36. CHROMATIC TONALITY: Some ethnic and Jazz harmonic personalities as perturbations of a diatonic chord scale. Chords-cycles or chord-scales and modes for Jazz re-harmonization

IN THIS ARRICLE WE DISCUSS HOW STARTING FROM A DIATONIC SCALE
WITH CHORDS IN STEPS 1M-2m-3m-4M-5M-6m-7d-1'M WE PASS TO ALL THE 12-TONES SCALE (WHICH IS AN ADDITIONAL PENTATONIC SCALE OF BLUE NOTES) BY A) CHANGING THE MAJOR CHORDS TO MINOR CHORDS AND VICE-VERSA B) BY ADDING MAJOR OR MINOR OR DIMINISHED CHORDS ON THE CHROMATIC OR BLUE NOTES: 2bM 3bM 5bM 6bM 7bM OR 2bm 3bm 5bm 6bm 7bm OR 2bdim 3bdim 5bdim 6bdim 7bdim

See also posts 153, 155 about re-harmonization ,harmonic personalities and perturbation of a diatonic scale of chords.  

The concept of harmonic personality is a concept of chromatic tonal music and not a concept of multi tonal or atonal music. (See post 263 )

Triads of chromatic tonality that are often met and are based in one of the chromatic 7-notes scales the harmonic minor, the meapolitan and the double chromatic minor are the next

3M7-6m-2m  (harmonic minor)

7M7-3m-6m (Neapolitian)

6M7-2m-5m (harmonic minor)


All the three above triads (double harmonic minor)

2M7-5m-1m

5M7-1m-4m

1M7-4m-7m

4M7-7m-3m

Chromatic shifts of them by an interval of 2nd are e.g. the next

7M7-3m-6m->
1M7-4m-7m

Or 

1M7-4m-7m->
2M7-5m-1m

Or 

6M7-2m-5m->
1M7-3m-6m

Etc

Cycles of 6 chords in harmonic relations are the next 7

1M7-4m-7m->
3M-6M-2M

2M7-5m-1m->
4M-7M-3M

3M7-6m-2m->
5M-1M-4M

4M7-7m-3m->
6M-2M-5M

5M7-1m-4m->
7M-3M-6M

6M7-2m-5m->
1M-4M-7M

7M7-3m-6m->
2M-5M-1M



According to musicologists of Jazz and Ethnic music (as appearing e.g. in music arrangement software like the music machines of Microsoft), the next scales of chords (that cover the steps of the chromatic 12-tone scale) correspond to the next harmonic personalities.


HARMONIZING ALL 5 BLUE NOTES OR CHROMATIC NOTES (2b  3b   5b   6b and 7b) which is  in its own a pentatonic scale   FROM THE 7 NOTES OF THE DIATONIC SCALE TO THE 12 NOTES OF THE FULL WESTERN MUSICAL (CHROMATIC) UNIVERSE

I BELIEVE THAT THE MAIN USE OF THIS CONCEPT IS IN JAZZ WHERE THE ROLE OF  THE DIATONIC SCALE (TONALITY) IS RATHER LOOSE,IN THE SENSE THAT IT IS REQUIRED AT LEAST 50% OF THE TIME THE NOTES OF THE MELODY AND CHORDS TO BE IN THOSE OF THE DIATONIC SCALE AND THE REST OF THE TIME IN THE 12-NOTES FULL CHROMATIC SCALE. THUS THE TYPES OFTHE CHORDS WITH ROOTS ON THE REST OF THE NOTES OF THE 12-NOTES CHROMATIC SCALE COMPARED TO THE 7-NOTES DIATONIC SCALE IS SO AS TO APPLY FOR THE REST OF THE MELODY AND ITS CHORDS. E.G. THE SOFTWARE MIDI-GUITAR ALLOWS WITH AN ARPEGGIATOR TO ACCOMPANY AUTOMATICALLY ANY MELODY WITH CHORDS OVER THE MELODY'S NOTES, THAT IN PRACTICE ARE CHORDS THAT  SOUND ONLY FOR THE CENTERS OF THE MELODY THAT ARE NOTES THAT SOUND LONGER. THERE ARE THOUGH OTHER USES OF THIS 12-NOTES SCHEME OF HARMONIC PERSONALITIES.

This concept also can be considered as chromatic wheels of chords or chord-scales as described in post 83. They can be considered either as 12-cycle of chords or only as 7-cycles of chords. Such 12-steps scales of chords can be considered also as scales of chords derived by perturbation a diatonic scale of chords (see also post )

It gives also a system to create chords that cover any scale ( but not necessarily belong to it too ) , including of course the diatonic scale modes.

But it is also a system to adopt and re-harmonize a song from its original chord progression to another that has the particular personality  (as we may change a song from a minor mode to a major mode and vice-versa) or asit it ususal in swing Jazz and Gypsy Jazz to re-harmonize songs.

HOW IT APPLIES TO SONGS

RE-HARMONIZATION TO AN PARTICULAR HARMONIC PERSONALITY 

1) The way that the table below can be used on an existing song with melody written say on a known particular diatonic scale and mode (at least in its musical score)   is the next.

2) Take the known chord progression of the song, and substitute, each chord of it with root R with the corresponding chord of root R  in the table below. 

3) The step 2)  applies to all possible roots R in the 12-notes chromatic scale, and in the 7 tone scale of the song too (covering the case of chords outside the 7-notes scale in the case of multiple modulations to different scales during the song).  We may consider the 12-notes redundant and use only the 7-notes. But if we would start from a song not written on single diatonic scale, but in many scales with modulations, and still inside the 12-notes scale, the step 2) can still apply. Notice that the this re-harmonization is not a 1-1 correspondence of chords , and two different chords with the same root at different times may result to the same chord of the 12-notes personality scale of chords.

