219. A REMARKABLE IMPROVEMENT OF THE STANDARD 6-STRINGS TUNING OF THE GUITAR . C2-G2-D3-G3-B3-E4 (5-5-4-3M-4) 4 INSTRUMENTS IN ONE TUNING

As alternative we may apply the 5-5-4-3M-4  E.g.  C2-G2-D3-G3-B3-E4  of the 6-string guitar or  1+6 courses oud.

It can be considered a type of modification of the overtones tuning 

1-1'-5'-1''-3''-7'' C₂-C₃-G₃-C₄-E₄-G₄                 
to the 
1-5-2'-5'-7'-3''

The D3-G3-B3-E4  part is a 4-string Greek Bouzouki in G major

The G2-D3-G3 part is a 3-string Greek Bouzouki in Bb major or G major

The C2-G2-D3-G3 is a bass Irish 4-string Bouzouki

The C2-G2-D3 is a low tambouras or saz with privileged scale the C major.


AS AN ALTERNATIVE INSTEAD OF UTLIZINGTHE G MAJOR (E MINOR)  AS PRIVILEDGED SCALE WE COULD UTILIZE THE Bb MAJOR (G MINOR) AS PRIVILEDGED SCALE WITH THE TUNING

The F3-Bb3-D3-G4  part is a 4-string Greek Bouzouki in Bb major

The Bb2-F3-Bb3 part is a 3-string Greek Bouzouki in Bb major

The Eb2-Bb2-F3-Bb3 is a bass Irish 4-string Bouzouki

The Eb2-Bb2-F3 is a low tambouras or saz with privileged scale the Eb major.

The highest 3 strings (1st 2nd 3rd) give in the 2-frets triad chords  the Aeolian (6th step) mode of the privileged scale (e.g. Bb)

The 2nd 3rd 4th strings give in the 2-frets triad chords the Ionian (1st step) mode of the privileged scale (e.g. Bb)

The 6th, 5th, 4th strings in the 2-frets triad chords give the Lydian (4ths step) mode of the privileged scale (e.g. Bb) 

As a contrast, the standard 6-string guitar tuning in the same sets of strings and on 2-frets triad chords give only the Aeolian and the Ionian mode!

Some further advantages of this guitar tuning are 

1) It  goes lower than a standard  guitar and as low as the cello

2) Still at the 4 higher strings all the chord-shapes and chords of the standard guitar can be played without any note missing. Thus we reduce all well known guitar chord playing in the higher 4-strings

3) Nevertheless in the lower 3 strings it plays also the triad-chords of 3 strings of an octave mandolin or mandocello! 

4) It plays all the tunes of Irish bouzouki on the lower  4 strings and all tunes of the Greek 4-strings Bouzouki in the higher 4 strings.  Including the isocratic melodies with two strings playing as drone an interval of 5th

5) In the 3rd 4th 5th strings it plays all the tunes of a Greek 3-strong bouzouki, including the isocratic with two strings playing as drone an interval of 5th

6)Thus it combines playing with ancient tunings that require strings tuned at  intervals of 5th (melodies orientation) and more modern tunings like that of the standard guitar or 4-strings Greek Bouzouki (chords or harmonic orientation)

7) The simplest patterns of 2-frets triad (3-strings) chords have 3 modes of the privileged scale in this tuning (Ionian, Aeolian, Lydian) compared to the 2 only modes (Aeolian , Ionian) in  the standard tuning of the 6-strings guitar

218 . THE CONCEPT OF SIMPLICIAL SUB-PROGRESSION OF CHORDS IN IMPROVISATION.

This concept of simplicial sub-progression of chords is entirely analogous to the concept of simplicial sub-melody of a melody. The basic application is of course that we try to find simplicial sub-progression of chords that are triads of chords where the subconscious feeling of the improvisation is very familiar and easier.

We enlarge more on this concept

217. POWER-CHORD OF 3RD OR 5TH AS WAVES OF A SIMPLICIAL SUB-MELODY

For the concept of simplicial sub-melody see e.g. post 104

This simplicial sub-melody is a bit different than the other types of simplicial sub-melodies , as it
utilizes 3 notes (a1, a2 a3) per chord X(i) , and they are the notes of power-chord of interval of 3rd or 5th which exist in the chord X(i). E.g. if  X(i)=C4 major then the (a1, a2 a3) could be (c4-e4-c5) or (c4-g4-c5) or (e4-g4-e5) etc.

