463. THE PASSEPARTOUT OF IMPROVISATION AND COMPOSITION . RHYTHMIC PATTERNS HARMONIC TRANSITIONS AND MELODIC SHAPES INVARIANTS.

 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).