Martino Excerpts from
THE NATURE OF GUITAR Automation
View The circle visually alters perspectives. It reveals a balance that’s invisible when seen in any other way.
a. HORIZONTAL: A Twelve Tone Scale, from E to Eb
b. CIRCULAR:
Chromatic
The Twelve Tone Scale on a Circular Staff
THE AUGMENTED PARENTAL FORM
THE DIMINISHED PARENTAL FORM
Eg. 1
TWO IMPORTANT SHAPES AUGMENTED
DIMINISHED
I
6
6
II 5
5
4
4 2
3 2 1
3 1
The two chord forms displayed above are unlike any others found on the guitar. What’s unique about them, (compared to other chord forms) is how the fingerings for either of them, (always 3, or 4) never change as their inversions unfold horizontally. Although vertically, the string groups they take place upon cause them to have various shapes, but once located on any specific group they invert horizontally from one end of the fingerboard to the other automatically. DIMINISHED: 12
9
6
3
:fret 6 5 4 3 2 1
In this special way what this causes is the “automation of chord inversions”, (as well as their alterations). They can be defined as “parental forms”, if only due to the fact that they automatically give birth, (in the case of the triangle into pure major, or minor triads, and the diamond into V7th, or Mi7b5 clusters). That process is also a result of natural variation, with ascent, or descent, (at singular points) within those forms.
THE AUGMENTED TRANSFORMATIONS! into Major Triads
Aug. Source
3 Major Key Centers
F, A, or Db Aug
A Ma 3
2
Db Ma 1
3
F Ma
2
1
3
2
1
6 5 4 3 2 1
6 5 4 3 2 1
1
6 5 4 3 2 1
2
6 5 4 3 2 1
3
Automatic transformations take place on the guitar by either lowering, (or raising) any single tone in the augmented, or diminished forms. In the augmented form, (thru the process of lowering) its new position becomes the Perfect 5th of a major triad, (one of three). In fact, the notes within the augmented chord itself embody the key centers of those major triads.
H O R I Z O N T A L = the positions of the Root 2nd String 13
12
11
10
9
4th String 8
7
10
3
9
9
8
8
7
7
6
6
2
1
A Ma
Db Ma
6 5 4 3 2 1
11
10
4
6 5 4 3 2 1
12
11
5
6 5 4 3 2 1
13
12
6
Inv 2
Inv 3
13
3rd String
F Ma
Inv 1
5
5
4
4
3
3
2
2
1
1
V! ! E! ! R! ! T! ! I! ! C! ! A! ! L
The application of the same procedure, (now thru raising any single note) causes its new position to become the Root of a relative minor triad, (in junction with the prior major forms, one of three). The tones within an augmented chord, (! step higher) embody the key centers of these relative minor triads.
THE AUGMENTED TRANSFORMATIONS! into Minor Triads
Aug. Source
3 Minor Key Centers
F, A, or Db Aug
Gb Mi 4
3
Bb Mi 2
3
2
D mi 1
3
2
1
6 5 4 3 2 1
6 5 4 3 2 1
1
6 5 4 3 2 1
2
6 5 4 3 2 1
3
H O R I Z O N T A L = the positions of the Root 3rd String 13
12
11
10
2nd String 9
8
7
10
3
9
9
8
8
7
7
6
6
2
1
Gb Mi
Bb Mi
6 5 4 3 2 1
11
10
4
6 5 4 3 2 1
12
11
5
6 5 4 3 2 1
13
12
6
Inv 2
Inv 3
13
4th String
D Mi
Inv 1
5
5
4
4
3
3
2
2
1
1
V! ! E! ! R! ! T! ! I! ! C! ! A! ! L
The following transformations reveal 4 V7th forms developed from the basic diminished form. They spread horizontally, as well as vertically in the same way the augmented form did.
