420. FUGA AS PARALLEL MELODIES IN 4 MODES AT SUCCESSIVE MELODIC RELATIONS

 (where at each beat we are almost always about on the same step ofthe mode) 

419. A SYSTEMATIC WAY TO REHARMONIZE WITH MORE CHORDS A SONG IN THE STYLE OF GYPSY JAZZ . CHROMATIC MELODIC AND HARMONIC SPEED (DENSITY) IN CHANGING CHORDS.

 A SYSTEMATIC WAY TO REHARMONIZE WITH MORE CHORDS A SONG IN THE STYLE OF GYPSY JAZZ  BY USING INTERMEDIATE MELODIC OR CHROMATIC RELATIVES OF  THE INITIAL CHORDS AND NEIGHBORING DIMINISHED CHORDS. 

CHROMATIC MELODIC AND HARMONIC SPEED (DENSITY) IN CHANGING CHORDS.

418. The Upper and lower melodic transpositions reverse the triplet of majors to minors (the upper) and the triplet of minors to majors (lower).

417 . THE PARETO DISTRIBUTION IN THE DENSITY OF NOTES AND THE STEHANE GRAPPELLI MELODIC IMPROVISATIONS

416. ΤHE "INHALE" MIXOLYDIAN TETRACHORD AND THE "EXHALE" IONIAN PENTACHORD IN MELODIC IMPROVISATION

 One of the common secrets of an emotionally good melody is that it reflects the inhale-exhale cycle in the human emotional sensitivity. To give relaxation the exhaleing is longer than the inhaling

On the other hand a common harmic cycle in  simple improvisation is the 1M 4M 5M cycle (e.g. in Blues)

When we combine these two cycles at the context of melody, we may divide the 7 notes diatonic scale to the ionian 5-chord 1-2-3-4-5 and the mixolydian tetrachord 5-6-7-1'. As the Ionian is longer it may correspond to the exhaling while the mixolydian to the inhaling. My improvising melodies with this duality and over the chord triad 1M 4M 5M we get the emotional effect of inmhaling exhaling.

415 THE 7 MAIN SUBSTITUTIONS OF A MAJOR CHORD IN THE TRIPLET OF MAJORS 1M, 4M 5M IN IMPROVISATION AND COMPOSITION.

We are here in an assumed improvisatio which alternates the 3 major chords 1M 4M 5M of a diatonic scale, and thus if the melodic theme is within a single chord, we alternate the Ionian, Lydian and Mixolydian modes

The usual 1ST TYPE substitutions are the lower melodic relative chord or major with its major 6th

1M with 6m (Aeolian modulation) 

4M with 2m  (Dorian modulation) 

5M with 3m   (Frygian modulation) 

But it can as well be the 2ND TYPE upper melodic relative chord (substitutes with maj 7nth)

1M with 3m (Frygian modulation) 

4M with 6m  (Aeolian modulation) 

5M with  7d  (Locrian modulation) 

Beaitifull substitutions are THE 3RD TYPE with double relative to an harmonic minor will be

1M with 6M7 which contains the 3-note chord 1#dim

4M with 2M7 which contains the 3-note chord 4#dim

5M with 3M7 which contains the 3-note chord 5#dim

(example of such substitutions is in the famous by Bach prelude in C major  BWV 846 on which it was based also the Ave Maria) 

Or also the 4TH TYPE 

1M with 3M7  which contains the 3-note chord 5#dim

4M with 6M7  which contains the 3-note chord 1#dim

5M with  7M7 which contains the 3-note chord 2#dim

Also the 5TH TYPE 

1M with 1m 

4M with 4m 

5M with  5m 

Also the 6TH TYPE  (usual in Bach) 

1M with 1dim7 

4M with 4dim7

5M with  5dim7

Also the 7TH TYPE  (usual in Bach) 

1M with 1aug

4M with 4aug

5M with  5aug

We cannot stress much the importance of triads of chords (but also of notes intervals and scales) in improvisation.

A good application is to realize that as a diatonic scale is characterized as chords on the wheel by 4ths by its 3 chords on the steps 1M, 4M , 5M  (harmonic triplet of chords) ,  OR 7d 1M 2m (chromatic tripler of chords) the same can apply for the modes of the diatonic scale.

The chords of a mode of a diatonic scale at the steps 1,4,5 (or 7,1, 2) of it characterize its mood.

For example for the mixolydian mode of the diatonic scale from C ,(G, A, B , C, D, E, F, G) the chords at the steps 1,4 ,5 are the G, C, Dm) thus the 1, 2, 5 or I, ii, V of the original ionian and are the base of blues jazz.


