If 1,1#, 2, 2# ,......7, 1 is the full 12-notes chromatic scale based on a 7-notes diatonic scale, and
a1, a3 , a5 , a7 is the first chord C1 while
b1, b3, b5, b7 is the 2nd chord C2
The transitional chromatic arpeggio is a choice of notes some from the first line and some of the 2nd line of the
C1: A1, a2,A3 , a4, A5 ,a6, A7
C2: B1, b2, B3, b4, B5, b6, B7
capitals are inside the chords small outside the chords.
Such a pattern applies by substituting different chords transitions C1->C2.
WHAT IS THE SYSTEMATIC RE-HARMONIZATION OF A SONG BY GYPSY JAZZ?
IT IS THE RELATIVIZED HARMONIC REFINMENT.
RELATIVIZED HARMONIC REFINMENT=
1) We substitute a major chord X, with an harmonic pair (Y1,Y2) (harmonic pair means that Y1, Y2 have a distance at the roots an interval of 4th, that is Y1 resolves to Y2, so that usually Y1 is a chord with a 7nth)
2) and so that either Y1 or Y2 is relative to X (melodic relation which means the roots or middle note have a distance an interval of 3rd ) including the case Yi=X, and including 2nd relative (same root but the one major the other minor chord) ,
3) And the other chord to the relative can be major or minor.
An example is converting the chord progression
4M 1M 5M7 1M as a cycle , to the gypsy jazz re-harmonized chord progression as a cycle
(2m, 5M7), (1M, 4maj7), (7dim7, 3M7) , (3m, 6M7).
(See also post 466)
Example the reel Beatrix by Sharon Shannon.
According to this rule, the melodic improviser so as to improvise may assume either a major or a minor or both scale over the 3 chords of the blues.
https://www.youtube.com/watch?v=C8EAAVxvB4A&ab_channel=JamesHargreavesGuitar
According to this rule, at each change of a (major) chord in the blues, the melodic improviser assumes a change of the scale too with root note the root of the (major) chord! Thus he makes 3 transpositions
Actually this rule may go far beyond the 12 bars blues, to any chord progression!
https://www.youtube.com/watch?v=C8EAAVxvB4A&ab_channel=JamesHargreavesGuitar
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).