428. THE THEMES VARIATION PATTERN METHOD OF COMPOSING MELODIES. E.G. ONE MELODIC THEME FOR EVERY 15-SYLLABLES POETIC LINE. CYCLES OF MELODIC THEMES.

 This method does not start from the chord progression pattern. Instead it starts from an equally simple pattern which is the pattern of variations of the melodic themes.

In other words if A1 , A2 are the basic melodic themes, and B1, C1, D1 , and B2, C2, D2 , are their variations correspondingly  (modulation-translations, transposition-translations , pitch inversions , rhythmic inversions etc)  then a pattern of the melodic themes variations could be

(A1 B1)  (A1 C1) 

(A2 B2)  (A2 C2) 

  ETC

E.g. this pattern  of melodic themes is of the folk Celtic song Donegal.

Under each melodic theme we put either 1) a single chord 2) a pair of chords 3) a triad of chords 4) four chords etc

Of course same melodic themes (and symbol) require same underlying chords. But the converse is not true. Different melodic themes may still have the same underlying chord. E.g. the mentioned folk celtic song Dionegal with the above melodic themes patterns utilizes only 2 chords D7 and G. 

A1(=G D7)         B1(=D7 G)               C1(=D7 G D7 G) 

A2(=G D7)         B2(=D7 G)               C2(=D7 G D7 G) 

For a 15-sylalbes poetic lyrics, a full 15 syllables  poetic line of total syllables (4+4)+(4+3)=15 would correspond to a single melodic theme A1 , or B1 , C1, A2 etc. and thus here to 2 chords.  This is convenient for the arpeggio-tail method of composing melodies. While the simplicial sub-melody method would require 4 chords per 15-sylalbles poetic line. But these 4 chords could as well be 2 only e.g. in the form 5M7  1M  1M 5M7

We may utilize for a full 15 syllables poetic line harmonic pairs of chords or chromatic pairs of chords that define the modes of a diatonic scale or even melodic pairs of chords

The chromatic airs of chords in the diatonic scale  may get the the names ofthe modes of the scale too

1M-2m=IONIAN

2m-3m=DORIAN

3m-4M=FRYGIAN

4M-5M=LYDIAN

5M-6m=MYXOLYDIAN

6m-7d=AEOLIAN

7d-1M=LOCRIAN

(see also post  364 , 225 and 325  )

It is important also to realize that these 7 pairs of chords in chromatic relation define not only tetrachords but also hexatonic scales (and corresponding harmonicas) as in the post 291.

We may extract pairs of chords that define modes as follows

1. IONIAN  :  HARMONIC pair (5M, 1M)
2. DORIAN  : HARMONIC PAIR ( 6m, 2m)
3. PHRYGIAN : HARMONIC PAIR (7d, 3m)
4. LYDIAN: HARMONIC PAIR  (1M 4M)
5. MIXOLYDIAN: HARMONIC PAIR  (2m, 5M)
6. AEOLIAN: HARMONIC PAIR (3m 6m)
7. LOCRIAN: pseudo HARMONIC PAIR  (4M 7d)

Melodic pairs of chords would be

 1M-3m    IONIAN

2m-4M      DORIAN

3m-5M      FRYGIAN

4M-6m   LYDIAN

5M-7d  MYXOLYDIAN

6m-1M      AEOLIAN

7d-2m     LOCRIAN

The diatonic songs have a subtle balance of happy (major) and sad (minor) compared to chromatic tonality. A good example are the Irish folk songs

A good mix of modes for such songs is a moving melodic  5 cycle in the diatonic harmony. In other words an harmonic  triplet of chords that define the mode plus 2 more intermediate chords with melodic relation to the neighboring chords. E.g.  for the Ionian mode triplet  5M 1M 4M , we interpolate at melodic relations  the 3m (between 5M, 1M)  and 6m (between 1M and 4M) to get the melodic  5 cycle  5M 3m 1M 6m 4M. 

We may compare it with a moving harmonic 5-cycle e.g. 6m 2m 5M 1M 4M

or 3m 6m 2m 5M 1M etc

CYCLES OF MELODIC THEMES AND HAPPINESS.

Each melodic theme eventually is one of the 3 types (polarity). A pitch-vector going up, or going down or staying the same pitch. And one of the best  combination of such melodic themes  is the cycle, and

 1) especially the one that starts from a high pitch goes down and returns back to high pitch as the songs of the birds. 

