32. Cycles of chords of a diatonic scale: Root based cycles. The minor (sad) and major (joyful) cycles. Closed cycles of relative chords. The open cycle of chords by intervals of 4ths.

The diatonic progressions is the sequence (iii->vi->ii->V->I->IV->VII->iii), This progression leads from sadness to joy, from the triad of minor chords to the triad of major chords. In the symbolism of the 24-cycle of  chords the diatonic scale is the arc of the next chords   (x-2, X-1,x-1,X,x,X+1,x+1)=(vii,V,iii,I,vi,IV,ii). (see post 34). 

There is also the inverse or descending  diatonic progression which is the (I->V->ii->vi->iii->VII->IV->I)

In a diatonic scale, the triad of minor chords (sad triad) is the (iii->vi->ii) where the (iii, vi) and (vi,ii) are consecutive in the cycle of pure 4ths, with standard resolutions (iii7-> vi) , (vi7->ii) and the 
(ii, iii) are complementary chords, in other words all of their notes give all the notes of the scale except one. 

The triad of joy or triad of major chords  is the (V, I, IV) , where the (V, I) and (I,IV) are consecutive in the cycle of pure 4ths, with standard resolutions (V7-> I) , (I7->IV) and the  (IV, V) are complementary chords, in other words all of their notes give all the notes of the scale except one. 

The bridge between these two triads is the well known jazz progression (ii7, V7, I) , where again  the (ii, V) and (V,I) are consecutive in the cycle of pure 4ths, with standard resolutions (ii7-> V) , (V7->I), and  the  (ii, I) are complementary chords, in other words all of their notes give all the notes of the scale except one. 



Alternative closures 
The diatonic progression closes also to a cycle by utilizing the triad progressions 
(IV->IV#7->VII7->iii) or (IV7->VIIb->vi). 
Or IV->V7->I or IV->ii7->V7->I
Or IV->IVdim7->G7->I   (see e.g, Bach prelude and Fugue C major, BWV 846)
Or IV->IV#dim7->VII7->iii


The 4-chords (3333444)=(C,D#,F# ,A,C,E,G#,C) is  closed cycle of relative chords:   Cdim7, Am, Eaug, G#



The 7-chords (3334434)=(C,D#,F#,A,C#,F,G#,C) is  closed cycle of relative chords: Cdim, D#dim, F#m, Aaug, C#, Fm, G#


The 7-chords diatonic closed cycle of relative chords is the  (4343343)=(CEGBDFAC):
C, Em,G, Bdim, Dm, F,Am

The 24-chords chromatic closed cycle of relative chords (434343434343434343434343):

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


We may add two more series based on that mnot-major chords with the same root are relative chords too, so as to havea 2-dimensional grid based of the relation of relatives.


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

This grid which is also a table as below shows clearly the chords that are  harmonically in series(interval of 4th or 5th) and chords that are harmonically in parallel (intervals of 3rds or 6ths). But it does not show of course the relations of chords that are melodically in series

Gm

Cm

Fm

Bbm

Ebm

Abm

Dbm

G

C

F

Bb

Eb

Ab

Db

Em

Am

Dm

Gm

Cm

Fm

E

A

D

G

C

F

	Gbm		Bm		Em		Am		Dm
	Gb		B		E		A		D
Bbm		Ebm		Abm		Dbm		Gbm		Bm
Bb		Eb		Ab		Db		Gb		B

It is often very instructive to chart the chords of  a  song over this 24-cycle of relatives (or double cycle of 4ths) or the above 2-dimensional grid.

Most often a song is a sequence of connected intervals or arcs of chords in the cycle of 12ths shifting by relatives to a corresponding similar connected arc in the parallel cycle of 4th in the overall cycle of fifths. We call this concept a harmonic multi-tonality. Simple  tonality is simply 3 -successive major chords in the 12-cycle of 4ths. 