 4) The result is that there is a change in the "personality" of the sound of harmony of the song. By changing the chord-type we may need to change some of the notes of the melody to fit in the new type chord as it was flitting to the old type of chord. This is in accordance to our philosophy which in general defines the harmony of a song not through a single scale but throughout chord progression (see post 49) 

For the definition of the chords see e.g. www.all-guitar-chords.com, or the internet.

M symbolizes  major, m symbolizes  minor, dim=diminshed, aug=augmented.
For example C63=CEA, C65=CGA, C42=CDFG, C43=CEFG, C7#9=CEGBbD#, Cm7b5=CEbGbBb, Cm11=CEbGBbDF, Cdim9=CD#F#A#D, C9#11=DF#CEBb , Cm67=CEbGAB
C2=CDEG,

One particular more familiar way to utilize this table for a song already written in one of the scales major, minor, harmonic minor, or the modes Mixolydian, Phrygian, Dorian ,  so as to give it the corresponding jazz personality, is to alter a major or minor chord of the song and at any root, with the attributes below (dim, ,7, 63, 65, 9, 11, 7#9 etc) and making it thus sound with a different personality. This concept is based on tonality but it is actually beyond one only scale and tonality, it is different than the substitutes the concept of modulation, it is re-harmonization and is based rather on the concept of covering sets of chords of all possible steps of any melody. 

The set of chords of a personality, is indeed based on tonality, but only at the level of the chords. Not at the level ofthe melody. The melody need not be within a diatonic scale. The fact that personality chords are defined even for steps outside a diatonic scale makes it clear.

COMPOSITION   IN A PARTICULAR  HARMONIC PERSONALITY 

Another way to utilize it, is to compose songs regardless of scale, but utilizing the chords of a particular personality , and as the chords of a personality have roots all the 12 notes, one has all possible roots for chords of the song  over a melody with all possible notes. This concept resembles  tonality but it is actually beyond one only scale and tonality.  It substitutes the concept of modulation and is based rather on the concept of covering sets of chords of all possible steps of any melody, creating so composite chord-melodies (see also post 11).

ALTERNATIVELY, the table below can be used as a guide of the kind of chord we would choose in the maximal correspondence of each note of a melody with a chord with the root on it before we simplify the chord progression to one with fewer chords.

Still, ALTERNATIVELY we may use the corresponding chord types as in the table when the underlying note of the simplicial sub-melody (see post 65 ) is the one in the corresponding position in the full 12-notes scale.

Steps of the chromatic scale/Harmonic Personality

1

1#

2

2#

3

4

4#

5

5#

6

6#

7

Righteous(Major)

M(ajor)

Dim7

m(inor)

Dim7

m

M

Dim7

7

Dim7

m

4,2

Dim7

Honest (major)

M

Dim7

m

Dim7

m

M

Dim7

7

Dim7

m

M

dim

Hopeful (Mixolydian)

M

M

m

M

dim

M

m

m

M

m

M

dim

Serious (Phrygian)

m

M

6,3

M

6,3

m

6,3

dim

M

6,5

m

6,5

Upbeat(Mixolydian)

M

M

m

M

m

M

M

M

M

m

M

dim

Searching(Dorian)

m

M

m

M

dim

M

dim

m

M

dim

M

dim

Lonely (major)

7

Dim7

m7

Dim7

7

7

Dim7

7

7

7

7

7

Funky(Mixolydan)

7#9

7

m7

9

m7

9

7

7

7

m7

6,3

7

Sad(minor)

m7

M

6,3

M7

6,3

m7

6,3

m7

M7

6,5

M

6,5

Romantic(major)

M

6,3

m7

6,3

m7

M7

6,3

9s

6,3

m7

M

m7b5

Boogie(major)

7

Dim7

7

Dim7

7

7

Dim7

7

Dim7

7

7

7

Noble(major)

M

6,3

m

6,3

6,3

M

6,3

M

4,3

6,3

4,2

6,3

Bittersweet(Harmonic minor)

m

6,5

m7b5

M

Dim7

m

Dim7

7

M

m7b5

M

dim7

Adventurous(H-minor)

m

M

6,3

M

6,3

m

6,3

m

M

6,5

M

6,5

Striving(minor)

M7

M

6,3

M7

6,3

m7

6,3

m7

M7

6,5

M

6,5

Sophisticated(major)

6,9

Dim7

m11

Dim9

m7

M9#11

Dim7

13

Dim7

m11

9#11

Dim9

Miserable(mixolydian)

13

Dim7

m11

Dim9

m11

13

Dim7

13

Dim7

m11

9#11

Dim9

Complex(major)

2

6,3

m11

Dim7

m6,7

2M7

6,3

9s

2M7

6,3

2

6,3

An alternative way of course would be to correspond personalities only to the 7 modes, and then besides the 3-notes chords with roots one every note of the 7-tone mode, add all the other notes to make 12-notes of the chormatic scale, and extend, the triads to 4-notes chords making sure the added note (that would be of the melody) is always the highest. In this way 5 mores composite chords (for chord-melodies) are added to the mode which is now the chromatic 12-tone scale.

Still an alternative and simple way is  to consider the above table only at the 7 steps of a diatonic scale, and use it to adopt the chord progressions of single diatonic scale harmony songs , to a  new one  (the roots of the chords are kept the same) but the harmony of the song changes and possible and some of the notes of its melody.

