4. Learn easier and more diatonic scales positions with the three , 1-string scale-triads and their 2 transitions. Aplication in playing solos in 2-string.

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. 

Improvisations solos in 2-strings  only is essentially usefull for the  traditional 3-string Greek Buzuki.

Inspite the fact that I give here an easier method to learn the various positions of  the diatonic scales based on the 1-string triads and their transitions, I still have doubts for the value of learning the scales positions, as far as improvisations is concerned. There  are probably useful only if one wants to improvise strictly inside a scale. But most often the improvisations are among many different scales, and have as centre a chord each time, which only requires to learn the 3 different positions of each chord.
What I consider more useful is not to learn the scale-positions, but to learn how to create almost automatically the scale starting from its root on any fret of any string , with the only element in the memory, the intervals-shape of the diatonic scale. Here is how this is done

https://youtu.be/L6E-HNioxHk

A VERY USEFUL REMARK IS ABOUT THE EXCEPTION OF TUNING OF THE STRINGS 3,2 OF THE GUITAR.BECAUSE THEY ARE TUNED BY A MAJOR 3RD (4 SEMITONES) INSTEAD OF  PERFECT 4TH (5 SEMITONES). EXACTLY AT THE 3RD STRING WE MUST SHIFT OUR HAND ONE FRET TO HIGHER NOTES, AND CONTINUE THE SAME PATTERNS. IT IS EASER TO JUST KNOW THAT WE MUST SHIFT THE LEFT HAND ONE FRET TO HIGHER NOTES AND KEEP THE PATTERNS THE SAME RATHER THAN LEARNING MODIFIED PATTERNS.

The best practice to prepare yourself for playing melodies is he chromatic scale of 5 frets (4+1 , the last 1 is by moving the left hand one fret to higher notes) as below. Remember also the rule of moving the left hand altogether one fret to higher note when we reach the 3rd string and repeat the same pattern of the previous strings. The next image should be the simple mental image of the music here.

If we do not utilize the rule of one fret higher at the 2nd string, the image would be the next (but I recommend the simple rule of the left hand one fret higher thus the previous image)

Another useful remark to save memory, is to learn the diatonic scale of one only octave, on 2-strings and on 3-strings and then repeat to other strings , instead of learning it on all 6 strings. 

IN THE NEXT WE SHALL EXPERIMENT WITH SCALES BY THE RULE 2 OR 3 NOTE PER STRING (SEE POST 43)

In this way one has to learn ONLY ONE major scale pattern on 3-strings. The next pattern is directly derivable after one has learnt the intervals within 3 strings (see post 40) . The intervals of M2, M3, P4, P5, M6, M7 is all the pattern.

It is also based on the simple idea that the (B previous octave-C), (E-F) semitones of the diatonic scale have distance of a pure 4th (5 semitones) thus they should be parallel frets in two successive strings tuned by pure 4th, while the semitones (E-F) , (B- next octave C) have distance a pure 5th (7 semitones) thus these they should appear shifted by 2 frets. And this gives the next shape:


As we shall see below in this post , this pattern is made only from the 1-string triads 

(1-2), (2-2) and with only the parallel (1-2)->(1-2) transition and the cross transition 
(1-2)->(2-1). 

Another seemingly unusual way to play a diatonic major scale is going backwards among  the frets along a string but forwards among strings. The next is an example, and the symmetry of this way of playing the diatonic, is that it has the next simple rules 
1) two notes per string 
2) the two notes on each string are alternating of 2 frets distance or one fret distance 3) at each higher string the note starts one fret to the left from the fret that was the first note on the previous string.

Many Jazz guitarists suggest that it is a very good idea to practice the scales in general with the rule 4-notes or more instead of 3 notes per string, even if repeating a note at the beginning of the next string. The reason is that many scales are built by combining two tetrachords-scales (that is short sequences of 4 notes) united at a note or separated by a semitone or a tone.  Therefore the rule is that we play one  tetrachord at one on string and then the next tetrachord at  the next string. In this way we have a clear image of its intervals structure and we may therefore easily remember many different scales. This applies very well  to the oriental scales of the Greek folk songs with Buzuki, like Harmonic minor and double minor, Melodic minor and double minor or other scales like those of the post 52 etc. 

Here is an example of how the C major scale would be played in that way. 1st tetra-chord=(C,D,E,F),  2nd tetrachord =(G,A,B,C). The tetra-chords  are separated by one tone, so in passing to the next string we take care of it. For tetra-chords see also the post 58. 

The idea behind this technique is to play the diatonic scale till the step which is of one semitone (E-F in the C major diatonic) , and then as the next step is for certain one tone we shift to the next string which will be 3 frets behind. Thus the transition to the next string is only once and always of one tone or 3 frets.

