Before this post the reader must study the posts 40 (that classifies intervals), the classification of 2-string triads , and 38 (that classifies 3-string triads) and 35.
By restricting the playing of the guitar on the 4 higher strings,or playing corresponding isosmorphically tuned to these 4-strings of the guitar instruments (like ukulele, Greek buzuki, etc) I discovered the remarkably simple DAE system, which handles all the major and minor chords as having only one of the 3-shapes of D (like open D major) A (like open A major) and E (like open E major).
Approximately the 3 shapes have the next distribution on the fretboard
This distribution of the chord suggest also a way to play simultaneously melodies with chords: We play the melody on the strings D,G,B,E (higher 4) and then at each note we try the roots maximal chordification (each note of the melody as root of a chord minor or major or dim7 or augmented according to what that fits in the scale), and then we simplify the chordification to less chords with rules that successive chords in resolution relation are better than in relative relation which in its turn is better than the complementary relation, so as to result in to a stable simple harmonic background.
Also the neighborhoods define by restriction in them different shapes of various scales. An good example is the Harmonic minor and Harmonic double minor e.g. with root on D.
Approximately the 3 shapes have the next distribution on the fretboard
D4
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E4
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F4
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G4
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A4
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B4
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C5
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D5
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|||||
A3
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B3
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C4
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D4
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E4
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F4
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G4
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A4
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|||||
E3
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F3
|
G3
|
A3
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B3
|
C4
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D4
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E4
|
This distribution of the chord suggest also a way to play simultaneously melodies with chords: We play the melody on the strings D,G,B,E (higher 4) and then at each note we try the roots maximal chordification (each note of the melody as root of a chord minor or major or dim7 or augmented according to what that fits in the scale), and then we simplify the chordification to less chords with rules that successive chords in resolution relation are better than in relative relation which in its turn is better than the complementary relation, so as to result in to a stable simple harmonic background.
Also the neighborhoods define by restriction in them different shapes of various scales. An good example is the Harmonic minor and Harmonic double minor e.g. with root on D.
The optimality of restricting on the higher 4 strings of the Guitar. The simpler DAE systems versus the more complicated CAGED system. The Shape G as backward extension of the shape E, and the shape C as forward extension of the shape D , in the lower 2 (6th and 5th) strings.
The DAE system indentifies chord shapes by restricting only on the higher 4-strings of the guitar. A general chord shape on the fretboard is extended on all of the 6 strings, and then identified as shape by its shape on teh highest 4 strings of the guitar. The advantage of course is that we have only 3 shapes for all minor and major chords of the guitar, which exhibit particular high symmetries in chord relations like dominant-root resolutions , relative chords, same chord in 3 different positions etc.
Here is an application of the 3 neigbourhoods of the guitar on the chords A, E, F#m, D,
(see also post 13 and 23 )
https://www.youtube.com/watch?v=aO1XZJvFXu8
In relation with the 12-chords cycle of chords by intervals of 4ths (see post 34 ) the DAE system has the next keys and correspondences.
The sequence X=(nE)Y1, X+1=((n)A)Y2, X+2=((n)D)Y3 is of course a vertical sequenceof chords in thefretbaird and a sequence of 3 successive chords in the cycle of 4ths and symbols of post 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.
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
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
This positioning is essentially as the positioning of the open chords on the guitar fretboard as the shape D, is the essentially the shape C, and the shape A is essentially the shape A. This positioning is the only one, where all the minor chords of the diatonic scale, are set vertically (to the strings) in the fretboard
I=(nA)I, ii=((n+2)Am)ii , iii= ((n-1)D)iii, (nD)IV, V=(nE)V, vi=((n+2)Em)vi
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
This positioning is the only one, where all the major chords of the diatonic scale, are set vertically (to the strings) in the fretboard. Notice also the similarity of the D-root positioning with the A-root positioning, if we interchange the minor with the major chords.
In short the three main major chords I, IV, V are the
I=(nE)I, IV=((n)A)IV, V=((n-2)D)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
This positioning is the only one, where the minor chords of the diatonic scale, are not set vertically (to the strings) in the fretboard. It is also the only positioning that requires 5 frets instead of only 4 frets!
The previous ways to play all the chords of a diatonic scale are most compact relative to the 3 shapes D, A, E.
There are of course the translation ways to play all the chords of the diatonic scale utilizing each time only one shape. E.g. only the D shape or only the A shape ot only the E shape. But the positions is obvious based on the pattern 2-2-1-2-2-2-1 semitones or frets.
When adding the minor chords of the diatonic scale, if the roots is an A-shape we have the following positions
Here a video that palys chords on all neighbourhoods one chord at a a time
https://www.youtube.com/watch?v=O4ejQ6gfMno&t=30s
(The post has not been written yet completely)
Here is an application of the 3 neigbourhoods of the guitar on the chords A, E, F#m, D,
(see also post 13 and 23 )
https://www.youtube.com/watch?v=aO1XZJvFXu8
As for the equivalence of chords in different positions and shapes on the fretboard for the shapes D, A and E hold the rules
1)The D shape sounds as the same chord with A shape 5 frets higher , In symbols e.g. (1D)D=(5A)D and in general (nD)X=((n+5)A)X
2) The A shape sounds as the same chord with E shape 5 frets higher , In symbols e.g. (1A)A=(5E)A and in general (nA)X=((n+5)E)X
3) The E shape sounds as the same chord with D shape 2 frets higher , In symbols e.g. (1E)E=(2D)E and in general (nE)X=((n+2)D)X
In relation with the 12-chords cycle of chords by intervals of 4ths (see post 34 ) the DAE system has the next keys and correspondences.
The sequence X=(nE)Y1, X+1=((n)A)Y2, X+2=((n)D)Y3 is of course a vertical sequenceof chords in thefretbaird and a sequence of 3 successive chords in the cycle of 4ths and symbols of post 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.
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
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nD=I
|
This positioning is essentially as the positioning of the open chords on the guitar fretboard as the shape D, is the essentially the shape C, and the shape A is essentially the shape A. This positioning is the only one, where all the minor chords of the diatonic scale, are set vertically (to the strings) in the fretboard
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
|
This positioning is the only one, where all the major chords of the diatonic scale, are set vertically (to the strings) in the fretboard. Notice also the similarity of the D-root positioning with the A-root positioning, if we interchange the minor with the major chords.
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.
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=ii
|
nE=I
|
|||
nA=IV
|
(n-1)Am=iii
|
|||
nDm=iv
|
(n-2)D=V
|
This positioning is the only one, where the minor chords of the diatonic scale, are not set vertically (to the strings) in the fretboard. It is also the only positioning that requires 5 frets instead of only 4 frets!
The previous ways to play all the chords of a diatonic scale are most compact relative to the 3 shapes D, A, E.
There are of course the translation ways to play all the chords of the diatonic scale utilizing each time only one shape. E.g. only the D shape or only the A shape ot only the E shape. But the positions is obvious based on the pattern 2-2-1-2-2-2-1 semitones or frets.
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
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
|
|
| ||
e4
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(0A)A
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(0D)D
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g4 (3E)A
| (3A)C | (3D)F | ||
a4 (5E)A
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(5A)D
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(5D)G
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b4 (7E)B
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(7A)E
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(7D)A
| ||
d5 (10E)D
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(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
Here a video that palys chords on all neighbourhoods one chord at a a time
https://www.youtube.com/watch?v=O4ejQ6gfMno&t=30s
(The post has not been written yet completely)