Such personalities therefore is a generalization of the 7 modes of the diatonic scale , to any scale of any number of notes and in a different way..

We may compare the above method of personalities with the Personalities of the modes of the   as it was traditional to define in older music but which cannot be played anymore in the 12-equal semitones of Bach. .

Each mode of the diatonic scale can be grasped from the central triad  5-1-4 (in steps) of it thus a triad of chords as center of an harmonic personality, which blends in various proportions minor and major chords (see also post 222)

Various interpretations of the "character" imparted by the different modes have been suggested. Three such interpretations, from Guido of Arezzo (995–1050), Adam of Fulda(1445–1505), and Juan de Espinosa Medrano (1632–1688), follow:

Name	Mode	D'Arezzo	Fulda	Espinosa
Dorian	I	serious	any feeling	happy, taming the passions
Hypodorian	II	sad	sad	serious and tearful
Phrygian	III	mystic	vehement	inciting anger
Hypophrygian	IV	harmonious	tender	inciting delights, tempering fierceness
Lydian	V	happy	happy	happy
Hypolydian	VI	devout	pious	tearful and pious
Mixolydian	VII	angelical	of youth	uniting pleasure and sadness
Hypomixolydian	VIII	perfect	of knowledge	very happy

In modern times the names are somehow reserved but the exact frequency structure of the modes has been lost. Here is the modern version

Mode	Tonic relative to major scale	Interval sequence, T=tone, s=semitone	Example
Ionian	I	T-T-s-T-T-T-s	C-D-E-F-G-A-B-C
Dorian	II	T-s-T-T-T-s-T	D-E-F-G-A-B-C-D
Phrygian	III	s-T-T-T-s-T-T	E-F-G-A-B-C-D-E
Lydian	IV	T-T-T-s-T-T-s	F-G-A-B-C-D-E-F
Mixolydian	V	T-T-s-T-T-s-T	G-A-B-C-D-E-F-G
Aeolian	VI	T-s-T-T-s-T-T	A-B-C-D-E-F-G-A
Locrian	VII	s-T-T-s-T-T-T	B-C-D-E-F-G-A-B

See e.g. https://en.wikipedia.org/wiki/Mode_(music)


CHROMATIC TONAL MUSICAS CONTRASTED TO MULTI-TONAL MUSIC OR ATONAL MUSIC.

IN SUMMARY BOTH EARLY WESTERN AND EASTERN (GYPSY) JAZZ MAY MAKE THE NEXT 7 TEMPORARY CHANGES IN THE CHORDS OF THE DIATONIC SCALE DUE TO THE 4 FIRST BLUE NOTES 

3m becomes 3M

7dim becomes 7M

5M becomes 5#dim

2m becomes 2M

6m becomes 6M

4M becomes 4m or 4dim

1M becomes 1#dim

Obviously not all of these changes occur necessarily simultaneously in a single song. maybe only few of them. And usually at least 50% of the time the chords are the normal of the diatonic scale. Other ways to organize them and perceive them are as triads of harmonic pairs of chords (see post 215  IMPROVISATION OVER A PAIR OF CHORDS . TRIADS OF HARMONIC PAIRS OF CHORDS. ). This awareness of these alterations of the normal chords of a diatonic scale (by blue notes) allows for a consistent and rich system of harmony for composing and improvising early jazz type of jazz.

There are musicians that consieve these changes as modulations say from the C major scale to th Fmajor scale and/or to the A major scale. But the above approach based on the harmonic minor and double harmonic minor seems more correct.

1ST CHROMATIC TONALITY 7-CHORD-SCALE OR 7-CHORD CYCLE  

THEREFORE IT IS A VERY COMMON IN WESTERN JAZZ GYPSY JAZZ CLASSICAL MUSIC ANDEAN MUSIC ETC THE NEXT CYCLE OF CHORDS OR SCALE OF CHORDS THAT CAN BE CALLED  1ST CHROMATIC TONALITY 7-CHORD-SCALE OR 7-CHORD CYCLE  THE NEXT

6m->2m->5M->1M->4M->7M->3M->6m

or with 7nths in Jazz

6m7->2m7->5maj7->1maj7->4maj7->7M7->3M7->6m7


There are even pocket chord-harmonicas (e.g. tombo pocket-chord harmonica) designed to play exactly this cycle of chords

AS WE MAY NOTICE THIS SYSTEM OF HARMONY WITH THE FIRST 4 BLUE NOTES (AND  5TH BLUE NOT 6#=7b  MAY BE ADDED) IS ESSENTIALLY A METHOD TO PLAY SOONER OR LATER IN THE MELODY ALL THE 12 NOTES OF THE FULL CHROMATIC SCALE STARTING FROM THE 7 NOTES OF THE DIATONIC SCALE AND RETURNING TO THEM AGAIN.

CONVERSELY ANY MELODY WHICH STARTS AS MELODY OF A DIATONIC SCALE AND THEN EVOLVES WITH ANY TURN AND ANY MOVE INSIDE THE 12-NOTES FULL CHROMATIC SCALE CAN BE COVERED OR ACCOMPANIED WITH THE NEXT ALTERNATIONS OF THE CHORDS OF THE DIATONIC SCALE. IN WESTERN JAZZ IT IS CONCEIVED AS ALTERATIONS DUE TO THE BLUE NOTES WHILE IN EASTERN JAZZ AS ALTERATIONS DUE TEMPORARY CHANGE OF THE NATURAL MINOR TO ONE OF THE CHROMATIC MINORS (HARMONIC, DOUBLE HARMONIC , NEAPOLITAN , PARACHROMATIC MINORS ETC) THIS MAY BE CALLED CHROMATIC TONAL MUSICAS CONTRASTED TO MULTI-TONAL MUSIC OR ATONAL MUSIC.