As example of folk song with such power chord of 3rd waves is the Bearcice Reel

https://www.youtube.com/watch?v=E9D7RqdmV7U

216 RELATIONS OF TRIAD SCALES OF CHORDS (TRIAD HARMONIC PERSONALITIES) FOR IMPROVISATION WITH MELODIES

See also post 214 for scales of triads of chords  and 148 for scales of chords in general
322 also 426
We recall from post 214 that

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.

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

215. IMPROVISATION OVER A PAIR OF CHORDS . TRIADS OF HARMONIC PAIRS OF CHORDS.

See also post 203  and 321, 322.

This is harmonic improvisation and parallel melodic improvisation much like the jazz Blues that are using 3 only chords I IV V, or improvisations as in Irish reels with 2 only chords or  improvisations as in Cretan condillies with 2 only chords. Also some folk songs of the Cape Verde with only 2 chords.

Here we have similarly the general rule of a scale of chords of 2 only chords . There 3 types of such pairs of chords HARMONIC PAIR (roots an interval of 5th or 4th away) , MELODIC PAIR (roots an interval of 3rd away) CHROMATIC PAIR (roots an interval of 2nd  away) . E.G. I it is X7 Y where the one is a 7nth chord and the second has a root which is an interval of 4th away from the root of the first chord it is an harmonic pair. .In other words the two chords are in the harmonic relation (see post  30 )   are successive in the wheel of 4ths.   The reason for this is so as to have in the subconscious a simple pattern in harmony (although with random variations from random sequences of these 2 chords)
Also another important reason is that the 2 chords define usually at least one diatonic or other scale which simplifies the melodic improvisation.

In a diatonic scale some choices for such a pair of chords could be

V7  I   (5M7  1M)   HARMONIC PAIR

I7 IV  (1M7  4M)   HARMONIC PAIR

vii  iii   (7dim  3m)  HARMONIC PAIR

iii7  vi  (3m7  6m)  HARMONIC PAIR

vi7  ii   (6m7 2m)  HARMONIC PAIR

ii7  V   (2m7 5M)  HARMONIC PAIR.

About the symbols: In a C major scale the symbols denote the next chords

I=1M=C

ii=2m=Dm

iii=3m=Em

IV=4M=F

V=5M=G

vi=6m=Am

vii=7d=Bdim

Such triads of harmonic pairs may be already in the 3 main relations Harmonic relation , Melodic relation and chromatic relation defined from the interval of the roots of the first chord of each pair.  

E.g. the triad of harmonic pairs vii  iii   (7dim  3m) ,  (3M7  6m), (6m7 2m) are in harmonic-harmonic-harmonic relations . While the triad of harmonic pairs

(6m7 2m) , (3M7  6m), (5M7  1M)  are in harmonic-melodic-chromatic relation.

All  6   combinations (the inverses not included) of such triads of harmonic pairs on the first pair are


HARMONIC-HARMONIC
HARMONIC-MELODIC
MELODIC-MELODIC
HARMONIC-CHROMATIC
CHROMATIC-CHROMATIC
CHROMATIC-MELODIC

ETC


By fixing particular pattern of permutations and repetitions of these 2 chords (as in variations of the rhythm and chord progressions in 12-bars blues) e.g.

X7 X7 X7 X7
Y Y X7 X7
X7 X7 Y Y

etc

we have the backtrack of an easy harmony to define with melodic improvisations.

The improvisation is spending most of the time between the elements of each harmonic pair by oscillating or alternating them and then after repetition is sufficient it moves to another harmonic pair staying again there sufficient ime. This is very common in early New Orleans Jazz songs.

Also the simplicial submelody of such improvisations will be fixed following the chord progression pattern.

The chromatic pairs 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.

