79. THE MELODIC-HARMONIC 7 NOTES, 2 OCTAVES SCALE (WHEEL OF 3RDS). The 7 notes 3 and 4 octaves scales of 4ths and 5ths.

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. 

This scale is also the Harmonic tuning of the guitar (see post 1) which is optimal when chord playing is mainly the traget and not soloing so much

OPTIMAL GUITAR TUNING FOR CHORDS PLAYING MAINLY

2.) An more optimal but unkown tuning for the 6-string guitar when chord-playing is the main target and not so much solo playing is and even better by alternating minor and major 3rds. In semitones for the 6 strings   4-3-4-3-4 or 3-4-3-4-3
E.g. Bb2- D3-F3-A3-C4-E4 or F2-A2-C3-E3-G3-B3 or A2-C3-E4-G4-B4-D4
THIS MAY BE CALLED THE HARMONIC TUNING OF THE GUITAR AS IT IS BASED ON THE HARMONIC 2-OCTAVES 7-NOTES SCALE (see also post 79)
The latter is the most natural open tuning. There the same shape for major and minor chords and only 3 of them and in only one or frets compared to the 6 in the standard tuning guitar. If we want also dominant and major 7nth chords we use again only 2 frets. The same with the aug chords Only the dim7 chords require 3 frets. Because  of the symmetry of the tuning among the strings, the relations of relative chords and also chords in the wheel of 4ths is immediate to grasp also geometrically. Of course when we say shape of chords as it is standard in jazz, we do not play all 6-strings but only 3 or 4 strings.
Within 3 frets exist all chords of the  8-notes scale with interval structure 2-2-1-2-2-1-1-1 which is an extension and variation of the melodic double minor 2-2-1-1-1-1-2-2 or (1-1-1)-(2-2)-(2-2-1)
But also all chords of diatonic scale!

All the next chords are superposition of 2-notes relatives chords of types major, minor, diminished, and augmented. 


Discussion of the defnition-creation  and roles of the 8 basic such chords (in root position)
433=majVdim=R7
434=majVmin=Rmaj7
343=minVmaj=Rm7=R'6, where R' the root of  a  relative chord
333=dimVdim=Rdim7
334=dimVmin=Rm6=R'm7b5 , called also half diminsihed where R' the root of  a  relative chord
444=augVaug=Raug
344=minVaug=Rminmaj7
443=augVmaj=Rmaj7#5 

4 of the above chords can be 4-notes chords of the diatonic scale e.g. the R7, Rmaj7, Rm7, Rm7b5. But the Rdim7, Raug, Rminmaj7, Rmaj7#5 cannot be 4-note chords of the diatonic scale. Nevertheless there exist in other scales as we shall see like Harmonic minor, and harmonic double minor Melodic minor (Hindu)and Melodic double minor (Arabic) and other oriental scales as in the scales of post 52.

Some of the above  chords appear as chords of the HARMONIC LONG 12 NOTES 7 OCTAVES SCALE  (see post 42, and 34)  Wheel of 3rds
(successive distance in semitones) (434343434343434343434343) 

Besides the long scale we may define the HARMONIC 2 OCTAVES , 7 NOTES SCALE of 7 notes that spans 2 octaves, and every 3 or 4 successive notes is a chord of the above types 

Here it is (STARTING FROM THE  C3)

etc -C3-E3-G3-B3-D4-F4-A4-C5- etc  (all steps intervals of 3rds)

As a structure of intervals over semitones it is the next sequence

-4-3-4-3-3-4-3-

And the sequence of 3-notes chords , by successive 3 notes in this scale is the chord progression

C->Em->G->Bdim->Dm->F->Am

while as sequence of 4-notes chords is the

Cmaj7->Em7->G7->Bm6->Dm7->Fmaj7->Am7 or 

Cmaj7->G6->G7->Bm7b5=Dm6->F6->Fmaj7->C6

THE MELODIC CORRIDOR 

Constructing therapeutic harps, or similar instruments (e. thump  pianos https://en.wikipedia.org/wiki/Mbira or hang and handpans ) or such keyboards with this scale, has the property that almost what ever we play sounds harmonic as 3 or 4 notes in sequence are well known cords, and overlapping such triads , are relative chords. In fact we may design such an harmonic diatonic  double row keyboard

 as follows 

  -D3-F3-A3-C3- E4-G4-B4-

-C4-E3-G3-B3-D4-F4-A4-C5- 

Similarly this can be a beautiful , practical and harmonic tuning for harmonicas.