2) In general up moves of pitch are happy, 

3) also melodic or harmonic intervals (large arpeggio part and small tail in he melodic theme) plus 4) large range melodic themes 

4) and most important  fast rhythm. 

 Diatonic harmonic triads 

(Xn)m->(Xn+1)M->(Xn+2)M     (e.g. 2m7->5M->1M) Myxolidian  harmonic triad

(Xn)m->(Xn+1)m->(Xn+2)m   (e.g. 3m7->6m->2m) Aeolian harmonic triad

(Xn)M->(Xn+1)M->(Xn+2)M     (e.g. 5M7->1M->4M)  Ionian harmonic triad

All of them  are the next

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

427. SIMPLICIAL SUBMELODY COMPOSITION METHOD AND ARPEGGIO-TAIL COMPOSITION METHOD OF THE MELODIES.

I have developed in previous posts the method of composing a melody over a chord progression based on the simplicial sub-melody , which has one note per chord.

On the other hand it is widely known in popular and folk music the structure of a melodic theme over a chord as having an arpeggio  (harmonic-melodic) part and a tail (chromatic) part (see e.g. post  421 )

The linking of thee two methods is the obvious that we substitute the one note of the simplicial sub-melody, with the arpeggio part of the melodic theme, and we leave the tail as the bridge of two notes of the simplicial submelody.

If we eliminate thus the tails (chromatic bridges) instead ofte simplicial submelody we get an arpeggio submelody . or harmonic submelody.

There is an issue of beats per minutes though. If we utilize the simplicial submelody method then there are one or few only notes per underlying chord while if we utilize the  arpeggio-tail method there are many notes per underlying chord. This suggests that the simplicial submelody method has double the number of beats per minute compared to the  alternative composition with the arpeggio-tail method. 

Obviously by letting more time  for each chord, the melodic theme will have larger part as arpeggio (e.g. 2/3 of it time) and less (e.g. 1/3) as tail. This is according to the older tradition in folk music.

E.g. a full 15 syllables poetic line (in 15-sylalble poetry) could be only two chords 5M7-> 1M or 

1M->5M7 etc. 

For a 15-sylalbes poetic lyrics, a full 15 syllables  poetic line of total syllables (4+4)+(4+3)=15 would correspond to a single melodic theme A1 , or B1 , C1, A2 etc. and thus here to 2 chords.  This is convenient for the arpeggio-tail method of composing melodies. While the simplicial sub-melody method would require 4 chords per 15-sylalbles poetic line. (see also post 428)

426. THE ORGANIZING RULE OF TRIADS OF CHORDS IN HARMONIC PROGRESSIONS OF CHORDS

See also posts 322,  205, 206, 215, 216 etc

An harmonic chord progression  X1 X2 X3 X4 .... is a progression of chords that are successive in the wheel by 4th, in other words, they are in harmonic relation (their roots are in intervals by 4ths)

This is general concept in the harmony  of songs, by far more powerful and simple that the concept of scale, as it involves 2, 3 or more scales.

The rule of triads refers in choosing the attribute of major or minor in triads Xn-> Xn+1->Xn+2 

E.g. Diatonic harmonic triads 

(Xn)m->(Xn+1)M->(Xn+2)M     (e.g. 2m7->5M->1M) Myxolidian  harmonic triad

(Xn)m->(Xn+1)m->(Xn+2)m   (e.g. 3m7->6m->2m) Aeolian harmonic triad

(Xn)M->(Xn+1)M->(Xn+2)M     (e.g. 5M7->1M->4M)  Ionian harmonic triad

All of them  are the next

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

Harmonic minor triads

(Xn)M7->(Xn+1)m->(Xn+2)m     (e.g. 3M7->6m->2m)

(They can be of course in all permutations e.g. 2m->3M7->6m )

Double harmonic minor triads

(Xn)M7->(Xn+1)M7->(Xn+2)m     (e.g. 7M7->3M7->6m)

Other non-singe-scale hybrid diatonic-harmonic minor ( harmonic  triads)

(Xn)m7->(Xn+1)M7->(Xn+2)m  (harmonic Xn+2 minor and diatonic Xn+2 major) 

(Xn)M7->(Xn+1)m7->(Xn+2)M   (harmonic Xn+1 minor and diatonic Xn+3 major) 

 Hybrid diatonic-harmonic minor (harmonic-melodic triads) 

1M->3M7->6m or  (harmonic 6m minor and diatonic 1M major, in other words in melodic relation) 

1M->6M7-2m or  (harmonic 2m minor and diatonic 1M major, in other words in chromatic relation) 

5M->7M7-3m or  (harmonic 3m minor and diatonic 1M major  in other words in melodic relation) 

5M->3M7->6m  (harmonic 6m minor and diatonic 1M major  in other words in melodic relation) 

So with these rules if we have a 6, 7,8 , 9 harmonic progression we split it in to successive triads that 

are of the above 3 kinds. so as to give a meaningful harmony to the harmonic progression based on the older concept and function of diatonic scales. 