From the triplets of chords that correspond to modes as below

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)

If we re-harmonize the above triplets to include the lue notes 5# for the harmonic minor and 23, 5# for the double harmonic minor we get a latin jazz style of them as follows

1. IONIAN  :  HARMONIC TRIPLET (1M, 4M, 5M)
2. DORIAN  : HARMONIC TRIPLET (2m, 5M, 6m) or in Hminor 6M7, 2m , 5m)
3. PHRYGIAN : HARMONIC TRIPLET (3m, 6m, 7M7)
4. LYDIAN: HARMONIC TRIPLET  (4M, 7d,1M)
5. MIXOLYDIAN: HARMONIC TRIPLET  (5M, 1M,2m)
6. AEOLIAN: HARMONIC TRIPLET (6m, 2m, 3m) or in Hminor 3M7, 6m,2m 
7. LOCRIAN: HARMONIC TRIPLET  (7d, 3m, 4M)

In the next we may compose songs with first part (couple) a sad triplet or pair signifying a mode and resolving to the refrain to a happy triplet or pair (usually the Ionian or Mixolydian) 

Here are examples of chord progressions of  such songs

E. g. Aeolian-> Ionian 

2m, 3M7

6m, 2m 

Resolving to

1M 4M

5M7 1M 

Frygian-> Ionian 

3m 6m

7M7 3m 

Resolving to

1M 4M

5M7 1M 

Dorian-> Ionian

6m 2m

2m7 5M 

Resolving to

1M 4M

5M7 1M 

We may extract pairs of chords that define modes as folows

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)

Arpeggios of such a pair ofchords in chrmatic relation is often performed on the guitar by what is called sweep picking 

https://en.wikipedia.org/wiki/Sweep_picking#:~:text=Sweep%20picking%20is%20a%20guitar,fast%20and%20fluid%20in%20sound.

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

214 TRIAD HARMONIC (CHORD) PERSONALITIES OR TRIAD CHORD SCALES FOR MELODIC IMPROVISATIONS

See also post 203

This is harmonic improvisation and parallel melodic improvisation much like the jazz Blues that are using 3 only chords I IV V, or improvisations as in Irish reels with 3 only chords or  improvisations as in Cretan condillies with 3 only chords.

Here we have similarly the general rule of a scale of chords of 3 only chords X2 X2 X3 . The reason for this is so as to have in the subconscious a simple pattern in harmony (although with random variations from random sequences of these 3 chords) Of course an even simpler pattern would be 2 only chords. But we will discuss the case of 2 only chords in another post (there are capo verde folk sings and Irish folk songs and Cretan folk songs with two only chords).
Also another important reason is that the 3 chords define usually at least one diatonic or other scale which simplifies the melodic improvisation.

Besides the very common (which are also a connected arc in the cycle of 4ths)

I IV V  (1M  4M 5M)

ii V I  (2m 5M 1M)

vi  ii  V  (6m 2m 5M)

iii  vi  ii  (3m 6m 2m)

vii  ii  vi  (7dim 3m  6m)

V  I   iv   (5M 1M 5m)


we have also the alternating major-minor like the next

2m 5M 1m

6M 2m 5M

etc

About the symbols: In a C major scale the symbols denote the next chords

I=1M=C

ii=2m=Dm

iii=3m=Em

IV=4M=F

V=5M=G

vi=6m=Am

vii=7d=Bdim

So the possible combinations for triads are 

I, IV, V  

vi , IV, V 

I , ii, V 

I, IV, iii   

iv , ii, V 

I , ii, iii 

vi, IV, iii  

vi, ii, iii  

vi-vii-iii 

I -vii -V  

By fixing a particular pattern of permutations and repetitions of these 3 chords (as in variations of the rhythm and chord progressions in 12-bars blues) e.g.

X1 X1 X1 X1
X2 X2 X1 X1
X3 X3 X1 X1

etc

we have the backtrack of an easy harmony to refine with melodic improvisations.

Alternatively

THE IMPROVISATION IS A SEQUENCE OF "ROTATIONS". EACH "ROTATION" HAS THE NEXT 3-LEVEL  RHYTHMIC OR MORPHOLOGICAL STRUCTURE

THE 4 PARTS A1 A2 A3 BI STRUCTURE 

This structure is rhythmic morphological and comes as a pattern from the 15-syllable poetry.

