songs sung by slaves.
In jazz, improvisation is heavily relied on to allow the musicians to "speak" and express themselves "in the moment". Jazz is not a style of music that can be tied down by a score.
As the character Sebastian says in this La La Land clip: "every one of these guys is composing, they're rearranging, they're writing and they're playing the melody [....] it's conflict and it's compromise and it's new every time. It's brand new every night and very very exciting!"
Jazz is typically built on these musical features:
Blue notes, which are flattened degrees of the scale to give a bluesy sound and allow the melody to be emotive and expressive. The blues scale is shown below in the key of C.
Swung and syncopated rhythms, to provide an unpredictable and exciting feel.
A walking bass line to provide a sense of momentum and drive
Extended and altered chords to provide a complex sense of depth in the harmony
A repeating open-ended structure. A performance will usually begin with the head, a section where the melody is played. Improvised solos then follow this, for which the same chord progression or changes are used. The head is usually brought back in at the end of the piece.
Oscar Peterson was a famous jazz pianist and his live performance of "C Jam Blues" illustrates the above musical features really well.
He begins the piece with an extended and improvised introduction. At about 0'36, a finger begins to click on beats 2 and 4 of the bar, bringing out the backbeat. This is later joined by the bassist tapping his instrument and the drummer stamping the hi-hat.
At 2'37, the head of C Jam Blues starts. The melody is incredibly simple, notated below, and harmonised using the 12-bar blues. At 3'04, Peterson starts his improvised solo. It is accompanied by a backbeat and a walking bass line and includes some highly virtuosic melodic passages that show off his remarkable skill on the instrument.
Jerome Kern's "All The Things You Are" is a well-known jazz standard. This big band performance by Ella Fitzgerald also uses lots of the musical featured mentioned above including:
a swung metre
syncopated stabs from the brass
improvised fills from the piano
In terms of jazz harmony, chords tend to be extended, which means that they often use not only the 7th, but the 9th, 11th and 13th too (stacking up notes in 3rds).
In addition, some of these notes can be chromatically sharpened or flattened and this makes the chord altered. Common altered chords include flattened 5ths and 9ths as well as sharpened 9ths and 11ths.
These altered chords sound dissonant and can be dark and jarring. A jazz pianist or guitarist would pick and choose how they extend and alter the chords in a performance to allow for individual expression and harmonic colour. The voicing of the chord is also a really important consideration.
The first 16 bars of All The Things You Are have been written out using a selection of altered and extended chords, suggested voicings and a walking bass line. It is worth having a go playing it. Some of these chords are used in the set work.
Jazz harmony is a very complicated area and doesn't need to be understood in depth for GCSE but spotting jazz chords that have been extended/altered is a useful skill.