AN EXCELLENT SOFTWARE TOOL TO UNDERSTAND THE BASIC 3 CHORD REATIONS IS THE SOFTWARE NAVICHORD (FOR IOS). IT HAS A HEXAGONIC TOUCH-SCREEN KEYBORD OF THE NOTES WHERE THE CHORDS ARE TRIAGNGLES AND ARE PLAYED BY TOUCHING THE CENTER OFTHE TRIANGLE
SUCH HEXAGONIC KEYBOARDS HAVE BEEN PATENTED ALSO IN THE TERPSTRA KEYBOARD. THE 3 BASIC LOCAL RELATIONS OF THE CHORDS (NO-COMMON NOTE OR CHROMATIC RELATION, ONE COMMON NOTE OR HARMONIC RELATION AND TWO COMMON NOTES OR MELODIC RELATION) ARE IMMEDIATELY VISIBLE.
THE NAVICHORD IS ALSO A CHORD LOOP SEQUENCER WHICH PRODUCES CHORD PROGRESSIONS AND BACKTRACKS.
WE DESCRIBE TWO METHODS , ONE WITH TRIANGLES OF CHORDS AND ONE WITH PARALLELOGRAMS OF CHORDS.
The two methods to create chord progressions from the 7 chords of a diatonic scale are like creating words of a language which has as alphabet the 7 chords of the diatonic scale. It allows of unlimited combinations with varying degrees of symmetries.Of course always of a diatonic scale. we include also modulations of a certain type which are change of the natural minor of the diatonic scale to a same root harmonic minor or double harmonic minor.
A) THE CHORD PROGRESSION IS A CYCLE OR SEQUENCE OF TRIADS (TRIANGLES) OF CHORDS AS BELOW.
For happy melodies obviously, the triad is the I, IV, V. According to the degree of sadness we want to impose, we substitute any of the major chords with its lower minor relative. In other words vi for I, ii for IV and iii for V.
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 are
I, IV, V (1M, 4M,5M majors harmonic triad)
vi , IV, V (4M, 5M , 5m, chromatic triad, e.g, part of the Andalusian cadenza when reversed)
I , ii, V ( 2m, 5M ,1M harmonic triad)
I, IV, iii (3m 1M, 4M, melodic-harmonic triad)
IV , ii, V ( 1M, 4M, 2m, harmonic-melodic triad)
I , ii, iii (3m, 1M, 2m, melodic chromatic or only chromatic triad)
vi, IV, iii (3m, 6m, 4M, harmonic-melodic triad)
vi, ii, iii (3m, 6m, 2m, harmonic triad)
vi-vii-iii (7d, 3m, 6m, harmonic triad)
I -vii -V (5M, 1M , 7d, harmonic-chromatic triad)
In case we want to alter the natural minor ofthe scale to an harmonic minor or double harmonic minor the the usual changes of the harmonic personality as in post 158 apply.
In more detail:
In general starting from a diatonic harmonic personality
1M, 2m 3m 4M 5M 6m 7dim 1M
the next are the effects of turning the natural minor to harmonic minor or double harmonic minor.
The effect of the 1st blue note 5# of the harmonic minor on the harmonic personality is that
the 3m turns in to 3M and the 5M may turn into 5b5 or better sounding 5#m or 5#dim or 5aug, or 1dim
Also the 7dim may turn in to 7m7b5 as 4 notes chord.
While the effect of the 2nd blue note of the double harmonic minor 2# (or 3b) is that the 7dim turns in to 7M or 7b5 and , the 1M may become 1aug and also the 2m may become 2#dimb3 or better sounding 2#dim or 2#M.
Further changes with augmented chords because of the harmonic and double harmonic minor we involve not only diminished chords but also augmented chords.
E.g.
In C major
Am Bdim E Am (repeated many times) then
C Bd G C (repeated many times) then
Am Dm E Am (repeated many times) then again
Am Bdim E Am (repeated many times) etc
Listen also to
and to
Of course the next critical issue is to determine the simplicial sub-melody that goes parallel to the chord progression. This determines also the chord progression as triads of notes and the correct voicing of the chord progression, so as to play directly also the simplicial submelody through the correct voicing of chord progression as triads of notes only. In other words
THE SIMPLICIAL SUBMELODY IS OF EQUIVALENT DETERMINATION WITH THE VOICING OF THE CHORD PROGRESSION AS TRIADS OF NOTES.
Triads of chords with minor chords in them most often are correlated with straight descending shape of the theme of the simplicial sub-melody. While triads of chords with all three chords major chords are correlated with straight ascending shape of the theme of the simplicial sub-melody. Usually we prefer the middle note (3 from 1-3-5) of the chord for the note of the simplicial sub-melody. But we should study also the harmonic, chromatic and default simplicial sub melodies discussed in posts 66, 109.