The blue is blowing and the red is draw. Then with the key we may have the sharps too thus in total

-D3#-F3#-A3#-C3#- E4#-G4#-B4#-

 -D3-  F3- A3-   C3-  E4-  G4-   B4-

-C4-  E3-  G3-  B3  -D4  -F4-  A4-  C5- 
-C4#-E3#-G3#-B3#-D4#-F4#-A4#-C5#- 

OR 

-D3#-F3#-A3#-C3#- E4#-G4#-B4#-

 -D3-  F3- A3-   C3-  E4-  G4-   B4-

-C4#-E3#-G3#-B3#-D4#-F4#-A4#-C5#- 

-C4-  E3-  G3-  B3  -D4  -F4-  A4-  C5- 

This type of tuning can be applied also as setting to 4 strings  frets of  the fretboard of the artiphon the midi-controller, and give it sound of adouble diatonic harp or flute etc.

(for he artiphon see here https://artiphon.com/  )


THIS KIND OF KEYBOARD OR TUNING OF INSTRUMENTS (FLUTES, HARMONICA, ARTIPHON , KEYBOARD ETC)  ALLOWS FOR MELODIES IMPROVISATION IN A FAST  WAY EASILY WITHOUT COMPLICATED FINGERINGS OBSTRUCTIONS AS LONG AS THE MELODY IS A DIATONIC SCALE. IT IS A BIT BETTER THAN PIANO KEYBOARD AS IT FOLLOWS THE SHAPING OF CHORDS BY INTERVALS OF 3RDS. IT IS EVEN AEASIRT THAN SINGING OR WHISTLING FROM THE HARMONY POINT OF VIEW!


The melodic corridor can be also be spotted  on the fretboard of the standard tuning 6-string guitar. It will also define an unusual shape  of the diatonic scale with 2 only notes per string. More on that on the post 94.

Similar to this harmonic scale is the next , with interval pattern 

-4-3-4-4-3-3-3-

or C3-E3-G3-B3-D#4-F#4-A4-C5

And the sequence of 3-notes chords , by successive 3 notes in this scale is the chord progression

C->Em->Gaug->Baug->D#->F#dim->Adim

Which when projected within one octave it is the 

C3-D3#-E3-F3#-G3-A3-B3-C4

which in interval structure it is the

-3-1-2-1-2-2-1

which is nothing else than the Harmonic minor (here we consider a sequence of notes and circular permutation of them the same scale)     

The last remaining permutation of harmonic 2 octaves scale , is the


-4-4-4-3-3-3-3 - or  3-3-3-3-4-4-4- 

e.g. 

C3-E3-G3#-C4-D#4-F#4-A4-C5  or as interval structure within one octave


C3-D#3-E3-F#3-G#3-A3-C4   

3-1-2-2-1-3- 

which is a 6-notes scale which is very close the 7-notes scale

3-1-2-2-1-2-1 

 which is the  2nd Harmonic minor or  Kurdi or Kassigar (see post 72).

Similar to the above 7 notes 2 octaves scale by 3rds are the 7 notes scales by 4ths and 4-octaves scale by 5ths.

In other words the next 7 notes scales

(We may agree to start from the 2nd octave)

7-notes 3 octaves scale by 4ths:

B2-E3-A3-D4-G4-C5-F5-B5

7-notes 4 octaves scale by 5ths:

F2-C3-G3-D4-A4-E5-B5-F6

See also the symmetric scales post 95 and the hexagonal pattern (Terpstra, Keyboards) of harmonies and melodies of the diatomic scales in post 99. 

(This post has not been written completely yet)