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. 

413. THE VERY SIMPLE CONCEPT OF CHORD-MODULATION OF A MELODIC THEME OVER 2 OR 3 CHORDS BY CHANGING THE UNDERLYING CHORDS

 This is a very simple and very usefull in improvisation and composition concept of chord-modulation , which is different from the concept of modulation by changinf the modes of the scale, and thus cahnging the melody.

E.g. Let a say that the melody are the notes x1, x2, x3 x4 x5 x6 over the chords A=(a1,a2,a3)  and B=(b1,b2b3)  with x1=a1, x3=a3, x4=b1, x6=b3. 

We changethe chords A , B to A'=(a'1,a'2,a'3) B'=(b'1,b'2,b'3) . Then modulating the same melodic theme over the new chords means that we keep the pitch order relations and rhythm of the new melodic theme but we change the notes so that now it fits the new chords. Most probaly the a1 to a'1 , a3 to a'3 , b1 to b'1 and b3 to b'3. 

This concepts allows to create nice melodies once a) the chord progression is predetermined b) an initial melodic theme has been created over a pair or triple of chords.

There are mainly 3 rules for the creation of melodic themes

1) Utlize 2 or 3 consecutive chords for none melodic theme

2) Make it connected by 2nds inside the main scale to give it naturality of singing

3) If one more of the 2 pr 3 chords are chromatic relative to the main scale make the melody pass from the external to the diatonic scale chromatic notes of the chords.

Here are 6 rules 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) 

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. 

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

412 THE MOST COMMON IN BRAZIL FULL CHROMATIC TONALITY OF 12 NOTES THROUGH 3 DIATONIC SCALES IN HARMONIC RELATION

 3 Diatonic scales in harmonic relation e.g.

G, C F.

Chords from the 3 diatonic scales  the numbers are the notes of the middle diatonic scale

G      7m      2M                      4#M

C           1M 2m 3m (3M7) 4m 5M 6m 

F                                               5m     7b M

Thus 6 chromatic chords

3M7,  5m, 7b M, 7m,  2M 4#M

2 ofthem are with roots outside the middle diatonic scale.

There are mainly 3 rules for the creation of melodic themes

1) Utlize 2 or 3 consecutive chords for none melodic theme

2) Make it connected by 2nds inside the main scale to give it naturality of singing

3) If one more of the 2 pr 3 chords are chromatic relative to the main scale make the melody pass from the external to the diatonic scale chromatic notes of the chords.

Basic Jazz Chord Progressions

·        Major ii-V-I  (2m-5M-1M) . The major ii-V-I is easily the most important chord progression to get a handle on when it comes to jazz. ...

·        Minor ii-V-i. This chord progression has the same function as the previous major ii-V-I, but of course is in a minor key. ... (In 6 Aeolian mode would give the chords 7m 3M 6m  and in the Ionian mode it would be 2m  5M  1m )

·        Major I-vi-ii-V. ...(1M-4m-2m-5M)

·        Minor i-vi-ii-V. (In 6 Aeolian mode would give the chords 6m 2m 7m 3M and in the Ionan mode it would be 1m 4m 2m 5M)

The next is an example of a chord progression for a song with full chromatic harmony based on 3 diatonic scales in harmonic relation e.g. G major C major F major

Here is an example of a paritioned chord progression with chords from 3 tonalities related harmonically (this is common inthe harmony of brazilian songs) e.g. C-F-G.

I have improvised at first these chords inthe ukulele,soI that i like them and make the necesary corections

The melodic phrase chords are 3 , and I write the chord progression so that each line is a traid of melodic phrase chords. 