Based on this perception, the 7 modes of the diatonic scale have the following chord triads:

(that is chords on their 1st 4th and 5th step, and we symbolize by m=minor M=major d=diminsihed.
Based on this perception, the 7 modes of the diatonic scale have the following chord triads:

(that is chords on their 1st 4th and 5th step, and we symbolize by m=minor M=major d=diminsihed.



1. IONIAN  :  HARMONIC TRIPLET (1M, 4M, 5M) 
2. DORIAN  : HARMONIC TRIPLET (2m, 5M, 6m) (Can be conceived as 5th type substitution) 
3. PHRYGIAN : HARMONIC TRIPLET (3m, 6m, 7d) (Can be conceived as 5th type substitution) 
4. LYDIAN: HARMONIC TRIPLET  (4M, 7d,1M) (Can be conceived as 5th type substitution) 
5. MIXOLYDIAN: HARMONIC TRIPLET  (5M, 1M,2m) (Can be conceived as 5th type substitution) 
6. AEOLIAN: HARMONIC TRIPLET (6m, 2m, 3m) (Can be conceived as 5th type substitution) 
7. LOCRIAN: HARMONIC TRIPLET  (7d, 3m, 4M) (Can be conceived as 5th type substitution) 

We may clasify them according the the major and minor chords

A.ALL 3 MAJOR CHORDS (ALL HAPPY) 

1. IONIAN  :  HARMONIC TRIPLET (1M, 4M, 5M)

B. 2 MAJORS AND ONE MINOR OR DIMINISHED CHORD (ALMOST HAPPY, ALMOST MAJOR)

4. LYDIAN: HARMONIC TRIPLET  (4M, 7d,1M)

5. MIXOLYDIAN: HARMONIC TRIPLET  (5M, 1M,2m)

C.  2 MINORS (OR DIMINISHED) AND ONE MAJOR  (LITTLE SAD,  ALMOST MINOR )

2. DORIAN  : HARMONIC TRIPLET (2m, 5M, 6m)

7. LOCRIAN: HARMONIC TRIPLET  (7d, 3m, 4M)

D. THREE MINORS OR DIMINISHED (ALL SAD) (ALL MINOR) 

3. PHRYGIAN : HARMONIC TRIPLET (3m, 6m, 7d)

6. AEOLIAN: HARMONIC TRIPLET (6m, 2m, 3m)

We may compare the basic harmonic triplets with the basic chromatic triplets (see also post 322)

1. IONIAN  :  CHROMATIC TRIPLET (7d, 1M, 2m)
2. DORIAN  :  CHROMATIC TRIPLET (1M, 2m, 3m )
3. PHRYGIAN : CHROMATIC TRIPLET(2m,3m, 4M)
4. LYDIAN:  CHROMATIC TRIPLET(3m, 4M, 5M)
5. MIXOLYDIAN: CHROMATIC TRIPLET (4M, 5M, 6m)
6. AEOLIAN:  CHROMATIC TRIPLET (5M, 6m, 7d)
7. LOCRIAN:  CHROMATIC TRIPLET (6m, 7d, 1M)



If we want an ordering of how much "minor" and "sad" or "anxious" is a mode and how much "major" and "happy" or "serene" is a mode based on the ordering d<m<M then we get the next partial ordering (non-linear ordering)

PHRYGIAN<AEOLIAN<DORIAN<MIXOLYDIAN<IONIAN

and

LOCRIAN<DORIAN

LYDIAN<MIXOLYDIAN

But the Locrian and Lydian are not comparable with all the others so as to put all of them in a linear order.

Here is a musicological old qualitative description of it, but the names are not the standard but an older version of them (e. mode V is referred in this table as Lydian , while nowadays is named Mixolydian). To realize about which mode is referenced we must look at the 2nd column with the latin numerals.

Based on this concept it is possible to define tunings  of an harmonica (see post 274 ) with these types of triads of chords so as to improvise with the corresponding harmony on each of the 7 modes!

 FOR STEPS IN CREATING A MELODY SEE THE 6 STEPS BELOW AND THE 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.

414. HARMONIC TRANSPOSITIONS VERSUS HARMONIC MODULATIONS

 A transposition is to change the melody and harmony to another diatonic scale with a different root but same mode.

A modulation is to change the mode within the same diatonic scale (e.g. from Ionian to Aeolian, from Ionian to Dorian etc)

A transposition or modulation is called harmonic if the two roots differ by an interval of 5th or 4th

A transposition or modulation is called melodic if the two roots differ by an interval of  3rd

A transposition or modulation is called chromatic if the two roots differ by an interval of  2nd. 

We discuss in the next the advantage and disadvantages of an harmonic transposition versus an harmonic modulation.