THE DIMINISHED TRANSFORMATIONS! into V7 Forms
Dim. Source
4 V7th Key Centers
E, Bb, Db, or G Dim
A7
Eb7 3
2
1
3
2
C7 1
3
Gb7
2
1
3
2
H O R I Z O N T A L = the positions of the Root 1st String 13
12
11
10
3rd String 9
8
7
2nd String 6
5
4
3
4th String 2
1
6 5 4 3 2 1
Inv 4
13
11
10
10
9
9
9
8
8
8
7
7
7
6
6
6
5
5
5
4
4
4
3
3
3
2
2
2
1
A7
C7
6 5 4 3 2 1
12
11
10
Inv 1
6 5 4 3 2 1
13
12
11
Inv 2
Eb7
6 5 4 3 2 1
13
12
Inv 3
Gb7
1
1
1
6 5 4 3 2 1
6 5 4 3 2 1
6 5 4 3 2 1
1
6 5 4 3 2 1
2
6 5 4 3 2 1
3
V! ! E! ! R! ! T! ! I! ! C! ! A! ! L
The final series of diminished transformations has the parental form transformed into Mi7b5 clusters, by raising any of its single tones ! step, (one by one).
THE DIMINISHED TRANSFORMATIONS! into Mi7b5 Forms
Dim. Source
4 V7th Key Centers
E, Bb, Db, or G Dim
Gmi7b5 4
3
Emi7b5
Dbmi7b5 4
2
3
2
4
3
Dbmi7b5 4
2
3
H O R I Z O N T A L = the positions of the Root 3rd String 13
12
11
2nd String 10
9
8
4th String 7
6
5
1st String 4
3
2
1
6 5 4 3 2 1
Inv 4
13
12
11
Inv 3
10
9
8
Inv 2
7
6
5
Inv 1
4
3
2
1
6 5 4 3 2 1
13
12
11
10
9
8
7
6
5
4
3
2
12
11
10
9
8
7
6
5
4
3
2
Dbmi7b5
1
6 5 4 3 2 1
13
Gmi7b5
Emi7b5
1
6 5 4 3 2 1
Bbmi7b5
2
6 5 4 3 2 1
6 5 4 3 2 1
6 5 4 3 2 1
2
6 5 4 3 2 1
3
6 5 4 3 2 1
4
V! ! E! ! R! ! T! ! I! ! C! ! A! ! L
Eg. 2
Formulas and Transformations Geometric blueprints for both of these parental forms appear in the following diagrams:
The Augmented Formula The movement of any single tone 1/2 step MA 3rds
DOWN Abma
E D
Cma
D
b
b B
Ama
E
b
Fma
B
Bbma
E D
Dma
D
b
b
Gbma
B
Bma
E D
Ebma
D
b
b B
1/2 step down
b
B
E
b
Ami
E
A A
F
b
D
Dbmi
D
b
1/2 step up
G
b
B
E
b
C
Gbmi
B Bbmi
A A
Dmi
b
Gmi
G
G
b
B
E
b
Bmi
A
F
b
G
b
D
b
b
C B
Ebmi
b
D
b
b
Cmi
Emi
F
B
b
E
G
G
b
B
b
A A
D
D
b
E
F
b
b
B
b
A A
E D
b
F
b
C B
b
G
G
b
B
b
A A
D
D
b
G
b
A
b
A
B
A mi E
F
b
b
B
G
B
b
A A
Db mi E
F
b
G Mi
C
b
G Mi
E
b
G
B
D
F
Mi
E Ma E
E
C
G
G
F mi
b
C Ma
Ma
C
A A
E D
Abmi
E
Ma
A
G
B
E
D F
b
Ab Ma
Ma
G
4
C
Gma
G
3
C
Minor
G
2
C
Fmi
MINOR
RELATIVE
D
b
b
Major
RELATIVE
MAJOR
D
Dbma
F
1
C
Ema
E
Transformations
UP
b
B
G
b
A A
Eg. 3
The Diminished Formula
Like the Augmented parental form, (producing two pure triads, descent as a Major triad, and ascent as a relative Minor triad) the movement of any single tones by ! step within the Diminished form, produces two forms as well, (descent as V7s, and ascent as a Mi7 (b5)s.