Conversely any connected sequence of arcs of chords of this 24-cycle of chords (defining harmonic multi-tonality), is the chord progression  of a nice song with nice sounding modulations. Normally in harmonic multi-tonality  we are keeping the qualities major-minor as in the 24-cycle but a more free approach allows altering them , from minor to major and vice versa or to more complicated qualities like 7th, 6ths etc.  The same for chord progression for improvisation (see post 11) . To the rule of harmonic multi-tonality in the 24-cycle, we may allow as transition to a next chord, a shift by one semitone or tone of the root of the current chord. (see also post 30)

See also https://www.youtube.com/watch?v=TRz73-lSKZA


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

FOR PLACING THE HARMONIC CYCLE OF 24-CHORDS ON THE GUITAR FRETBOARD SEEING THUS THE CHORD-RELATION OF RELATIVES, AND CHORD RELATION OF DOMINANT7-ROOT RESOLUTION AS FRETBOARD-RELATIONS OF THE CHORD SHAPES IN THE DAE SYSTEM SEE POST 44.

But we may make some partial remarks about placement on the fretboard


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

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-1)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 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. 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 fretboard and a sequence of 3 successive chords in the cycle of 4ths and symbols of the post 23, and 34. 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  (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 and as upper relative chord the
 ((n-1)Dm)Zm (or ((n+2)Am)Ym )

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 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). 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!!!

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. 

In order to create the melody ove sucha  cycle of chords we may proceed as follows.

1)We compose 2 or 3  simplicial sub-melodies one for each part of the song ,  with one note per chord, over the cycle of chords preferably at a chromatic sequence ascending and descending . 

2) We create moves or waves for each note of the simplicial sub-melody by sequencing during the chord with two types of notes a fast (usually outside the chord) and a slow of double duration on the notes of the chord again ascending or descending with smaller waves

3) We arrange a continuous sound instrument to play the simplicial sub-melody only and a discrete sound (guitar mandolin etc) to play the full waves melody.

31. The circular ring Z(12) representation of the 12-semitones chromatic or equal temperament scale as a game. Chords melodically in series

(The post has not been written yet )

30.Transitions of chords in chord progressions . The 3 basic relations of chords.

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 3 basic harmonic relations of two successive chords are described as types of chord transitions below and are based on the 3 types of intervals 1) 4th as inverted perfect 5th 2) 3rd (either major or minor) 3) 2nd (either major or minor). 
AND OBVIOUSLY, SINCE THIS IS THE ORDER OF WHICH TYPE OF INTERVALS IS MORE HARMONIC (SEE POST 40 ) THE SAME APPLIES TO THE CORD RELATIONS: RESOLUTIONAL RELATION  IS MORE HARMONIC COMPARED TO RELATIVES RELATION  WHICH IN ITS TURN IS MORE HARMONIC COMPARED TO DIATONIC OR COMPLEMENTARY RELATION!

The most common transitions of chords in the songs are the next 3 

1) HARMONIC RELATION Successive  resolutional  relation  of chords (Wheel of 4ths)
R1(x)-->R2(y) where R2 is a perfect forth higher than R2, and x, y define the quality of the chord as major, minor, dim, 7th etc. Of course even more often x contains a  qualification as 7th chord resolving to a non-7th chord R2(y). E.g. G7-->C, or A7-->Dm etc

MAIN UTILITY: The main advantage of this chord transition is that with just the two chords we practically cover all the notes (except one) of a diatonic scale, and both the chords can be major or both can minor or alternating. We cover with such chord transitions melodies that may aextend a whole octave or more. By extending the first to dominant 7th chords we get also the emotion of anxiety resolution to serenity.

MELODIC MEANING : When such a pair of chords accompanies a melody then taking the themes of this melody either the theme is inside the chords is or is a bridge theme relating the two chords. This means that either the interval of 5 (4th) or 7 semitones (5th) appears as a shift or translation of the theme (chord-theme) or exists inside the theme (bridge-theme).


EMOTIONAL TRANSITION: The emotional impact is as it is very well known the resolution from anxiety to serenity (e.g. E7->Α). The reverse order has reverse emotional impact , but here enter the ingenious tricks of harmonic resolutions inversions (see post 29)

RELEVANT MELODIC DENSITY OR SPEED: The relevant melodies are the high harmonic density or high harmonic melodic speed (see post 68 ). Usually the notes x1,x2 of the simplicial submelody (see posts 9, 72 ) that correspond to the two chords of this transition are either an interval of 4th (5 semitones) apart or 1 semitone apart. 

In the symbolism of the post 23 of the chords as positioned by shape on the fretboard,
the next are in the resolutional relation relation 

The (nE)X major chord (which means the chord of E shape at the nth fret, and that sounds like X) resolves to the major  chord  ((n)A)Y while the relative to the same corresponding  relative.


