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)