The movement of any single tone by 1/2 step
MI 3rds
DOWN Eb
Eb7
E
UP G 7
F
D
Gb
Gb7
Bb 7 1
Db
TRANSFORMATIONS
G
DOWN
UP
Eb7
A7
Ab
C B
C7
Bb
A
Db 7
E 7
Eb
Db
Gmi7 (b5)
E
V7
G
V7
Db
Bb
E7
Eb
E
Gb7
F
D
G7
Ab 7 Gb
2
Db
Db
E
V7
B Bb
A7
C#
A
Eb
E
Db
V7
G
Bb Dbmi7 (b5)
E
V7
D
Gb 3
Db
Ab
Bb
V7
Db
G
B
A
Bbmi7 (b5)
E
Bb
E
C 7
V7
G
Db
V7
G
Ab
C Bb
Bb
G
C B
G
A 7
F
Db
D7
G
F 7 C7
B7
D
E
Bb
Ab7
Gb
E
Ab
C
F7
G
Bb Emi7 (b5)
Bb
D 7
Db7
F
B 7
G
Bb7
E
A
Eb 7
Gb 7
In retrospect, when eventually viewed fully both the Augmented, and the Diminished structures define themselves as distinct areas of chromatic families circumscribed around larger 12 point structures.
Eg. 4
The String Groups of the Guitar (viewed as Hexagrams) 1 String
.
.
2 String
.
.
3 String
.
. . . . ( the dotted hexagrams are the 2 string placement of octaves )
.
. . .
( the dotted hexagrams are the 7 common groups )
.
4 String
. . ( the dotted hexagrams are the 5 common groups )
5 String 6 String
Silence
If these same combinations are viewed as numbers, (instead of hexagrams) set up in vertical columns, they’ll appear as follows in example 17 b.
Numerical String Groups
Eg. 5
The columns displayed are not to be seen as the guitar fingerboard, but as combinations of different sets of strings. 6 Strings Full Use
6 5 4 3 2 1
= #1
5 String Groups
4 String Groups
3 String Groups
6 5 4 3 2 1
6 5 4 3 2 1
6 5 4 3 2 1
6 6 6 6 6
6 6 6 6 6 6 6 6 6 6
6 6 6 6 6 6 6 6 6 6
5 4 3 2 5 4 3 1 5 4 2 1 5 3 2 1 4 3 2 1 5 4 3 2 1
2 String Groups 6 5 4 3 2 1 6 5 6 4 6 3 2 6 1 6 5 4 5 3 5 2 5 1 4 3 2 4 1 4 3 2 3 1 2 1
5 4 3 5 4 2 5 4 3 2 5 3 5 2 5 4 3 2 4 3 2 4 3 2 5 4 3 2 5 4 3 5 4 2 5 3 2 4 3 2
1 1 1 1 1 1 1 1 1 1
1 String 6 5
4
3
2
1
5 4 5 3 5 2 5 1 4 3 4 2 1 4 3 2 3 1 2 1 5 4 3 5 4 2 5 4 1 5 3 2 5 3 1 5 2 1 4 3 2 4 3 1 4 2 1 3 2 1
6 5 4
#64 =
3
S ilen c e
2 1
Take Note:
String groups that are marked are common groups, (normally in use) while the groups that are darkened should also to be seen as valuable sets.