Steps of the chromatic scale/Harmonic Personality

1

1#

2

2#

3

4

4#

5

5#

6

6#

7

JAZZ PERSONALITY

1M(ajor) or 1m

1#Dim or 6M

2m(inor) or 2M(ajor)7

7M

3m or 3M(ajor)7

4M or 4m or 4Dim

2M7

5M7 or 5m

5#Dim or 3M7

6m or 6M7

5m

7Dim or 7Major7

35. Two-notes power chords . Major, Minor, and neutral power chords. Their special role in harmony. Improvisation method based on power-chords for relaxation and meditation music.

R5 chords do not have the attribute or quality of minor or major. 
The R5 chords have the highest harmonic score among all 3-notes chords within an octave (see post 40 )

Instruments design based on R5 chords is e.g. the 3-string Greek Buzuki (D, A, D), Tzuras, Baglamas etc. or 3-string ancient Sumerian instruments.

Interval-Chords or 2-notes-chords  are of the type an-b-a(n+1) , where an is a note and a(n+1) is the same note one octave higher, and the interval an-b is one of the intervals that occurs in the major, minor, diminished, augmented and  maj7, dominant7 chords. Therefore the interval an-b would be minor or major 3rd (3 or 4 semitones) in which case the interval-chord is denote by R3m, R3 respectively (where R is the root note) , or an-b would be a 4th or 5th interval (5 or 7 semitones) thus an R5m or R5 chord (actually the R5m is an inversion of R5), or an-b would be a minor or major 7nth interval (8 or 9 semitones) in which case we may denote it by R77, or R7maj7, so as not to confuse them with the standard notation of dominant 7nth R7 and major7nth Rmaj7 chords. Such interval chords are used to derive melodies from a chord progression (see posts 69, 68).

Such chords allow more freedom to melody that they accompany compared to 3-note chord. 

Improvisation method based on power-chords for relaxation and meditation music.

(See also post 93)

Within the current improvisation method of random melodies with high harmonic statistical profile as in post 93, is the improvisation method for relaxing and meditation based of power-chords . This is mainly alternating a power chord of interval of 5th/4th with a power chord of interval 3rd/6th, or in general alternating a power chord of interval 5th/4th with any 3 notes which are chords or not. The next videos describe it for the case of a Celtic harp.

https://www.youtube.com/watch?v=Z6JuEslUk_E

https://www.youtube.com/watch?v=aN-LFOZdqu4&t=33s

34. The 24-cycle of alternating major/minor 3rds as refinement of the cycle of 5ths with its symbolism for chord progressions. The 2-dimensional hexagonal or square, tonality grid for chords geometric representation.

HERE IS THE 24-CHORDS CYCLE IN THE REVERSE ORDER BY 5TH RATHER THAN BY 4TH WHICH IS THE ACTUAL 

THIS WHEEL IF WE WALK LIKE A ZIG-ZAG ALTERNATING MINOR WITH MAJORS IT IS NOT A WHEEL BY 4THS OR 5THS BUT A WHEEL BY THIRDS (ALTERNATING MINOR MAJOR THIRDS)

Also we may define a 24, cycle in alternating major/minor intervals of  3rds ,  and also alternating major/minor chords , so that consecutive chords are relative chords, and as 3s+4s=7s, it is also a refinement of the cycle of 5ths. In the next we state this cycle in the reverse order, which seems as if a refinement of the cycle of 4ths, with alternating steps of 8  and 9 semitones (small and big interval of 6th). As notes of the consecutive chords we have also the pattern (434343434343434343434343) which is (generalized) long scale as in the definitions of the post 42.

G        C         F         Bb          Eb        Ab         Db          Gb          B            E            A              D              G                 
      Em   Am     Dm        Gm       Cm       Fm        Bbm       Ebm     Abm       Dbm       Gbm         Bm             Em


This cycle of 24-chords seems that it is used for example in software that helps composing songs like the Harmony Navigator 2, see next video
https://www.youtube.com/watch?v=xa6eTlS3uDk
 https://www.youtube.com/watch?v=FfZygNUmFas
This pattern of the chords appears naturally on the fretboard of a bass or guitar tuned on all chords by pure 4ths!  In the next image we see only the positions or arpeggio pof the cmaj chord, and we can easily add the lower relative Am.Then put the same for all other postions of the other chords. The vertical direction from lower to higher notes is thesame as the direction of the 24-cycle of chords. Every vertical path inside a fret, spans with 3 of the positions of the major chords a diatonic scale.

As it is usual to apply  numbers for the chords on the steps of a diatonic scale giving some abstractness to chord progressions, we apply apply also the same here in the 24 double cycle o chords.