The (nA)X major chord (which means the chord of A shape at the nth fret, and that sounds like X) resolves to the major  chord  ((n)D)Y while the relative to the same corresponding  relative.


The (nD)X major chord (which means the chord of D shape at the nth fret, and that sounds like X) resolves to the major  chord  ((n+2)E)Y while the relative to the same corresponding  relative.

Obviously the sequence of the letters in the term DAE system, is the reverse order of the successive resolutions relations (E->A->D)

2) MELODIC RELATION Relative chords (Wheel of 3rds)
R1(x)-->R2(y) where R2 is a minor or major one interval of 3rd lower than R1, or a major or minor 3rd higher than R1, defining thus that the two chords are relatives (normally with two common notes) . Or R1=R2 but R1(x) is major and R2(y) is minor or versa,in other words relative chords with the same root. . Most often of course normally, the first is major and the second minor and vice versa. E.g. C-->Am or 

C-->Em, or Em-->G. 

MAIN UTILITY: The main advantage of this chord transition is that we may pass from a minor to a major or vice-versa, thus change from sadness to joy or vice-versa with slight only change of the notes of the melody and the chord!

MELODIC MEANING: When such a pair of chords accompanies a melody then taking the themes of this melody either the theme is inside the chords is or is a bridge theme relating the two chords. This means that either the interval of 3 (minor 3rd) or 4 semitones (major 3rd) appears as a shift or translation of the theme (chord-theme) or exists inside the theme (bridge-theme).

EMOTIONAL TRANSITION: The emotional impact depends to if we pass from a major to minor or from minor to major. When we pass from major to one of its three relative minors is a transition from joy to sadness and vice versa when we pass from a minor to one of its three relative majors. 

RELEVANT MELODIC DENSITY OR SPEED: The relevant melodies are the middle harmonic density or middle harmonic melodic speed (see post 68 ).Usually the notes x1,x2 of the simplicial submelody (see posts 9, 72 ) that correspond to the two chords of this transition are either an interval of 3rd (3 or 4 semitones) apart, and at least one of them is a non-common note.

All the above three relations support the declaration of melodic bridge from harmonic speed to diatonic speed.Often melodic bridges from a chord to the next, may start with harmonic speed or density covering the first chord A and then decelerate to diatonic speed or density when reaching to the next chord B. 

ONLY TWO RELATIONS FOR THE HAND:
From the point of view of the hand on the fret-board and not of the ear, the relations of two chords can be simplified to only 2: 1) The resolutional (Shape E -> to shape A-> to shape D etc) and 2) The shift of the chord by a tone or semitone on the fretboard. The reason is that the 3rd relation of relative chords can be derived by combining the resolutional backwards or forwards and then shifting forwards or backwards by a tone or semitone!
This gives a practical "rule of thump" way to find chords in melody, by experimenting proceeds in the resolutional wheel of 4ths together shifts back or forth by tones or semitones to chords, and making it as local as possible if the melody has also similar local (small distance) changes.

ONLY ONE RELATIONS (the resolution or wheel of 4ths)  FOR THE EAR:
From the point of view of the ear recognizes harmonically the resolution relation, that is the wheel of 4ths    The reason is that the 2nd relation of complememtary can be considered as x+3 in the wheel of 4ths while 3rd relation of relative chords can be considered as the x-4 and x-5 in the wheel of 4ths. Thus all the relations translate to the resolution relation.


In the symbolism of the post 23 of the chords as positioned by shape on the fretboard,

the next are in the upper and lower relatives  relation :
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. 


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. 

3) CHROMATIC RELATION Complementary chords or chromatic relation of chords (Wheel of 2nds) 
R1(x)-->R2(y) where R1(x) and R2(y) are of the same type,in other words both major or both minor and R1, R2 are one tone apart. If R2=R1# or R2=R1b , then we classify this relation as complementary-resolutional rather than simply complementary. In other words  the chord is shifted by one semitone higher or lower, and of course most often it retains its quality as major or minor (x=y). In the rare case of the Andaluzian cadenza, the R2 is one tone lower than R1. If R2 and R1 are one step difference in a diatonic scale we say also that the R1(x), R2(y) are complementary chords as all the notes of the two chords make 6 notes all the notes of the scale except one.