Eg. 6
The Common Augmented Inversions 13
12
11
10
9
8
7
6
5
4
3
2
1 6 5
4
Ab, C, & E Augmented
3 2 1
Series 3
13
12
Series 2
11
10
9
8
7
Series 1
6
5
4
3
2
1 6 5
A D J A C E N T
4
3 2 1
Series 3
13
12
11
10
Series 1
Series 2
9
8
7
6
C, E, & Ab Augmented
5
4
3
2
1 6 5
4
3 2 1
Series 3
13
12
11
10
Series 1
Series 2
9
8
7
6
E, Ab, & C Augmented
5
4
3
2
1 6 5
4
3 2 1
Series 3
13
Series 2
12
11
10
9
Ab, C, & E Augmented
Series 1
8
7
6
5
4
3
2
1 6 5
Ab, C, & E Augmented
4 3 2 1
N O N
Series
13
A D J A C E N T
12
3
11
Series 2
10
9
8
7
Series 1
6
5
4
3
2
1 6 5
4
C, E, & Ab Augmented
3 2 1
Series 2
Series 3
12
11
10
9
8
7
Series 1
6
5
4
3
2
1 6 5
4 3 2 1
Series 3
Series 2
Series 1
E, Ab, & C Augmented
Eg. 7
The Common Diminished Inversions 13
12
11
10
9
8
7
6
5
4
3
2
1 6 5
4
G, Bb, Db, and E Diminished
3 2 1
A D J A C E N T
14
13
12
11
10
9
Series 1
Series 2
Series 3
Series 4
8
7
6
5
4
3
2
1 6 5
4
3 2 1
12
11
10
Series 1
Series 2
Series 3
Series 4
9
8
7
Db, E, G, and Bb Diminished
6
5
4
3
2
1 6
5 4 3 2 1
12
11
10
9
Series 1
Series 2
Series 3
Series 4
8
7
6
5
4
3
2
1 6 5 4 3 2 1
N O N A D J A C E N T
14
13
12
11
10
9
8
7
6
5
G, Bb, Db, and E Diminished
Series 1
Series 2
Series 3
Series 4
E, G, Bb, and Db Diminished
4
3
2
1 6 5
4
3 2 1
Series 4
Series 3
Series 2
Series 1
Db, E, G, and Bb Diminished
Linear Inversions Ranges of chordal and linear activity organize in greater balance when they’re viewed as self contained divisions of the fingerboard, (similar to separate floors in a larger house). These vertical areas comprise linear as well as chordal inversions encompassing all twelve keys in each of their five separate positions. Eg. 8 12
11
10
9
8
7
6
5
4
3
2
1
open *1 6 5 4 3 2 1
FirstPosition
12
11
10
9
8
7
6
5
4
3
2
1 6 5 4 3 2 1
Second Position
12
11
10
9
8
7
6
5
4
3
2
1 6 5 4 3 2 1
Third Position
12
11
10
9
8
7
6
5
4
3
2
1 6 5 4 3 2 1
Fourth Position
13
12
11
10
9
8
7
6
5
4
3
2
1 6 5 4 3 2 1
Fifth Position
When each of these separate areas are mastered, the sixth, (full fingerboard) becomes activated as a free canvas for any improvisational topic.
13
12
11
10
9
8
7
6
5
4
3
2
1
*1 6 5 4 3 2 1
The Full Fingerboard
12
11
10
9
8
7
6
5
4
3
2
1
open *1 6 5 4 3 2 1
FirstPosition
Before beginning a discussion on line forms, and their inversions, it’s important to define the proper use of fingerings for what’s normally categorized as open strings.
Players often use a completely different arrangement of their fingers each time they use open strings in lower areas of the neck. By placing the first finger behind the “nut”, just as if it were another fret, familiar fingerings used in other areas take place in comfort here as well. The following patterns utilize this approach. Take note, the asterisk * when in use should be viewed as a reminder regarding placement of the first finger behind the nut whenever it appears on fingerings in the upcoming patterns.
The first and fourth finger of the left hand determine not only the beginning of the pattern, but also the position in which it unfolds vertically as well as horizontally. From “Fingering Inversions” patterns I and II reveal a full vertical / horizontal inversion.
