We discuss here the 4-cycle 5M-1M-4M-7bM and the coresponding transitions to harmonic minors triads (which are transition to a major chord a major third higher thus double melodic upper transition (first to the upper relative minor and then to the relative major with the same root) or a minor third lower double melodic lower transition). With these double melodic transition we may smoothly introduce the minorization of the major chords of the triad as well as the majorizations of the minor chords of he scale instead of direct double relative change onthe same root!
The correspondence of the simpler of such two cycles
5M-1M-4M and
3M7-6m-2m
is such that the roots differ by an interval of 3rd thus melodic transition from majors to minors and vice versa.
Once the harmonic minor is added to its original troads of majors , we have also chords for an andalucian cadenza)
1) for the 5M-> to the triad 7M7-3m-6m (harmonic 3 minor, andaluzian cadenza 3m-2M-1M-7M)
2) for the 1M-> to the triad 3M7-6m-2m (harmonic 6 minor, andaluzian cadenza 6m-5M-4M-3M)
3) for the 4M-> to the triad 6M7-2m-5m (harmonic 2 minor, andaluzian cadenza 2m-1M-7bM 6M)
4) for the 7bM-> to the triad 2M7-5m-1m (this involves the blue notes of the 7-notes blues scale and it is also an hamonic 5 minor , andaluzian cadenza 5m-4M-3bM-2M)
On the other hand if we make the double melodic lower transition then we have
1) for the 5M-> to the triad 3M7-6m-2m (harmonic 6 minor, andaluzian cadenza 6m-5M-4M-3M)
2) for the 1M-> to the triad 6M7-2m-5m (harmonic 2 minor, andaluzian cadenza 2m-1M-7bM-6M)
3) for the 4M-> to the triad 2M7-5m-1m (harmonic 5 minor, andaluzian cadenza 5m-4M-3bM 2M)
4) for the 7bM-> to the triad 5M7-1m-4m ( hamonic 1 minor , andaluzian cadenza 1m-7bM-6bM-5M)
If the arc of majors is longer like 7M-3M-6M-2M-(5M-1M-4M-7bM)
Then we add also the upper relative major transitions (upper double melodic)
1) for the 2M-> to the triad 4#M7-7m-3m (harmonic 7 minor, andaluzian cadenza 7m-6M-5M-4#M)
2) for the 6M-> to the triad 1#M7-4#m-7m (harmonic 4# minor, andaluzian cadenza 4#m-3M-2M-1#M)
3) for the 3M-> to the triad 5#M7-1#m-4#m (harmonic 1# minor, andaluzian cadenza 1#m-7M-6M 5#M)
4) for the 7M-> to the triad 2#M7-5#m-1#m ( hamonic 5# minor , andaluzian cadenza 5#m-4#M-3M-2#M)
Of course all the above structure of triads of majors transitioning to triads of major-min-min (harmonic minors) ,is tralslated also in to a structure of pentachords (internal to a chord) and tetrachords (bridge transitioning bewteen chords) which is a structured platformed forthe creation and composition od improvisational melodies. And for major chords the inner pentachords of the chord are called major pentachords while for minor chords minor pentachords. Similarly for augmented and diminished chords , they are called augmanted an diminshed pentachords.
The preVious melodic transitiosn are ofte 2nd order (because e.g. the 1M->3M is in 2 steps 1M->3m and 3m->3M) . Neverthleless there are also 1st order melodic transitions and here we give 3 examples of minorĪ¹zation of the majors
MINORIZATIONS
1) (5M-1M-4M)-> (4m-1M7)
2) (4M-5M-1M)-> (1m-5M7)
1) (1M-4M-5M)-> (5m-2M7)