We may symbolize any (major) chord of this cycle by capital X, and its next chord in the cycle by X+1, e.g. X=G, X+1=C or X=D, X+1=G etc. Now for the relative minor chords we reserve small variables like x, x+1, and we use the same x as the Capital X for the upper minor relative chords e.g. if X=G, then x=Em, if X=D then x=Bm,  And if x=Em then x+1=Am etc. I is important to realize some recursive equations here like (Xm=x+4) and (xmaj=X-4), where by Xm we denote the minor chord with the same root with  the major X and by xmaj the major chord with the same root as the minor x. 
Under this symbolism the 3 minor relatives chords of a major chord X would be the x, x-1, and x+4=Xm

Thus according to this symbolism an Andalusian cadenza progression like (Dm, C, Bb, A)  (see post 17) would be symbolized  by  (x, X-1, X+1, X-4) or (x, X-1, X+1, X+8), while the jazz progression (ii, V7, I)  would be symbolized by (x, (X-2)7, X-1) or (x+1, (X-1)7, X), where by (X-2)7 we symbolize the dominant seventh version of the major chord X-2. 

A double Andalusian Cadenza (see post 17) e.g.  (Am Dm)->(G-C)->(F Bb)->(E A) will become  (x, x+1)->(X-1,X)->(X+1,X+2)->(X-4,X-3) , from which we see directly the many consecutive positions in the cycle of 4ths and 24 chords  .

The advantage of this symbolism of progressions, is that it is scale-free, and the resolutions X7, X+1 (e.g. C7, F) are directly understood as well as the relatives relations like X-x (e.g. C, Am) etc.

The chords of a diatonic scale in this 24-cycle are easily defined as the chords of an arc of 3 consecutive major chords together with their 4 relative minors. The root of the diatonic scale is the middle major chord. In the symbolism above it is the next arc of 7 chords 
 (x-2, X-1,x-1,X,x,X+1,x+1)=(vii,V,iii,I,vi,IV,ii).

Notice that strictly speaking of for example X =C, then the x-2=Bm is not the exactly  a correct chord type of the scale as the Bdim (=xdim) is, but in the 24-cycle there are no diminished chords thus the 7th chord is represented there as minor chord. 


The best way to learn the fretboard is by chords and the best way to learn the fretboard by chords is to map the 24-cycle of chords on the fretboard!

A simple way to map the 24-cycles on the on the fretboard is to map the 12-cycle of chords by 4ths, in vertical lines relative to the strings , where three chords of shapes E, A, D are in the vertical line, and the continue the vertical line higher of lower in the fretboard. 


THERE ARE TWO WAYS THE THE WHEEL OF 4THS (OR 5THS) IS REPRESENTED WITH e, a, d SHAPE CHORDS IN THE FRETBOARD
1) THE FORWARD OR ASCENDING METHOD (NO REPETITION OF CHORDS)
2) THE BACKWARD DESCENDING METHOD WITH REPETITION ( A D-SHAPE CHORD IS NOMINALLY  IDENTICAL WITH THE NEXT E-SHAPE CHORD

STILL THE LARGEST ARC OF CHORDS IN THE WHEEL OF 4THS WITHOUT FLATS OR SHARPS THAT IS REPRESENTED IN THE FRETBOARD IS WITH THE BACKWARD METHOD, AND IS ANALYZED IN POST 13 AS THE MAIN 3-NEIGHBORHOODS OF THE FRETBOARD, THE G (1ST), A (2ND) AND b (3RD). 

THE STANDARD GUITAR TUNING IS ALMOST SUB-OPTIMAL IN REPRESENTING IN A QUITE SYMMETRIC WAY THE WHEEL OF 4THS IN THE CHORDS. PROBABLY THE BEST IN IN REPRESENTING IN A QUITE SYMMETRIC WAY THE WHEEL OF 4THS BY CHORDS IN NORMAL POSITION IS THE REGULAR TUNING BY 4THS. BUT IT HAS DIFFICULT SHAPES FOR THE INVERSIONS, WHILE THE STANDARD NOT SO MUCH.





Then the relative chords are discovered as relations of a chord at the vertical line with a chords at the neighboring vertical lines. The rules to do so are the next

In relation with the 24-chords cycle of chords by intervals of 4ths  the DAE system has the next keys and correspondences (with the symbolism of chords on the fretboard as in post 23 ).

 The sequence  X=(nE)Y1, X+1=((n)A)Y2, X+2=((n)D)Y3 is of course a vertical sequence of chords in the fretbaird and a sequence of 3 successive chords in the cycle of 4ths and symbols of the current post. Now after the X+2=((n)D)Y3, the cycle of 4ths continues either lower in the fretboard or higher in the fretboard

1) Lower in the fretboard is X+3=((n-2)A)Y4

2) Higher in the fretboard is X+3=((n+3)E)Y4

From this point of view, the area of the open chords of the guitar, is simply two such vertical 3-sequences of chords on the cycle of 4ths, as the C-shape is essentially a ((n-3)D)Y chord and D-shape and the G-shape is a ((n-2)A)Y chord and A-shape. 

For the relative chords of major chords the rules are :

The (nE)X chord (which means the chord of E shape at the nth fret, and that sounds like X) has as minor lower  relative  chord the ((n-1)Dm)Ym (e.g. F with Dm)  (or ((n+4)Am)Ym) and as upper relative chord the  ((n-3)Am)Zm (or  ((n+4)Em)Ym) 


The (nA)X chord (which means the chord of A shape at the nth fret, and that sounds like X) has as minor lower  relative  chord the ((n+2)Em)Ym (e.g. A with F#m) and as upper relative chord the
 ((n-1)ADm)Zm

The (nD)X chord (which means the chord of D shape at the nth fret, and that sounds like X) has as minor lower  relative  chord the ((n+2)Am)Ym (e.g. D with Bm) and as upper relative chord the ((n+2)Em)Zm

It is easy to see that the shape of lower relative minor chord of  major chord, compared to the shape of the major chord is simply the cycle of letters of the DAE system (D->A->E->D), which is the reverse order of the successive irresolution relations which is  E->A->D->E . That is the lower relative minor of major D shape chord is a minor A shape chord, the lower relative minor of major A shape chord is a minor E shape chord, the lower relative minor of major E shape chord is a minor D shape chord!!! Notice also that to find the lower relatives of the vertical sequence of successive resolutional chords E,A,D on the fretboard, we only need to go either 1 step lower in the fretboard (n-1) or 2 steps higher in the fretboard (n+2). 
One step lower for E and 2 steps higher for A and D, while always the shape of the relative is in the reverse order of the resolutional order E->A->D->E. 

