407. TUNING OF 4-STRINGS INSTRUMENTS WITH CONSECUTIVE RELATIVE MODES PER 3 CONSECUTIVE STRINGS IN THE PATTERN OF INTERVALS 5TH-6TH-5TH E.G. D2-A2-F3-C4 (AEOLIAN-IONIAN MODES)

 See also post 308 , 90 and 164 (Mexican instrument Jarana tuning)

The pattern of intervaslamong the strings are  5-6m-5 and 5-6M-5  where by 5 we denote interval of 5th (7 semitones) and by 6m interval of 6th minor (8 semitones)  and by 6M interval of 6th major (9 semitones) .

The modes are defined the the 3-notes chords that are shaped as triads across 3-consecutive strings.  The first chord is the open 3-strings chord. 

Pairs of modes , all the 7 , that can be tuning in this way 

AEOLIAN-IONIAN  e.g. D2-A2-F3-C4     (f -major) pattern 5-6m-5 

IONIAN-FRYGIAN  e.g. F2-C3-A3-E4      (f major) pattern 5-6M-5 

DORIAN-LYDIAN  e.g.   G2-D3-Bb3-F4   (f major) pattern 5-6m-5 

FRYGIAN-MIXOLYDIAN e.g. A2-E3-C4-G4  (f major) pattern 5-6M-5 

LYDIAN-AEOLIAN  e.g. Bb1-F2-D3-A3 (f major) pattern 5-6m-5 

MIXOLYDIAN-LOCRIAN e.g.  C2-G2-E3-Bb3  (f major) pattern 5-6M-5 

LOCRIAN-DORIAN e.g.  E2-Bb2-G3-D4  (f major) pattern 5-6m-5 

In total the advantages of this inverse tuning (e.g. D2-A2-F3-C4 )relative to the standard 4-strings tunings (e.g. C3-F3-A3-D4) are the next

1) It has two intervals of 5th among the strings that it sounds better in open and barre chords compared to intervals of 4th. 
2) It has larger range
3) It has the one-fret triad major  chords at higher strings and the one-fret triad minor chords at the lower strings,  thus  favors a bit mor joyfull music of major chords
4) It is more ergonomic in the fingers when playing the A-shape and E-shape chords The D-shape triad chords are almost the same difficulty. (the minor triad D-shape is slightly more difficult).

5) The 4-strings  chords span 2 octaves and have more magical and reach sound.

6) Because the chords are in one or 3 only frets, their arpeggios also and neighboring melodies are in fewer frets thus easier to play as finger picking style. 

Similarly we could utilize the inversions involving intervals of 4th and 3rds (instead of 5ths and 6ths) and have again all 7 pairs of relative modes

IONIAN-AEOLIAN  e.g. C2-F2-A3-D4     (f -major) pattern 4-3M-4 

FRYGIAN-IONIAN e.g. E3-A3-C4-F4     (f major) pattern 4-3m-4 

LYDIAN-DORIAN  e.g.   F2-Bb2-D3-G3   (f major) pattern 4-3M-4  

MIXOLYDIAN-FRYGIAN e.g. G2-C3-E3-A3  (f major) pattern 4-3M-4     

AEOLIAN-LYDIAN  e.g. A2-D3-F3-Bb3 (f major) pattern 4-3m-4   

LOCRIAN-MIXOLYDIAN e.g.  Bb2-E3-G3-C4  (f major) pattern 4-3m-4 

DORIAN-LOCRIAN e.g.  D3-G3-Bb3-E4  (f major) pattern 4-3m-4