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.