Notice also that the upper relative of a major chord X , is the lower relative chord of its previous chord in the cycles of 4ths, that is the lower relative chord of X-1. Summarizing upper relative of X=lower relative of X-1.  Therefore we need only memorize the lower relatives if we are familiar with the successive resolutional relations of chords.

While the shape of upper relative minor chord of  major chord, compared to the shape of the major chord is simply the reverse order of cycle of letters of the DAE system (D->E->A->D) exactly as in the relation of successive resolutions . That is the upper relative minor of major D shape chord is a minor E shape chord, the upper relative minor of major A shape chord is a minor D shape chord, and the upper relative minor of major E shape chord is a minor A shape chord!!!

For the relative chords of minor chords:

The (nEm)Xm chord (which means the chord of E shape at the nth fret, and that sounds like X) has as minor lower  relative  chord the ((n-2)D)Y and as upper relative chord the ((n-2)A)Z


The (nAm)Xm chord (which means the chord of A shape at the nth fret, and that sounds like X) has as minor lower  relative  chord the ((n+1)E)Y and as upper relative chord the ((n-2)D)Z

The (nDm)Xm chord (which means the chord of D shape at the nth fret, and that sounds like X) has as minor lower  relative  chord the ((n+1)A)Y and as upper relative chord the ((n+1)E)Z

Of course the in-place change of a chord from minor or major or vice-versa is also a relation of middle  relative chords. 

The 3 ways to play all the chords of a major scale on the fretboard within 4 or 5 frets,  with root-chords as D, A, or E shape and are the next. They are mostly convenient for 3 or 4 string instruments where even the D shape is played easily with all 4-strings (see post 67) 

1) With D-shape as root,   In the symbolism of post 23 the  (nD)X means at n-th fret play the shape D and it sounds as chord X. Here instead of X we will utilize the Latin symbols of the steps in a major scale, as it is standard in Jazz with small if the chord is minor and capital if the chord is major

So the chords I, ii, iii, IV, V, vi, vii, are played on the fretboard  as follows

I=(nD)I, ii=((n+2)Dm)ii , iii=((n)Em)iii, IV=((n+1)E)IV, V=(nA)V, vi=((n+2)Am)vi ,

  vii=((n+1)dim7)vii.

In short the three main major chords I, IV, V are the 

I=(nD)I, IV=((n+1)E)IV, V=(nA)V.

The geometry of the shapes E,A,D vertically and horizontally on the fretboard are as in the following table. We place vertically the E,A,D shapes of the major chords V,I,IV and 3 more minor chords that are complementary by one tone higher to V, I, and one semitone lower to IV, on the fretboard. Notice also that the minor chords are positioned vertically on the fretboard as  the also have mutual successive resolutional relation

(n+3)E=IV	(n+2)Em=iii
	(n+2)Am=iv		nA=V
	(n+2)Dm=ii		nD=I

2) With A-shape as root,  where the I, and V are on the same fret. In the symbolism of post 23 the  (nA)X means at n-th fret play the shape A and it sounds as chord X. Here instead of X we will utilize the Latin symbols of the steps in a major scale, as it is standard in Jazz with small if the chord is minor and capital if the chord is major

So the chords I, ii, iii, IV, V, vi, vii, are played on the fretboard only as shapes A and E as follows

I=(nA)I, ii=((n+2)Am)ii , iii= ((n-1)D)iii,  (nD)IV,  V=(nE)V,  vi=((n+2)Em)vi  

vii=((n)dim7)vii.

In short the three main major chords I, IV, V are the 

I=(nA)I, IV=((n)D)IV, V=(nE)V. 

The geometry of the shapes E,A,D vertically and horizontally on the fretboard are as in the following table.We place vertically the E,A,D shapes of the major chords V,I,IV and 3 more minor chords that are complementary by one tone higher to V, I, and one semitone lower to IV, on the fretboard. Notice also that the minor chords are positioned vertically on the fretboard as  the also have mutual successive resolutional relation

(n+2)Em=iv		nE=V
(n+2)Am=ii		nA=I
		nD=IV	(n-1)Dm=iii

3) With E-shape as root,   In the symbolism of post 23 the  (nE)X means at n-th fret play the shape E and it sounds as chord X. Here instead of X we will utilize the Latin symbols of the steps in a major scale, as it is standard in Jazz with small if the chord is minor and capital if the chord is major

So the chords I, ii, iii, IV, V, vi, vii, are played on the fretboard  as follows

I=(nE)I, ii=((n+1)Em)ii , iii=((n-1)Am)iii, IV=((n)A)IV, V=((n-2)D)V, vi=((n-1)Dm)vi ,

  vii=((n-1)dim7)vii.

In short the three main major chords I, IV, V are the 

I=(nE)I, IV=((n)A)IV, V=((n-2)D)V.