Then we proceed with the embellishments and waving around the simplicial submelody to derive a full dense and even fast melody.
For example if we chose the next two triads of chords for te chord progression in a song in the C major scale
(Am ,Bdim, E) and (C Bdim G7) then the chord progression is
Am-> Bdim-> E-> Am repeated 4 times and
C-> Bdim->G7->C repeated 4 times and
and all together repeated 3 times.
Then the first triad of chords which has the minor chord Am signifies sadness and the simplicial submelody is chosen descending with a middle waving . So it is the a5->d5->e5->a4 . One note for each occurence of a chord which belongs to the chord . And the triads of chords C-> Bdim->G7->C has more major chords which signifies happiness so the simplicial submelody is defined as straight ascending . So corresponding one note (which belongs to the chord) to each chord it may be the c4->d4->g4->c5 . We may also create an introductory part A of the song which is both parts B , C of the simplicial submelody with the necessary waving embellishments around it c4->d4->g4->c5->a5->d5->e5->a4 which we repeat two times each time we repeat the parts B and C above of the two triads of chords.
The two methods to create chord progressions from the 7 chords of a diatonic scale the one here with triads (triangles) if chords and the one in post 148 with parallelogram diagrams of chords are like creating a language which has as alphabet the 7 chords of the diatonic scale. It allows of unlimited combinations with varying degrees of symmetries.
B) THE GENERAL PARALLELOGRAM PATTERN OF PROGRESSIONS WITH ALTERNATING CHORD-RELATIONS OF CHROMATIC-MELODIC ,CHROMATIC-HARMONIC , HARMONIC-MELODIC , HARMONIC-HARMONIC, MELODIC-MELODIC, CHROMATIC-CHROMATIC CHORD-TRANSITIONS.
This is a progressions X1->X2->X3->...->Xn where the Xi->Xi+1 and Xi+1->Xi+2 is an alternation of chord relation and transitions of the chromatic-melodic , chromatic-harmonic, melodic-harmonic, chromatic-chromatic, melodic-melodic or harmonic-harmonic relations.
Such constant alternating patterns of chord relations somehow determine also that the melodic themes (either within a single chord or within a chord transition), are structured and translated or inverted or expanded with similarly alternating intervals of 2nd, 3rd or 4th/5th.
THE GENERAL PATTERN OF A CHROMATIC PARALLELOGRAM DOUBLE SCALE OF CHORDS
Here is an alternative way to produce not harmonic scales of chords (based on the harmonic relation of chords) but chromatic scales of chords based on the harmonic relation of chords but which still involve the other two chord relations the melodic and the harmonic
WE START WITH A CHROMATIC CADENZA OR ASCENZA in semitones 2->2->1 or 1-3-1 or 1-3-1-1-3-1 in harmonic and double harmonic minor scales, and we paralel chords rooted on such notes X1->X2->X3->X4 with chords
Y1->Y2->Y3->Y4, such that the relation of Xi with Yi is either in a relation of being relative chords (melodic relation of chords) or a 4th apart (harmonic relation of chords)
Of course the less total number of different chords that we may use is better and it sounds more familiar if such chords belong to an harmonic personality (diatonic or harmonic minor or double harmonic minor etc).We may use either minor or major chords.
TRIPLE ALTERNATION OF CHORD-TRANSITIONS
More generally and we paralel chords X1->X2->X3->...->Xn that are in one of the relations chromatic, melodic harmonic , with chords X1->X2->X3->...->Xn so that the relation of Xi with Yi is always constantly in one of the 3 basic relations relative chords (melodic relation of chords) or a 4th apart (harmonic relation of chords) .
When playing the scale as progression X1->Y1->X2->Y2->... it is equivalent with having a triple alternation of chord relation and transitions of the chromatic-melodic , chromatic-harmonic, melodic-harmonic, chromatic-chromatic, melodic-melodic or harmonic-harmonic relations and a third which is variable.
Here is an alternative way to produce not harmonic scales of chords (based on the harmonic relation of chords) but chromatic scales of chords based on the harmonic relation of chords but which still involve the other two chord relations the melodic and the harmonic
WE START WITH A CHROMATIC CADENZA OR ASCENZA in semitones 2->2->1 or 1-3-1 or 1-3-1-1-3-1 in harmonic and double harmonic minor scales, and we paralel chords rooted on such notes X1->X2->X3->X4 with chords
Y1->Y2->Y3->Y4, such that the relation of Xi with Yi is either in a relation of being relative chords (melodic relation of chords) or a 4th apart (harmonic relation of chords)
Of course the less total number of different chords that we may use is better and it sounds more familiar if such chords belong to an harmonic personality (diatonic or harmonic minor or double harmonic minor etc).We may use either minor or major chords.