Eg. 9
Once again, when we give thought to a practical use of the opposites, (yin & yang) and view the outer fingers of the hand, (eg. 22) the two patterns seen above, (eg. 21) are perfectly in line with the fourth and first fingers. Vertically, pattern I begins at the lowest point with the fourth finger followed by its next inversion, (in close range) beginning with the first finger. Those are the first two vertical inversions of this line form. Eg. 10
Also, take note that the positions of these fingers continue to represent the opposites, (in this case it represents the inside, (right) and the outside, (left).
Introduced in examples A, and B, the melodic line forms seen below are positioned in two opposite ways as well, vertical, and horizontal. Both sets are subjects of the chordal inversions seen above them, and they continuously take place within the general areas of particular chordal inversions:. Eg. A
Eg. B
It’s important to remember how basic modifications of both the augmented, and the diminished parental forms automatically produce inversions. Similar types of inversion take place within linear patterns as well. In example A, (up above) take note of the 1 octave transposition of the melody itself within its two positions, (automatically below, or above one another). What’s displayed in example B, is the “unison” transfer, changing to the opposite fingerings, (now locating the melody itself beginning with the first finger).
That sets up the next series of inversions, (much like a mirror image of the two original fingerings).
Eg. C
When continued in this way, the inversions that take place are 12 in number, and can be fully viewed in example 26.
These are 6 patterns that begin with the first finger, and instead of the next 6 starting with the fourth finger, there are 5, with the addition of one that begins with the third finger, (due to the intervalic tuning of a ma 3rd, between the second, and third strings.)
Also, in the chordal inversions of example C, (above #2. starting with the fourth finger) the reason there are two separate forms is due to the number of frets that particular fingering covers. Both of those inversions are effected areas.
The following 12 patterns are to be seen as an introduction to vertical areas of the fingerboard that directly relate to a specific key center, (G minor) and they are collectively, (as a skeletal form) horizontal sets, (two in each). These are the six vertical positions that determine not only the linear inversions, but improvisational extensions as well.
Eg. 11:
12 Inverted Fingerings ( and positions of one pattern )
The patterns displayed next are twelve positions of vertical, and horizontal linear inversions of the same motive. In general these linear forms, (seen as fingerboard graphics in eg. 8) are extensions of eg. 9.
The following series in this study uses descending transpositions, (in a whole-tone scale) of the original form, to define its change of position across the fingerboard. What initially was demonstrated as a pattern that’s compatible with Gmi7 shall now be part of a descending framework that unfolds in six keys, beginning with : Dmi7, Cmi7, Bbmi7, Abmi7, Gbmi7, Emi7, continuing into a full series of five ascending positions. The sixth, (invisible) position forms at the twelfth fret, (beginning with the first finger at D on the fourth string. The reason that it isn’t included in the first string group, (4321) is that it’s used as the departure point, (one octave lower) for entrance into the second group, (5432). The dotted markings placed on Dmi7 in the example shown below represent the sequential inversions ascending horizontally across the entire fingerboard. The “boxes” represent the beginning of each series. Eg. 12 E Eb
F
D
5 Positions Gb
Db
G
Ab
C B
A Bb
Series 1 Dm7 Cm7
Series 2 Dm7 Cm7 Bbm7
Series 3 Dm7 Cm7 Bbm7
Abm7 Gbm7
Series 4 Dm7 Cm7 Bbm7
Abm7 Gbm7 Em7
Series 5 Dm7 Cm7 Bbm7
Abm7 Gbm7 Em7
Bbm7 Abm7 Gbm7
Abm7 Gbm7 Em7
Em7
Em7
This study is also arranged into three separate adjacent string groups, 4321, 5432 and 6543. These string groups offer insight within areas of activity, that automatically transpose themselves vertically through various key centers, and horizontally across the framework of the fingerboard. The following shall be marked in full as Eg. 13.
COMPLEXITY TO SIMPLICITY The transfer of chordal frameworks Into unified substitutions