MAIN UTILITY: The main advantage of this chord transition is that with just the two chords we practically cover all the notes (except one) of a diatonic scale, and we may pass from a major to a minor chord or vice versa or remain to major or minor and cover with such chord transitions melodies that may extend less than  whole octave .

MELODIC MEANING: When such a pair of chords accompanies a melody then taking the themes of this melody either the theme is inside the chords is or is a bridge theme relating the two chords. This means that either the interval of 1 (minor 2nd) or 2 semitones (major 2nd) appears as a shift or translation of the theme (chord-theme) or exists inside the theme (bridge-theme).


EMOTIONAL TRANSITION: The emotional impact depends to if we pass from a major to minor and if we step one tone higher or one tone lower. When we pass from major to a minor one step lower or one step  higher, it is a transition from joy to sadness. When  we pass from minor to a major  one step  higher, it is a transition from sadness to joy.

RELEVANT MELODIC DENSITY OR SPEED: The relevant melodies are the chromatic/diatonic  harmonic density or chromatic/diatonic melodic speed (see post 68 ).Usually the notes x1,x2 of the simplicial submelody (see posts 9, 72 ) that correspond to the two chords of this transition are either an interval of 2nd (1 or 2 semitones) apart. 

In the symbolism of the post 23 of the chords as positioned by shape on the fretboard,

the next are in the complementary by one tone  relation relation :

The (nE)X chord (which means the chord of E shape at the nth fret, and that sounds like X) has as lower  tone complementary  chord the ((n-2)E)Y and as upper tone complementary chord the ((n+2)E)Z

The (nA)X chord (which means the chord of A shape at the nth fret, and that sounds like X) has as lower  tone complementary  chord the ((n-2)A)Y and as upper tone complementary chord the ((n+2)A)Z

The (nD)X chord (which means the chord of D shape at the nth fret, and that sounds like X) has as lower  tone complementary  chord the ((n-2)D)Y and as upper tone complementary chord the ((n+2)D)Z

MORE ONCHORD RELATIONS AND THEIR PSYCHOLOGICAL MEANING HERE

M symbolizes major chord m the minor chord and the number in between the distance of their roots in semitones

https://www.youtube.com/watch?v=YSKAt3pmYBs

HARMONIC POLES AND HARMONIC WAVING IN THE CHORD PROGRESSION AND STRUCTURE OF THEMES IN THE MELODY:
The emotional parallel of the harmony of intervals, suggests that the chord progression and harmonic structure of the themes of the melody, waves (Harmonic waves) between the emotion of stress,intervals of 1 or 2 semitones to the pole of harmonic serenity ,intervals of 5 (4th) , 7 (5th) or 12 (octave) semitones.

Conversely any sequence of chords with the above rules defines an harmonically meaningful chord pattern for a nice song or improvisation. 

The order of the "average disance" of the chords in the above 3 harmonic relations are 
complementary chords< Relative chords  < Successive resolutional chords


This also corresponds to the 3-melodic densities or speeds  of the melodies that fit to such chord transitions of chord progressions. 

1) The complementary chords in a 2-chords transition corresponds to the chromatic/diatonic melodic speed or density. 
2) The relative chords in a 2-chords transition corresponds to the middle harmonic melodic speed or density. 
3) The successive resolutional  chords in a 2-chords transition corresponds to the high harmonic melodic speed or density. 


Based on the idea of the three relations of the chords, we may compose beautiful chord progressions. Two general rules are the next:

A11 . 1st general rule for harmonic chord progressions:  Progressions by arcs in the 12-chord cycle by intervals of 4th

This cycle defines by every connected arc of it a chord progression , where a chord may be substituted  with its same root relative major or minor chord , or its lower or upper minor relative chord. Of course  as they are an arc of the above 12-cycle they are successive chords or in the harmonic relation of resolution.

E.g. B7->Em->Am->D7->G->Bm-> etc 

Or B7->Em->Am->D7->G->C->(Am orA7)->D7 etc

E.g. The well known song of Frank Sinatra "Fly me to the moon" is using this technique in its sequence of chords 

https://www.youtube.com/watch?v=U8zvLvfUzCQ

Another example is the song of Nat King Cole L.O.V.E.

