Since the most detailed ontology is at the melody, then the 3 invariants (rhythmic, harmonic, motion shape) occur as invariants of the melody too.
For years I have
been looking for the most comprehensive and convenient concept for
improvisation and composition from the simplest to the most complex ie starting
from rhythm then harmony then melody. I had found it parts but not in total.
Listening to a young street musician explaining how she improvises a steel
percussion instrument called hand pan that plays also melodies, she flashed my
intuition. ....the most comprehensive concept is something very well known in
mathematics and geometry ......
https://www.youtube.com/watch?v=PEuwaKR0cbY&t=50s&ab_channel=AmyNaylor-HandpanConnect
It is Felix Klein's Erlangen program idea that every geometric structure is defined by the group of transformations that leaves it invariant.Here that every musical structure is defined and created by the rhythmic harmonics and melodic invariants of their variations......This girl said about the repetition of the invariants in improvisation: "repetition is your friend".I called the description of this in the context of music the PASSEPARTOUT of musical improvisation and composition.You keep one of the 3, rhythmic pattern harmony (chords transitions) melodic shape fixed and change the other two and thus you create the music, provided the emotion approves it. You keep the rhythmic pattern constant and change the melodic shape or the harmony (chords transitions) You keep the harmony (chords transitions) constant and change the rhythmic pattern or the melodic shape Keep the melodic shape constant and change the rhythmic pattern or harmony (chords transitions).