This can be generalized by playing the diatonic scale along a single string, and always we chose to shift to the next string only if he step is of one tone,  which will be 3 frets behind.

Again we do not mention the standard rule, of shifting the left hand one fret to higher notes at the 2nd string. 

Of course if one wants to learn all the 5 standard 6-string positions of the diatonic scales and even more positions, the best way to save memory is with the three 1-string triads, and their 2 transitions which I will explain in the next.

As it is well known the 5 positions of the major scale  are the next.

This is the shape of the major scale with the open chords where the Cmajor chord is played as a C-shape. One characteristic of this position (which is property of the open chords too) is that from the first fret all strings are used. This position of the major scale is often called also  the C-shape

 This is the shape e.g. of the C major scale around the 8th-10th frets  (first part of the 3rd neighborhood of the fretboard) where the chord Cmajor is played as an E-shape. One characteristic of this position  is that from the 4th fret all strings are used. This position of the major scale is often called also  the  E -shape

 This is the shape e.g. of the C major scale around the 10th-12th frets  (2nd part of the 3rd neighborhood of the fretboard) where the chord Cmajor is played as an D-shape. One characteristic of this position  is that both from the 2nd fret and 4th fret (which for Cmajor is the 12th) all strings are used.  This position of the major scale is often called also  the  D -shape

 This is the shape e.g. of the C major scale around the 3rd-5th frets  (1st part of the 2nd neighborhood of the fretboard) where the chord Cmajor is played as an A-shape. One characteristic of this position  is that  from the  5th fret (which for Cmajor is the 5th  too, where all strings are tuned) all strings are used.  This position of the major scale is often called also  the  A -shape

  This is the shape e.g. of the C major scale around the 5th-7th frets  (2nd part of the 2nd neighborhood of the fretboard) where the chord Cmajor is played as an G-shape (which is as we have taught a forward extension of  the A-shape) . One characteristic of this position  is that  from the  2nd fret (which for Cmajor is the 5th, where all strings are tuned) all strings are used.  This position of the major scale is often called also  the  G -shape

LET US LIST NOW THE BASIC 3 ONE-STRING TRIADS.

The particular notes in the images do not matter what matters is the shape and combination of intervals

1STR TRIAD=T1 in semitones it is T1=(2-2)

2ND TRIAD=T2  in semitones it is T2=(2-1)

3rd TRIAD=T3  in semitones it is T3=(1-2)

                                                     THE TRANSITIONS 

In the next we observe that there are only two types of combinations or transitions, symbolized by Ci, i=1,2,3 ,for each of these triads from one string to the next, in the pattern of diatonic scales on all the fretboard e.g. here the C-major scale 

The next are the 1-string triads  transitions.

Each 1-string triad has two only transitions for the next string (we do not count here the obvious left hand shift modifications at the 2nd string).

 1ST TRANSITION  THE CROSS. Here the triad T3=(1-2) becomes the triad T2=(2,1) in the next string. 

(1-2)->(2,1)  or 

2ND TRANSITION  THE PARALLEL A TRANSITION 
Here the triad T3=(1-2) becomes again the triad T3=(1-2) in the next string which creates a parallel shape.


 (1-2)->(1-2)

3RD TRANSITION THE PARALLEL B TRANSITION 

Here the triad T2=(2-1) becomes again the triad T2=(2-1) in the next string which creates a parallel shape.

 (2-1)->(2-1)

4TH TRANSITION THE PARALLEL C TRANSITION 

Here the triad T1=(2-2) becomes again the triad T1=(2-2) in the next string which creates a parallel shape.

 (2-2)->(2-2)

5TH TRANSITION THE SKEW A TRANSITION 


Here the triad T2=(2-1) becomes  the triad T1=(2-2) in the next string which creates a skew shape.

 (2-1)->(2-2)

6TH TRANSITION THE SKEW B TRANSITION 



Here the triad T1=(2-2) becomes  the triad T3=(1-2) in the next string which creates a skew shape.

 (2-2)->(1-2)

EACH 1-STRING TRIAD HAS ONLY 2 TRANSITIONS FOR THE NEXT STRING.

We may notice from the above that each of  the three 1-string triads has only two transitions for  the next string


(1-2)    either parallel (1-2)  or  cross (2-1)

(2-1)    either parallel (2-1)  or skew   (2-2)

(2-2)     either parallel (2-2)  or skew   (1-2) 

This is a SIGNIFICANT SYMMETRY  of the pattern of  the diatonic scale on the guitar fretboard, which can be used to compose complete patterns of known or alternative positions of the diatonic scales and modes on the guitar fretboard! In particular we do not derive  the exact above 5 positions of the major scale, but slight modifications of them. What is lost is that they are not played now within only 4 or 5 or 6 frets , but maybe on 5 or 6 frets , but what is gained is a more uniform and simple way to generate all necessary positions the of the major scale around all the 3 different positions of the root chords.