(main arc is the (Em or E7)->A7->D7->G(or Bm or Gm7) ->E7 etc with backwards retraces by one chord)

https://www.youtube.com/watch?v=cZ4TfRt1NK0&list=PLCD6F28C13A0A9AC2&index=12

 A12 . 2nd general rule for harmonic chord progressions:  Two arcs  in the 12-chord cycle by intervals of 4th (substituting any of the chords with its minor if it is major or vice versa) that have distance at the closest ends either 1 , or 2 or 3 or 4 semitones!

E.g. D7->G ,(1 semitone apart)  Db7->Fm 

or D7->G, (2 semitones apart) E7->Am 

or D7->G , (3 semitones apart) B7-> Em 

or Am->D7->G, (1 semitone apart) F#7->B7->Em

ANGLES IN FRETBOARD AND MELODIC SPEEDS

1) When playing the melodies on the fretboard in the guitar, the chromatic/diatonic speed is played mainly along the length of a string, so it is the zero angle.
2)  When playing the melodies on the fretboard in the guitar, the middle harmonic  speed is played mainly at an angle which relative to the horizontal is about 45 degrees and moves from the keys of the guitar to the sounding body as the melody descends in pitches! This is is because it consists of intervals of 3 or 4 semitones that in two successive strings is such an angle.
3)  When playing the melodies on the fretboard in the guitar, the high  harmonic  speed is played mainly at an vertical  angle  relative to the horizontal because the strings are tuned at intervals of 5 semitones (and one string in 4 semitones). Also the interval of 7 semitones (5th) when played in descending the pitches makes an angle  larger than vertical or 90 degrees (e.g. 135 degrees) and moves from  the the sounding body of the guitar to the keys of the guitar  as the melody descends in pitches!

Nevertheless from the point of view of common notes, the relative chords have 2 common notes, then the successive resolution chords have one common note and the complementary chords none common note.

The 3 harmonic relations of chords, with of course the chord-shapes is also a method of walking inside the fretboard.

THE USUAL 4 WAYS TO WALK INSIDE THE FRETBOARD ARE

1) By knowing patterns of scales

2) By known the shapes of chords, and then walk around the chord shapes

3) By knowing all the names of the notes of all the frets of the fretboard, and utilizing the 3 fretboard-neighborhoods.

4) Without any mental image, but simply by the feeling of the desired note, and the feeling-familiarization of the fretboard. At this it must be made the use of the belief that one "knows" simply by the feeling which fret sounds which note !

E.g. see https://www.youtube.com/watch?v=d7-ZnzAqt0A

The meaning of course of these 3 types of transitions is that when  listening to the harmony and melody of the song, the melodically connecting element when the chord changes is 1) either a resolution in the cycle of 4ths, or 2) a relation of relatives of the chords (common notes of the chords), or 3) a small move of the root of the chord, complementary chords. Or in other words that the parallel melody during the transition of the chord most often is also doing one of the next correspondingly to the above 3 transition types  1) Moves by one semitone (resolution in the cycle of 4ths) 2) Remains the same note or moves by a 3rd (transition to a relative chord) 3) Moves by 1 semitone or by 1 tone (shift of the root of the chord by 1 semitone or 1 tone). 

For the correlation of melodies with chords that fit to them, or conversely , melodies that can be improvised over a chord progression the next local concept is very significant: The melodic closure of a chord: This is defined as the closed interval of notes from all the 12-tone (chromatic) scale) with lower end the lowest note of the chord, and highest end the highest note of the chord. The chord is assumed within an octave, and normal positions, 1st inversion, and 2nd inversion have different closures. The melodic closure is also conceivable as transportable  in all octaves, and not only where the chord is It holds the next interesting theorem. If we define randomly a melody within a the closure of a chord  in normal position  and no other note outside it, with uniform probability of occurrence of any of the notes of the closure, then according to the local condition of fit of a piece of melody with a chord  the only chord  in normal position  that would fit this melody is the one with this as its closure!. Or more generally of we  define  as probabilities of sounding a note on all the octave an equal value for all notes    except at the notes of the chord X where we have as probability the double this value (e.g. sound each note of the octave once but the notes of the chord twice) then any such random melody with this probability structure will have as its fitting underlying chord the chord X.