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.

Besides the basic harmonic triplets (in other words a sequence of 3 chords X1,X2,X3 so that X1-X2 , X2-X3 are harmonic relations od chords, in other words chords that their roots differ by an interval of 4th (5th)) , there are also the chromatic triplets (in other words a sequence of 3 chords X1,X2,X3 so that X1-X2 , X2-X3 are chromatic relations od chords, in other words chords that their roots differ by an interval of 2nd). BOTH  ARE BASIC TYPES OF TRIPLETS. In other words with the 3 CHORDS OF THE TRIPLET WE CAN ACCOMPANY ANY MELODY IN THE DIATONIC SCALE. WE CANNOT HAVE THIS PROPERTY OF BEING HARMONICALLY A BASE OF 3 CHORDS FOR MELODIC TRIPLETs (in other words a sequence of 3 chords X1,X2,X3 so that X1-X2 , X2-X3 are melodic relations of chords, in other words chords that their roots differ by an interval of 3rd) 

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.

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)

We may compare the basic chromatic triplets with the basic harmonic triplets (see also post 222)

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


Besides these 2 types of basic triplets we have also a 3rd type X1 X2 X3 , where X1-X2 is a chromatic relation and the X2-X3 is an harmonic relation or vice versa. We may call them the mixed
basic chromatic-harmonic triplets. E.g.  the basic triplet that is used sometimes in blues 1M 2m, 5M , is such as 1M-2m have chromatic relation while 1M-5M harmonic relation.

To convert a basic harmonic triplet to another chromatic or mixed basi triplet we utilize correspondences where we correspond each of the 3 main major chords of the diatonic scale with their lower minor relative and the 5M7 with the 7d. Therefore

2m<->4M
3m<->5M
6m<->1M
7d<-> 5M7

The same arguments may apply for the chromatic tonality where some of the mnor chords become major and some of the major chords minor. E.g. We have the harmonic triplet (3M7, 6m ,2m ) of the frygian mode and the harmonic triplet (7M7-3M7-6m) of the Locrian mode which are combined with the more standard harmonic triplets of the diatonic tonality of the dorian mode (2m-5M7-1M) or the myxolydian mode (5M7-1M7-4M) .

For  alternative basic chromatic triplets of the chromatic tonality (that corresponds to the harmonic minor and double harmonic minor) we have the triplets (we notice that thsi type of chromatic tonality gives for the basic chromatic triplets, cases of 2 major chords and one minor, thus the major chords are dominating!)


IONIAN MODE: 7M-1M-2m
DORIAN MODE: 1M-2m-3M
FRYGIAN MODE: 2m-3M7-4M
LYDIAN MODE: 3M-4M-5M
AEOLIAN MODE: 5M-6m-7M
LOCRIAN MODE: 6m-7M-1M

A triad of chords is called HARMONIC TRIAD OF CHORDS iff the chords (as roots) are consecutive on the wheel by 4ths (either as major or minor) E.g. E Am Dm or G C F etc


A triad of chords is called MELODIC  TRIAD OF CHORDS iff the chords (as roots) are in consecutive melodic relation in other words iff they are consecutive on the wheel by 3rds E.g. Em C Am or  Am F Dm etc


A triad of chords is called CHROMATIC   TRIAD OF CHORDS iff the chords (as roots) are in consecutive chromatic  relation in other words iff they are consecutive as roots in (diatonic or not ) scale

E.g.  C Dm Em ,    or  Em  F  G  etc

Furthermore a triad of chords may have harmonic melodic or chromatic relation  with another triad of chords iff  the chords in sequence and 1-1 correspondence have this relation.

E.g. starting with the central major triad of a diatonic scale

5M-1M-4M the next triad is in chromatic relation with it  and chromatic parallel triad 

4#dim7-7dim7-3dim7 or also 4#M-7M-3M which is closer to the double harmonic minor  modulation of its natural minor with its standard chord covering.