LET US SEE HERE THE ADVANTAGE! IT IS EASIER TO REMEMBER THE 3 TRIADS, AND THEIR 2 TRANSITIONS, THAT DERIVE THE 5 (MODIFIED) POSITIONS AND MORE, THAN ALL THE 5 POSITIONS!




Allan Holdsworth about chord-scales (the advantage of the guitar fretboard over piano to transpose scales). He suggests a rule of more than 3 notes per string e.g. 4 or 7 or 8  notes per string.

https://www.youtube.com/watch?v=4JjBdnGDuYM

Allan Holdsworth  is using chords defined by the notes a scale and having notes strictly inside the scale , but when  the scales are not the diatonic scale, the chords, may be quite weird. An alternative and more  Harmonic approach is described in post 27, and is the concept of chords COVERING a scale (that the chords may contain notes outside the scale). This approach is much more flexible, and we may choose chords of any good classical type e.g. only major, or only minor major, R5 etc 

Making the guitar a 3-string instrument tuned by 6ths for scale-butterflying:

For the sake of scale-butterflying improvisation (see post 55) we will present how the C-major scale is distributed in the strings 1st, 3rd, 5th , (or 2nd,4th,6th) with area of changing string, the 9th or 10th fret where the pitch is identical with that of two strings higher, so as to have in the scale-butterflying a maximum occurrence  of  moving the left hand along the length of a string rather than vertically to the string among the 6 strings. In this way it is as if  we are making the guitar a 3-string instrument for solos, tuned by intervals of 6th (E, D, B ) or (A, G, E) ! 

There is  small number of  exactly 10 characteristic tetra-chords (=4-notes sub-scales)  containing intervals of 1,2,3, semitones and where inverses and cyclic permutations of them do not count as different 

Diatonic

2-2-1, (major, natural minor, Ancient Greek syntono,  Rast, Ussak, Qurdi)

2-2-2, (major, augmented)

Melodic minor, melodic double minor (Shabach)

1-2-1

Harmonic minor (Hijazz,Huzam, Ancient Greek chromatic)

1-3-1

Harmonic double minor (Piraeus, Niavent)

1-2-3,
 Diminished 

3-3-3 , (diminished 7nth)

3-3-1, 

Pentatonic

3-3-2, 
2-2-3

Chromatic

1-1-1

We should be also familiar with the ways we can play them in 1 ,2 or 3 strings.

Correspondence of chord transitions of chord progressions to the 3-melodic densities or speeds  of the melodies that fit to such chord progressions
(See also posts 30,68)

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. 

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!

Instead of learning scales, at first an easier and simper technique is to learn how to modulate melodic themes by shifting them to different strings:

PLAYING ONE MELODIC THEME PER ONE STRING:CORRESPONDING THE GEOMETRY OF THE STRINGS TO HARMONIC MODULATIONS OF THE MELODIC THEMES.
This technique of playing a melody,is particular easy and simple when creating by improvisation the melody. Since the string in the guitar and the other portable string instruments are tuned by 5 or 7 semitones apart ( intervals of pure 4th or 5th) then shifting  a melodic theme by a 4th up or down , which is also the distance of chords in the resolutions relations and cycle of 4ths, means that we should play the theme shifted almost in the same place of the fretboard but on string higher or lower. In other words the different strings symbolize the  steps of modulating or shifting the melodic theme along the wheel of 4ths, which is also a very common pattern of harmony. So the different strings are to be used for different modulations of the melodic theme. This simple idea  corresponds, the geometry of the strings on the fretboard to the harmony of modulations of the melodic theme. 

In the 4-double strings instruments (see post 67) the melodic themes modulations are as follows
1) Assume that we are playing a melodic theme on the highest pair of strings .
2) We utilize the 2nd lower pair of strings to shift the melodic theme a) one pure 4th (or 5 semitones) lower b) one pure 5th (or 7 semitones) lower c) to play the second voice which is a third lower.
3) We utilize the 3rd lower pair of strings to shift the melodic theme, 3 semitones  tome higher but also one octave lower from that (interval of 6th or 9 semitones=+3-12=-9)
4) We utilize the 4th lower pair of strings to shift the melodic theme, one   tome lower but also one octave lower from that (or 14 semitones=-2-12=-14)
5) Of course when shifting the melodic theme among the strings we change it also in the 
absolute distances among its notes, or its rhythm, or from ascending to descending and vice-versa etc.