(n+2)Em=ii		nE=I
		nA=IV	(n-1)Am=iii
		nDm=iv		(n-2)D=V

2-dimensional hexagonal  tonality grid for chords geometric representation

This hexagonal grid,is defined by the following rules

1) Horizontal sequences of notes differ by the interval of perfect 5th (7 semitones) or its inverse perfect 4th (5 semitones). In the image below from left to right the interval is perfect 5th.

2) Diagonal sequences of notes differ by an interval of  major 3rd  (4 semitones) o minor 3rd (3 semitones). The diagonal left to right and up to down is a minor 3rd. While the diagonal left to right and below to up is  amjor 3rd.

Chords, are represented as triangles or rombuses in this hexagonal grid.

(See e.g. the visualization software for music MAM, http://www.musanim.com/

http://www.musanim.com/player/MAMPlayerUserGuide.pdf )

For the hexagonal representation of tonality effects see also the schismatic temperament 

https://en.wikipedia.org/wiki/Schismatic_temperament

As an alternative we may define a square grid. The rules are:

1) Horizontlly from left to right the interval  is a perfect 4th (5 semitones)

2) Vertically from down to up it is alternating 3rd major and 3rd minor intervals.


More about hexagonal ingenious keyboards here

Terpstra Keyboard :

https://www.youtube.com/watch?v=QUJ2oND3cdg
 AND

Lippens Keyboard:

https://www.youtube.com/watch?v=MHfG20HvPHA

In the latter square grid, every 3x3 square are the notes of a diatonic scale. The relation of scales and chords with common notes are directly asilly visible. Roots of alternating major moinor relative chords are on vertical lines.

We may also define a Z(12)^3   ring, of the chords , where each component Z(12) is the cycle of 4ths, and neigborhood chords among the three componenets are always relative chords.

The 5 -triads in successive resolution harmonic relation on the fretboard.

The best way to learn the fretboard is without mental images but only the feeling of the notes at each fret.But this takes too much practice and familiarization with the fretboard.
On the other hand the best way to learn all the fretboard through mental images,rather than feeling,is not by patterns of scales, neither by the names of all the notes of the frets, but rather with sufficient many chord-shapes that almost cover all the fretboard. And even better  if these chords are organized in to easy repeating patterns. Here we describe a method, based on the triads of chords in shapes of E, A, D, so that each is relative to its previous, at the harmonic relation of successive resolution in the cycle of 4ths (see also post 30, 23).

Here we list the chords of shapes E, A, D,on the notes of the e4-string

e4, g4, a4, b4, d5, 

For the symbolism of chords placed on the fretboard, see post 23

chords (E- shape) V	chords (A- shape) I	chords (D- shape) IV
e4  (0E)E	(0A)A	(0D)D
g4 (3E)A	(3A)C	(3D)F
a4 (5E)A	(5A)D	(5D)G
b4 (7E)B	(7A)E	(7D)A
d5 (10E)D	(10A)G	(10D)C

When adding the minor chords of the diatonic scale, if the roots is an A-shape we have the following positions

33. The emotions chart of a song.

x-axis=time
y-axies= sadness-joy
z-axies=anxiety-serenity

The reason we choose only these 2 emotional dimensions or 4 emotions is because, the middle not of a chord defnes the sadness-joy dimension, while the upper (dominant) note of the chor defines the anxiety-serenity emotinal dimension

The composed song  must have a definite phrase with start , tension, resolution and end, in the diagram of emotions. The emotions correspond not only to the harmony of the chords but also to the morphology of the melody dynamics and rhythm and of course to the meaning of the lyrics.

Summarizing in  a simplistic way the correspondence of melodic pitch dynamics and the 4-basic emotions in music (joy, sadness, anxiety, serenity) we have 
1) Up pitch moves correspond to joy
2) Down pitch moves to sadness
3) Small pitch intervals of 1 or 2 semitones (chromatic or interval of 2nd) correspond to anxiety

4) Large pitch intervals (e.g. 4th, 5th octave etc) correspond to harmony and serenity. 

E.g. in order to have mainly joy the next rules apply (see also post  73 )

5) Descend in melody with small steps (1 semitone, and intervals of 2nd or minor 3rds ) and ascend with larger steps (intervals of major 3rds, 5th or octave).Ascending with larger steps that those of descending indicates favor of joy. E.g. Ascend with intervals of 2nd and major 3rd and descend with 2nds and minor 3rds. 
6) While ascending, accelerate ascending (meaning use large and larger steps, or larger distances up)Accelerating ascending indicates more joy, while decelerating ascending less joy. The converse with descending. E.g. Ascend by first intervals of 2nd then 3rd and finally 4th or 5th while descend at first with intervals of 5th or 4th, then 3rds and finally 2nds. 
7) Melodies that move with steps of minor 2nds and minor 3rds mainly may be called minor feeling melodies, while melodies that move with steps of major 2nds and major 3rds mainly may be called major-feeling melodies.

We must emphasize a basic philosophy  here that when playing the musical instrument, we do not only produce musical sounds but also independently emotions in us. And I do not mean that the musical sounds produce the emotions I mean that our self is producing the emotions parallel and in fitness with the musical sounds

See also post 59 about the 4 basic melodic moves (spike, waving, scaling, isokratic) and their psychological meaning.

1) up/down spike (=large interval of 5th or larger in one or very few steps, extreme emotional effect, excitement , emotional intensity)

2) up/down waving (also called in this blog butterflying, emotional effect of playing either sad of with joy, emotional complication and ambiguity)

3) up/down scaling (direct ascending or descending of notes in a monotone order without waving, emotional effect straight usually with simplicity, emotional clarity)

4) Iso-kratic waving (=horizontal waving with repeating same note, peculiar emotional effect of internal symmetry , and emotional stability )

From these 4 patterns the 1) and 3) are simple and with emotional clarity. The 2) and 4) are with emotional complication and ambiguity.