Also the next triad is melodic relation with the original triad

3m-6m-2m 

ONCE IMPROVISATION OVER  A TRIAD OF CHORDS IS  MASTERED THEN THE NEXT STEP IS THE IMPROVISATION OF TWO OR MORE  TRIADS . ONE WITH MORE MINOR CHORDS AND ENDING WITH A  TRIAD WITH MORE (OR ALL) MAJOR CHORDS (IN THE EMOTIONAL INTENTION IS FROM SADNESS TO JOY).

This is done by combining successively the improvisations one two or more  triads of chords .


And here is  where  the relations of triads of chords becomes important.

Two triads of chords X1 X2 X3 and Y1 Y2 Y3 are  disjoint  iff  none of the X1 X2 X3 is identical with any of the Y1 Y2 Y3. 

Two disjoint triads of chords X1 X2 X3 and Y1 Y2 Y3  are in consecutive harmonic relation 
iff  the X3 is in harmonic relation with the Y1 (see also  post 30 on the harmonic melodic and chromatic relations of chords ) 

E.g.  X1=E X2=Am X3=Dm   and Y1=G Y2=C Y3=F 

Two disjoint triads of chords X1 X2 X3 and Y1 Y2 Y3  are in consecutive melodic relation 
iff  the X3 is in melodic relation with the Y1 (see also  post 30 on the harmonic melodic and chromatic relations of chords ) 

E.g.  X1=E X2=Am X3=Dm   and Y1=F Y2=Bb Y3=D# 

or E.g.  X1=B X2=Em X3=Am   and Y1=F Y2=Bb Y3=D# 

Two disjoint triads of chords X1 X2 X3 and Y1 Y2 Y3  are in consecutive chromatic  relation 
iff  the X3 is in chromatic relation with the Y1 (see also  post 30 on the harmonic melodic and chromatic relations of chords ) 

E.g.  X1=E X2=Am X3=Dm   and Y1=D#m Y2=G# Y3=C#    (Dm in chromatic relation with D#m)

or E.g. X1=G X2=C X3=F   and Y1=E Y2=Am Y3=Dm  (F in chromatic relation with E)

There are more relation when the 2 triads of chords X1 X2 X3 , and Y1 Y2 Y3 are not disjoint but have two consecutive chords common E.g.    X2=Y1 , X3=Y2  e.g.    (E Am Dm) and (Am Dm G) etc 

Here is an example of a quaternary of chords repeating in sequence as backtrack for melodic improvisation , which essentially originates from the triad of chords 1M-4M-5M or 2m-5M-1M.

The quaternary is 6m->2m->5M->1M

https://www.youtube.com/watch?v=gUNWjgaJEik

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

425. The major harmonic 5-cycle 6 (n or M) 2 (m or M) 5M 1M 4M and the minor harmonic 5-cycle 3(m or M) 6 (n or M) 2 (m or M) 5M 1M in composing songs.

In a diatonic scale we may have harmonic cycles of 5 chords e.g.

3m->6m->2m->5M->1M which has more  minor chords than major and may be called the minor harmonic 5-cycle and the

6m->2m->5M->1M->4M which has more major chords than minor chords and may be called the major harmonic 5-cycle.

Upon these cycles we may add the 5# blue note (from the harmonic minor Aeolian mode) or other blue notes by converting major chords to minor chords etc.

So when composing songs we may start the couple with the minor harmonic 5-cycle and end at the refrain with the major harmonic 5 cycle.

A characteristic example is the melody by Luiz Bonfa Black Orpheus, or Manha de Carnaval (Morning carnival) a melody from a film, composed by which nevertheless has an original version under the name samba de Orfeu, which is a bit different and more happy version of the melody.

E.g. see for the sad version Manha de Carnaval 

https://www.youtube.com/watch?v=nVkDfnGobmI&ab_channel=varadero1839

and the happy version samba de Orfeu

https://www.youtube.com/watch?v=LRhPocYpbYo&ab_channel=JanAdamec

or 

https://www.youtube.com/watch?v=zHo4dF5HyQ0&ab_channel=GunhildCarling

The sad version Manha de Carnaval is utilizing the minor harmonic 5-cycle of chords

3m->6m->2m->5M->1M . It alters also the 3m to 3M7

while the happy version is utilizing the major harmonic 5-cycle

6m->2m->5M->1M->4M . 

It alters also 6m to 6M7. I addition at a point it alters 5M to 5m and 4M to 4m !