For simplicity all chords have the same duration

1st verse minor feeling, the translation of t he melodic theme is upwards. It is inthe tonalitis C and  F (with harmonic minors)

Dm      E7      Am

Gm      A7      Dm

1st chorus resolution to a major triad, which is alower shift ofthe melodic theme

Bb       C7       F

Here the next verse moves to the tonality G

E7       Am        Am

B7       E7          Am

Again a chorus resolution to major triads of the toanlity G

C        B7         G

Am   D7          G

Chromatic shift to the 7nth degree of the toanlity G as a new verse

F#7    Bm     Bm

B7     Em      Em

And a resolution to tonal of G tonality

D7      G        G

Now we add the simplicial submelody notes of the melody , one note per chord

We try it in a convenient instrument . I did so in the ukulelel and also on the digital ukulele (Geoshred) in the tablet.  I try to whistle also  threr simplicial submelody

1st verse minor feeling, the translation of t he melodic theme is upwards. It is inthe tonalitis C and  F (with harmonic minors)

Dm  (f5)     E7  (g#4)     Am (c5)

Gm   (Bb5)   A7  (c#5)    Dm  (f5)

1st chorus resolution to a major triad, which is alower shift ofthe melodic theme

Bb  (d5)     C7   (e5)    F (a4)

Here the next verse moves to the tonality G

E7  (e5)     Am    (a5)    Am  (a4)

B7   (f#5)    E7    (g#5)      Am  (e6)

Again a chorus resolution to major triads of the toanlity G

C   (e5)     B7    (d#5)     G  (b4)

Am  (c5)    D7   (f#5)       G  (g5)

Chromatic shift to the 7nth degree of the toanlity G as a new verse

F#7   (F#5)  Bm   (b4)   Bm  (b4)

B7    (f#5) Em   (b5)     Em  (B5) 

And a resolution to tonal of G tonality

D7  (d5)    G (g4)       G (g4)

Finally we write all these in a midi editor and and we enhance the simplicial submelody to an actually rhythmic melody with transition notes also outside the chords. 

In this way it is as if we write a text first fromthe verbs then the subject  and obkect ofthe verb and then the relations of the phrases. 

Here si another example

https://www.youtube.com/watch?v=4JHA1SIJkNM&ab_channel=DrKCostas

411. THE MOST COMMON FULL CHROMATIC TONALITY WITH ALL 12 NOTES AND 5 CHROMATIC CHORDS WITH ROOTS IN THE DIATONIC SCALE

 

6 Diatonic chards= 1M 2m 3m 4M 5M 6m

5 Chromatic chords=3M7 (from harmonic minor) 6M7 , 7M7 (from double harmonic minor)  5m

it contains all 5 blue or chromatic notes

 5# from the 3M7

2# from the 7M7

1# from the 6M

4# from 7M7 

7b= from 5m 

There are mainly 3 rules for the creation of melodic themes

1) Utlize 2 or 3 consecutive chords for none melodic theme

2) Make it connected by 2nds inside the main scale to give it naturality of singing

3) If one more of the 2 pr 3 chords are chromatic relative to the main scale make the melody pass from the external to the diatonic scale chromatic notes of the chords.

Basic Jazz Chord Progressions

·        Major ii-V-I  (2m-5M-1M) . The major ii-V-I is easily the most important chord progression to get a handle on when it comes to jazz. ...

·        Minor ii-V-i. This chord progression has the same function as the previous major ii-V-I, but of course is in a minor key. ... (In 6 Aeolian mode would give the chords 7m 3M 6m and in the Ionian mode it would be 2m  5M  1m )

·        Major I-vi-ii-V. ...(1M-4m-2m-5M)

·        Minor i-vi-ii-V. (In 6 Aeolian mode would give the chords 6m 2m 7m 3M and in the Ionan mode it would be 1m 4m 2m 5M)

An example of a  song chord progression with the simple full chromatic harmony is the next

3M7-> 6m

5M7-> 1M 

2m  6m

3M7 6m

5m 6M7

2m 2m 

7M7  3M7

6m 6m 

Here is another example 

https://www.youtube.com/watch?v=4YESQFQJR0Y&t=2s&ab_channel=DrKCostas

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.