TRIPLE ALTERNATION OF CHORD-TRANSITIONS
More generally and we paralel chords X1->X2->X3->...->Xn that are in one of the relations chromatic, melodic harmonic , with chords X1->X2->X3->...->Xn so that the relation of Xi with Yi is always constantly in one of the 3 basic relations relative chords (melodic relation of chords) or a 4th apart (harmonic relation of chords) .
When playing the scale as progression X1->Y1->X2->Y2->... it is equivalent with having a triple alternation of chord relation and transitions of the chromatic-melodic , chromatic-harmonic, melodic-harmonic, chromatic-chromatic, melodic-melodic or harmonic-harmonic relations and a third which is variable.
Such constant alternating patterns of chord relations somehow determine also that the melodic themes (either within a single chord or within a chord transition), are structured and translated or inverted or expanded with similarly alternating intervals of 2nd, 3rd or 4th/5th.
PRODUCING CHORD PROGRESSIONS FROM CHORD-SCALES
Now when we want to improvise based on such a scale of chords (harmony first), we may start with one such chord from this scale and play a melodic theme that fits it. Then we move to the next melodic theme, with all the know so far rules of good melody composition (e.g. variations of translation, inversion, homeomorphism) and try to fit it also to one of the chords of the previous scale of chords. If we succeed in this we repeat it , with the next melodic theme, and appropriate chord from this set of chords or scale of chords, and so on. In this way we have an inter play with harmony and melody at the very process of improvisation or composition.
This method of composing a melody, is more general and more comprehensive than composing a melody within a single scale of notes. It results composing melodies in many different scales and modulations between them, but the simplicity is still kept as set of chords (scale of chords) rather than scale of notes.
Here is a way when the scale of chords is identical with the chords of diatonic scale of notes.
An relatively easy and safe way to produce such mesmerizing monotone but beautiful flows of improvisation , is to use scale of chords as in post 148. And in particular a very familiar scale of chords that are the chords of diatonic scale:
I , ii, ii, IV, V vi, vii, I' (=1M, 2m, 3m, 4M, 5M, 6m, 7dim 1'M)
and in addition to an instrument tuned by the harmonic tuning (see post 90) so that there is a densest possible opportunity of major or minor chords per number of frets.
Some of the variation techniques to walk this scale of chords are
1) Walk in the chromatic order up and down (all then only odds then only even)
2) Walk in the relative chords order up and down
3) Walk in the resolution or harmonic order by 4ths or 5th order up and down
4) Walk only the minor chords first descending and then the major chords ascending
5) Walk in the 4-notes chords (major 7nth extension of the chords) up and down, all then only even then only odd
6) Walk in a half scale (in the chromatic order) up down then other half up and down.
7) Walk in a random way either 3-note chords or 4 notes chords
8) Alter some chords to include the 5#, or 2# of the harmonic minor or double harmonic minor, or other like 6#. E.g. alter the 3m to 3M7 or 3dim etc
This method of composing a melody, is more general and more comprehensive than composing a melody within a single scale of notes. It results composing melodies in many different scales and modulations between them, but the simplicity is still kept as set of chords (scale of chords) rather than scale of notes.
Here is a way when the scale of chords is identical with the chords of diatonic scale of notes.
An relatively easy and safe way to produce such mesmerizing monotone but beautiful flows of improvisation , is to use scale of chords as in post 148. And in particular a very familiar scale of chords that are the chords of diatonic scale:
I , ii, ii, IV, V vi, vii, I' (=1M, 2m, 3m, 4M, 5M, 6m, 7dim 1'M)
and in addition to an instrument tuned by the harmonic tuning (see post 90) so that there is a densest possible opportunity of major or minor chords per number of frets.
Some of the variation techniques to walk this scale of chords are
1) Walk in the chromatic order up and down (all then only odds then only even)
2) Walk in the relative chords order up and down
3) Walk in the resolution or harmonic order by 4ths or 5th order up and down
4) Walk only the minor chords first descending and then the major chords ascending
5) Walk in the 4-notes chords (major 7nth extension of the chords) up and down, all then only even then only odd
6) Walk in a half scale (in the chromatic order) up down then other half up and down.
7) Walk in a random way either 3-note chords or 4 notes chords
8) Alter some chords to include the 5#, or 2# of the harmonic minor or double harmonic minor, or other like 6#. E.g. alter the 3m to 3M7 or 3dim etc
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)
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
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
