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 RELATIVEZED 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 t he 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) , (6m, 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).
VECTORS, WAVES AND SPIKES
https://www.youtube.com/watch?v=kr8XbNHk5QA&ab_channel=SoundGuitarLessonsWithJared
SIMPLICIAL SUBMELODY =1 5 1 4 1
The 3 chord progressions
1M 5M7 1M 4M 1M
6m 3m 6m 2m 6m
4M 1M 4M 7dim 4M
Actually at least 5^3=125 alternative chord progressions for the melody
We can infer that for any harmonic pair of successive notes of the simplicial submelody n1, n2
The corresponding chords are either a) in harmonic relation majors b) in harmonic relation minors
c) In melodic relation from minor to major d) In melodic relation from major to minor
Therefore emotionally the harmonic transition of 2 successive (consecutive) chords of 2 successive (consecutive) notes of the simplicial submelody are one of the 4
1) happy to happy (harmonic transition)
2) sad to sad (harmonic transition)
3) sad to happy (melodic transition)
4) happy to sad (melodic transition).
1) Each harmonic pair (Xi,Yi) is usually alternated many times. This may be with an arpeggio type or more general chromatic arpeggio too (ostinatos).
Thus the melody are cycles with 2 melodic scales defined by each of the chords, with starting and ending persistent note on one of the notes of the chords
If the alternation of the chords of the harmonic pair is fast , the the melodic cycle is of diameter an interval of 4th or 5th. Otherwise it even can be longer than an octave.
2) We may have modulations (mode changes inside the diatonic scale) , but we make have transpositions also (translation of diatonic scale)
3) But the transpositions are of a local character. In other words chromatic, or melodic or harmonic
of the minimum intervals (2nds not 9th-10ths, 3rds not sixths) .
4) We may very well apply the "partida trick" when alternating the chords of the harmonic pair, and use as drone the repetition of their common note. In this way we may cycle with diameter a whole octave!
5) Practically the length of such random paths of harmonic pairs must not be very long, so as to fall in the listening habits of harmony. E.g. up to 3 diatonic scales transpositions that give the full chromatic tonality (all 5 blue notes) as in the folk music of Brazil. But for special compositions they can become long cycles covering 12 root notes etc.
6) The choice of the "state" being an harmonic pair gives high percentage of harmonic transitions in total for the chord progression, making it more beautiful. If the pairs (Xi,Yi) are not harmonic but melodic or chromatic, the chordicaster is called melodic or chromatic. In Latin music dominate the harmonic chordi-casters. In Scandinavian music exist also melodic chordicasters. And in Mediterranean music but also Irish music exist also chromatic chordi-casters.
Mathematically as improvisation it can be considered a stochastic Markov process, with states , that are the harmonic pairs, and transitions that are chromatic (interval of 2nd) , melodic (interval of 3rd) or harmonic (intervals of 4ths or 5ths) shifts of them.
From 12 bars blues, to Keith Jarrett's Ostinatos , and Iannis Xenakis random music, etc this idea is the abstract mathematical and algebraic formulation.
If we utilize the DEA system of chord-shapes in the guitar fretyboard, the process becomes simpler.
This will unlock the playing of chords across all of the guitar fretboard, in a way that when playing with these rules the harmony is always beautiful, what ever we play, while the melodic improvisations very easy familiar and beautiful too.
The harmonic pairs (Xi,Yi) are always (E,A) or (A, D) or (D,E).
An chromatic transition Yi-Xi+1 for the pairs (Xi,Yi), (Xi+1,Yi+1) will be such that
(Xi,Yi) to (Xi+1,Yi+1) is melodic on Xi-Xi+1
And a melodic transition at Yi-Xi+1 will be for the pairs (Xi,Yi), (Xi+1,Yi+1) such that
(Xi,Yi) to (Xi+1,Yi+1) is chromatic transition on Xi-Xi+1
THE LOCAL (CHROMATIC) TRANSITION RULES OF THE CHORDI-CASTER. Because chromatic transitions are always easier to visualize and execute. The rules for melodic or chromatic transitions become, a rule of chromatic transition of the pairs (Xi,Yi), (Xi+1,Yi+1) , either on Xi to Xi+1 of (Xi,Yi) or chromatic on Yi to Xi+1 of (Xi,Yi) correspondingly . The harmonic transitions work cyclically on the shapes E-A-D-E' etc. where D-E' is the usual positions. In an harmonic transition we set Yi=Xi+1. But alternatively it can be converted also to a chromatic shift rule, which is that in the pairs (Xi,Yi), (Xi+1,Yi+1), there is a chromatic transition of a tonal interval of 2nd from Xi to Yi+1.
Given a Chordi-caster as above, the soli-caster of Rory Hoffman (see post 455 ) is easier to create as it is melodic cycles and bridges in harmonic pairs (Xi,Yi) very well familiar from 12 bars blues and simple songs.
Example the Granada by I. Albeniz for guitar where the harmonic pairs are
https://www.youtube.com/watch?v=x4MIAUmW1tc&ab_channel=tubescore.net
(B7-E) (E-A) (G-C) (C-Fm) (C#-F#m) (B7-Em) (Em-Am) (B7-E)