Chromaticism & Tonnetz

A combination of the Chromatic Circle and the Euler Tonnetz. Use the circle to visualize the interval pattern of a scale — half step, whole step, half step, and so on. Simply enter any scale into the Tonnetz, for example one derived from two harmonies, and then read its interval structure directly from the circle.

Note: Notes are always entered manually.

The reverse approach is equally valuable. Create a collection of notes on the Chromatic Circle based on semitone relationships and transfer it to the Tonnetz to reveal the harmonic structures it contains.

Used together, these two tools open up a wide range of new harmonic possibilities on your instrument — not only for improvisation, but also for voicings, accompaniment, and composition.

Example

From Hexatonic Structures
to Dominant Chords

The following example illustrates how rearranging the notes of two triads—such as Em and Fm—can reveal additional triad pair interpretations, including C + Fdim and E + Csus4.

Even though all of these structures are derived from the same hexatonic collection, they can produce distinctly different melodic and improvisational results.

For example, there is a noticeable difference in sound between playing a line based entirely on Em + Fm over a G13b9 chord and combining Em + Fm with C + Fdim. While the note pool remains unchanged, the different triad pair groupings create new contours, accents, and harmonic colors within the line.

From Hexatonic Structures to Dominant Chords

The current Amazon edition of the book contains numerous examples that showcase creative discoveries within hexatonic structures and the Tonnetz, revealing new possibilities for harmony, voicings, and improvisation.