2 lines in a 15-syllables poetry are divided to 4 parts A1 A2 A3 B1, each of the Ai having 4 syllables and the B1 3 syllables. Similarly here in the melody the A1 A2 A3 , B1 are of 2 measures.  Each of the A1 A2 A3 B1 contain at least one melodic theme. If we put the restriction that both the melodic theme and its variations are consisting from intervals that are 2nds in less that 1/3 (=33%) of the cases, then we get an "Irish" but also "south american", melodic/harmonic sound in the melody. The melodic theme of A1 is translated or inverted to that of the A2 and that of the A2 to that of A2. Finally the melodic theme of A3 is mutated to that of B1. The simplicial sub-melody has one note in each measure therefore two notes in each of the A1 A2 A3 B. These two notes signify a MELODIC MOVEMENT (VECTOR) which is the basis of an emotion.  If we superimpose the melody at the first two levels, the detailed improvisational notes of the melodic theme (1st level) and the melodic move or vector of the simplicial submelody (2nd level) we get a new musical entity and concept that we may call WAVING MELODIC VECTOR. The wavings are as in the 7 melodic themes patterns asin post 231. Another classification of them is that they are of 3 classes a) Chromatic (of length an interval of 2nd) b) Melodic (of length an interval of 3rd) c) Harmonic (of length an interval of 5th). The choice in the improvisation of one of these 3 classes is similar to the choice in a chord progression if the chord-transition will me chromatic , melodic or harmonic. Very often the wavings are of diminishing amplitude as we reach the melodic center-end note of it. This is very convenient to have in mind when we improvise because we think that we will move from a persisting note a (melodic center) to a persisting note b (melodic center ) in a scale but with improvisational waving way that we may change each time at willAll the melodic movements of the A1 A2 A3 B make a DOLPHIN WORD (as defined also in post 101, 114 ). Each part A (thus melodic move too) has an underlying chord. The chords of two parts like A1 A2 may be the same or different chords. The melodic move can be also a melodic triad (alternating major minor vector interval of 3rd as in post 208) . The Dolphin word of the "rotation" may be a closed polygon (e.g, triangle) of waving melodic vectors , so that the length of the melodic vector indicates also the length-interval of the waving melodic vector, which may also be the distance as musical interval of the middle notes of the underlying chords, of the melodic move.
This melodic polygone allows for simple and very concise, simple and visually beautiful  methods of writing the improvisation with not less information than the necessary but no more than a minimum too, so that each time we see the written paper and play the melody a different melody will emerge (mainly at the first layer/level of it) while still it will be "the same" song. 

When playing again such an improvisation the simplicial sub melody is repeated (thus the "rotation" A1 A2 A3 B or Dolphin word of it), but the other notes inside the measures that are embellishments may change. All together the "rotations" or Dolphin words make the total melodic phrases of the song. Therefore we have here at least a 3-level structures of the melody a) notes b) melodic moves c) "rotations" or Dolphin words,and in time it is 1, 2^3=8 (2 measures)  and 2^5=32 (A1A2A3B parts).

Also the simplicial submelody of such improvisations will be fixed following the chord progression pattern.

If the improvisational rotation in  the SUB-SCALE

starts from the lower end and ends in it it is called UPPER CYCLIC (NEUTRAL/SAD)

If it starts from the upper end and ends in it it is called LOWER CYCLIC (NEUTRAL  HAPPY)

If it starts from the upper end and ends at the lower end  it is called  DESCENDING (SAD)

If it starts from the lower end and ends at the upper end  it is called ASCENDING (HAPPY)

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

Furthermore an harmonic triad of chords may have harmonic melodic or chromatic relation  with another triad of chords iff  the chords insequence 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 

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

ONCE IMPROVISATION OVER  A TRIAD OF CHORDS IS  MASTERED THEN THE NEXT STEP IS THE IMPROVISATION OF TWO OR THREE 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)

213 . MELODIC IMPROVISATIONS BY SHIFTING FROM THE IONIAN MODE TO THE CELTIC MINOR TO THE INDIAN PENTATONIC AND TO THE GREEK PENTATONIC SCALE

For the next see post 204
The celtic 6-notes minor scale 2-2-3-2-2-1 is a subscale of the 7-notes diatonic scale 2-2-1-2-2-2-1

The Greek pentatonic (5-notes) scale 2-2-3-4-1  is a subscale of the Celtic 6-notes  minor scale.

But also the India or Egyptian pentatonic scale 2-2-3-2-3 is also a a subscale of  the 6-notes celtic minor

This allows for interesting improvisations shifting from 

1) Ionian more of diatonic 2-2-1-2-2-2-1

2) Celtic minor  2-2-3-2-2-1

3) Greek pentatonic 2-2-3-4-1

4) Indian pentatonic 2-2-3-2-3

where in all cases the 3 first notes and interval structure in semitones 2-2 remain stable