Improvisation is the heart and soul of Jazz. It is spontaneous creativity while you play. Jim Hall once said that improvisation creates one minute of music in one minute’s time. Classical music, a more compositional based form, focuses on the interpretation of music composed and notated. Contemporary music allows for more unique personal interpretations of music. Jazz, Blues, Country, Rock etc all have some form of improvisation built into songs. Of all the forms, Jazz is most reliant on improvisation. It has been said that in jazz, a song is just an excuse to improvise.
Jazz improvisation is based on a knowledge of chords, chord progressions and scales. It is, in a sense, composition in which the music created is a one time thing – never to be repeated. It is not notated which is the tradition of composition. One of the most unique aspects of live jazz is the fact that that a specific performance will never be heard again. I think this is one of the most compelling aspects of live performance even as opposed to recordings. Once recorded, the “improvisation” will never change.
In a nutshell, the improviser tries to create and weave a new melody on top of and through the chord progressions which support the song. The chords for the improvisation are often the same chords that support the melody but not all the time. Other approaches to improvisation use a technique called modality or you can create a new chord progression to complement a song.
Connecting the chord tones with scale and arpeggio passages is the most typical starting point for jazz improvisation. Learn your chords – at least 4 part chords such as maj7, 7, m7, dim 7, half dim 7 and +7 in all keys. I call these the “Big Six Jazz Chords”.
Then learn the most important scales : Modes, Harmonic Minor, Jazz Melodic Minor, Diminished, Whole Tone , Blues, Pentatonic. There are many more chords and scales but that will get you started.
Ultimately, this subject is deep enough to easily justify formal study.