Another classification would make them 5!

1) Straight scaling up or down (including spikes) in one or more of the melodic speeds (straight sadness or joy). Here the notes of the simplicial submelody are the starting and ending notes.

2) Ascending or descending waving (complex sadness or joy). Here the notes of the simplicial submelody are the starting and ending notes.

3) Flat equilibrium waving (serenity and equilibrium emotion).Here the notes of the simplicial submelody are the upper level and lower level ofthe flat channel.

4) Flat diminishing waving (serenity and diminishing emotions). Here the notes of the simplicial submelody are the starting upper or lower level and h ending note of the diminishing channel

5) Flat expanding waving resolving up or down  (serenity emotions exploding to either sadness or joy). Here the notes of the simplicial submelody are the starting note and the ending note at the upper or lower level of the expanding channel.

MORE PITCH DYNAMICS AND THEIR PSYCHOLOGY

We may create more complex pitch dynamic patterns than these basic with recognizable psychological meaning. Eg. a melodic theme that has a spike up but then falls back to the same pitch level corresponds ton an emotion of "complaining" or "crying" or angry protest that turns to  sadness" 
In general when the melody is ascending through repetitive descending melodic themes, or is descending through ascending repetitive melodic themes, the emotion (either joyful or sad) is more dark emotion compared to than when the  the melody is ascending through repetitive ascending melodic themes, or is descending through descending repetitive melodic themes, the emotion (either joyful or sad) in which latter case it is an emotion more straight and transparent. 

Some instructive remarks in the composition of the melody based on the chord progression

1) In the part of the chord progression with minor chords, utilize descending melodic moves so that sadness from melody and sadness from harmony fit.Similarly ascending melodic moves for  major chords.

2) In the sad melody parts of the melody (and minor chords) utilize rhythmic patterns that start with faster notes and end with slower notes, and the reverse for the happy part (and major chords).

3) In a triad or 7 nth 4-notes chord the most characteristic notes are the middle 2nd note (in 1-3-5 interval notation  is the 3) and the 7 nth (if it exists). So for the anxiety part of the melodic moves we may utilize 1-semitone trills around these two notes, or waving with 1 or 2 semitones steps and notes outside the chord in the interval of minor 3rd (3 semitones) of the chord. Alternatively instead of trill or small amplitude waves we may utilize chromatic monotone scaling by steps of 1 semitone , or scaling with steps by intervals of 2nd of the scale,  that go from these previous notes of the chord to the same such notes in the next octave. But always make sure that the notes of the chord sound in the average longer, than the notes of these anxiety transition moves with notes outside the chord. 

4) Alternate up (happy) and down (sad) pitch moves , or chromatic moves (anxiety), with harmonic (on chord notes) moves (serenity-harmony).

5) Utilize at least 2 octaves, or even 3 for the melodic moves repeating the notes of the underlying chord on the next octaves , so there is sufficient space for melodic moves, to express with sufficiency the emotions.

6) For the duality of emotions anxiety-serenity, it may be utilized also harmonic waves or monotone scaling over 2 octaves at least,  on the notes of the chord, but also chromatic trill wave over the notes of this wave or scaling (modulated wave on wave or move) and then return to the pure harmonic wave or scaling on the notes of the chord.

7) A chromatic wave by 1-semitones steps or all notes of the scale (steps by intervals of 2nd) that goes up and down at least 2 octaves, corresponds to a chord sub-progression of the song , of our choice that utilizes almost all the chords of the scale!

After the chord progression and simplicial submelody we chose, 

THE DEFINITION OF MELODIC BRIDGES THAN LINK TWO SUCCESSIVE CHORDS BETWEEN THEM AND START AND END AT THE NOTES OF  THE SIMPLICIAL SUBMELODY.

1) WHICH CHORD-TRANSITIONS (PAIRS OF CHORDS) WILL HAVE A MELODIC BRIDGE! (Usually the chord-trasnitions that are in resolutional relation, or resolutional-like relation)

2) THEN WHICH BRIDGES WILL BE ISOMORPHIC IN PITCH AND RHYTHMIC DYNAMIC SHAPE AND WHICH DIFFERENT, DEFINING THEREFORE A PARTITIONING IN THE BRIDGES.

3) THEN IF IN EACH EQUIVALENCE CLASS OF  ISOMORPHIC MELODIC BRIDGES IN THIS PARTITIONING, THE BRIDGES ARE  EVENTUALLY ASCENDING OR DESCENDING (This besides the emotional significance, determines also where to play the chord in one of the 3 neighborhoods of the fretboard)

4) FINALLY  HOW IN EACH EQUIVALENCE CLASS OF  ISOMORPHIC MELODIC BRIDGES IN THE PARTITIONING, THE COMPLICATED PITCH DYNAMIC SHAPE  OR WAVING AND RHYTHM WILL BE AS A REPETITION  OF SUCH PATTERNS OF PREVIOUS ISOMORPHIC MELODIC BRIDGES, OR VARIATION OF  SUCH PATTERNAS S SO NOT TO BE TOO BORING. (This pitch dynamic shape has again a significant emotional meaning)

Harp therapy:

https://www.youtube.com/watch?v=q2PTxZITs8M

(The post has not been written yet completely)