Set Theory Improvisation

Juampy Juarez presents his original investigations into set theory applied to jazz improvisation — the mathematical system behind the music of Stravinsky, Bartok, Webern, Berg, and Schoenberg, brought onto the guitar and played over blues progressions and familiar cadences.

The class starts from the ground up with integer notation, the nomenclature created by Milton Babbitt that describes pitch sets by semitone count rather than note names. From there, Juampy opens up the 220 possible prime forms — each one a source of new scales, licks, and chords for your playing.

What's covered

• Integer notation explained from scratch: dyads, symmetry, and why no note in a set is more important than another
• Prime forms — the 220 mathematical sets that underlie 20th-century classical language, starting with the 0-1-2 trichord
• Octave displacement for turning small chromatic sets into wide, dissonant atonal intervals
• Building a 12-tone row by moving a trichord in minor thirds, in the tradition of Schoenberg
• Super sets, subsets, and nested pitch fields as improvisational devices
• Applying these sets to tonal situations — using 0-1-2 over C7 in a simple blues

For intermediate and advanced improvisers looking to expand beyond conventional scale-chord vocabulary. Atonal music favors dissonant intervals and wide leaps — this class gives you a structured way to bring those sounds into your own solos. Full video is 1 hour and 11 minutes.