410. PARTIONING AN HARMONIC CYCLE OF CHORDS IN CONSECUTIVE PAIRS GIVES CHROMATIC SEQUENCES AND PARTIONING IN TRIADS GIVES MELODIC SEQUENCES. APPLICATIONS IN THE COMPOSITION OF MELODIES

 Example 1. let us take as an example the famous song by Saint Preux, concert for one voice. 

1) Structure and size of the melodic theme based in the type of transition of chords, in the singles, pairs or triplets of underlying chords.

2) Sequemce of melodic themes modulating, chromatically (pairs of chords) , melodically (triplets of chords) or harmonically (singles of chords). 

Harmonic cycle partitined in consecutive pairs

1.B   3.A     5. G  7. F      ( Chromatic sequence) 

2.E    4.D     6. C              (Chromatic sequence) 

Or combining the andaluzian cadenze too

   1.A     3. G  5. F        7. E     ( Andaluzian cadenza) 

    2.D     4. C   6. Bb     8. A      ( Andaluzian cadenza) 

From the latter we can get the very nice chord progression for a  song

Am->GM->FM->EM

Dm->CM->BbM->AM

Am->Dm->GM->CM->FM->BbM->EM->Am

Harmonic cycle partitined in consecutive triplets

1.B    4.D     7. F      ( Melodic sequence) 

2.E     5. G                

3.A     6. C                ( Melodic sequence) 

THE NEXT ARE 6 STEPS IN COMP0SING A MELODY SEE ALSO POST 402.

1) CHOSE THE TYPE OF CHROMATIC-TONALITY HARMONY 

2) COMPOSE THE CHORD PROGRESSION AFTER THE CHOSEN CHROMATIC TONALITY

3) PARTITION THE CHORD PROGRESSION TO SINGLETS, PAIRS, TRIPLETS ETC OF CHORDS THAT  WOULD SUPPORT BRIDGING MELODIC THEMES

4) COMPOSE THE SIMPLICIAL SUBMELODY (A DEFAULT IS THE MIDLLE NOTES OF THE CHORDS) . For each partition segment of chords, the last note of the simplicial melody ofthe last chord is the main note of the simplicial submelody for this segment. 

5) COMPOSE THE MOVE OF THE BRIDGING MELODIC THEMES BY THE TRIAD UP-DOWN-STATIONARY BY FOLLOWING PRINCIPLES OF BALANCE AND THE EMOTIONS OF THE UNDERLYING PARTITIONED SEGMENT OF CHORDS. ONE POLARITY FOR EACH PARTITIONED SEGMENT OF CHORDS. E.g. partition segments ending in minor chord may be down-moves and those ending in major chord an up-move. If we assume the x-axis the time and the y-axis the pitch (the simplicial submelody set as basic pitch zero level) we may symbolize a rhythmic melodic bridge with a flag. Glag symmetric to a vertical axis are melodic bridges with inverse rhythmic pattrn. So such arrangments of the melody are like geometric frieze patterns and their 7 types of symmetry (see link below) . Of course most melodies are asymmetric

https://en.wikipedia.org/wiki/Frieze_group

6) COMPOSE THE RHYTHMIC PATTERN OF THE BRIDGING MELODIC THEMES AND THEMSELVES TOO.