THROUGH THE USAGE OF ORDERED INVERSION AND SYMMETRICAL GENERATION

Paul Amrod – MicrotonicsFirstly I will clarify the definition of a symmetrical generation. This reflects to what I formerly discussed in regard to sequences built upon the tritone or the augmented triad.
An Example could be as such. Ab – C- Eb- G followed by C – E- G- B and E – G#- B – D#.

The four notes sequenced over the augmented triad can be expanded with modal structures and because of the symmetrical construction, have a inner logic, connecting the modal movement. The modes can be freely constructed if the symmetrical matrix stays intact. An example can be Ab-B-C-D-Eb-E-G followed by Db-E-F-G-A-B-C and finally C-D#-E-F#-G-Ab-B.

Exactly the same idea can be utilized with pure inversions or a generation of inversions also used as a matrix for modal movement. For example, C-F-G-Bb can be followed by C-G-F-D, F-Eb-C-Bb, G-E-D-A and lastly Bb-Ab-Eb-Db. In this example each note is treated as the central point for each inversion. As explained above we can use the ordered inversion as matrixes for controlled transposition.

We can generate a succession of modes as such, C-Eb-F-F#-G-A-Bb- followed by D-F-G-G#-A-B-C, F-G-Bb-B-C-D-Eb, G-A-Bb-C#-D-E-F and finally Bb-Db-Eb-E-F-G-Ab.