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.