Classical music theory is based on the system of Western tonality, which uses a hierarchy of notes and chords to create a sense of tonal center and structure. This system is centered around the major and minor scales, and the chords that are derived from them. Chords are built using a combination of intervals, and they are used to create harmonies and progressions that support the melody.
Jazz theory, on the other hand, is centered around a different system of harmony and chord progressions. Jazz musicians often use extended and altered chords, as well as modes and other scales that are not commonly used in classical music. The chords used in jazz are often more complex and have a wider range of sounds and colors.
Another key difference between jazz and classical music theory is the way in which improvisation is incorporated into the music. In classical music, improvisation is not typically a part of the compositional process, and the written score is considered to be the definitive representation of the music. In jazz, improvisation is a central part of the music, and musicians are expected to be able to improvise within the constraints of the harmony and structure of the piece.
Jazz theory also places a greater emphasis on rhythm and groove. Jazz musicians often use syncopated rhythms and complex meter changes, which are not as common in classical music. They also pay close attention to the way that different rhythms interact with each other, and they use this interaction to create a sense of forward motion and energy in their music.
In conclusion, while jazz theory and classical music theory share some similarities, they are distinct systems of musical thought that have developed differently over time. Jazz theory places a greater emphasis on harmony, improvisation, and rhythm, while classical music theory is centered around the Western tonal system and the written score. It is important to note that these are generalizations and that there is a great deal of overlap and variation within each system.