193. THE PANDURI-MANDOLIN TUNING F2-A2-C3-G4-D4-A4 3M-3m-5-5-5 OF THE 6 OR 12 STRING GUITAR AND OUD

This tuning combines 3 strings that are in major or minor triad and a 5 away 3 strings that are again a 5th apart (e.g. mandocello) Or it can be in the reverse order first the 5ths then the major or minor triad. In this way both types of playing the ancient that can accompany a melody only with an interval of 5th or the modern that requires accompanying with triad major or minor chords can be played.

E.g.

C2-E2-G3-D3-A3-E4 3M-3m-5-5-5

 F2-A2-C3-G4-D4-A4 3M-3m-5-5-5

or
F2-C2-G3-D3-F4-A4  5-5-5-3m-3M

or
C2-G2-D3-A3-C4-E4  5-5-5-3m-3M

or

F2-C2-G3-D3-F#4-A4   5-5-5-3M-3m

or

Eb2-Bb2-F3-C4-E4-G4  5-5-5-3M-3m

192. SOME JONI MITCHEL TUNINGS FOR THE 6 OR 12 STRING GUITAR AND OUD

Here are some of the joni Mitchel tunings (from the book Joni Mitchel )

https://www.youtube.com/watch?v=zyDW7lslN5Y


Besides the overtone tuning of post 191, some tunis are variations produced by it

in the sense that they include a major chord 3M-3m abs is surrounded by intervals of 5 or 4

E.g.  5-4-3M-3m-4  or 5-4-4-3M-3m or  4-5-4-3M-3m  or 5-5-4-3M-3m or 5-5-4-3m-3M

etc

191. OVERTONES TUNINGS FOR THE 6 OR 12-STRING GUITAR THE OUD AND OTHER INSTRUMENTS

(see also https://en.wikipedia.org/wiki/Overtones_tuning   and in this blog posts 81 , 157 )

Among alternative tunings for the guitar, an overtones tuning selects its open-string notes from the overtone sequence of a fundamental note. An example is the open tuning constituted by the first six overtones of the fundamental note C, namely

C₂-C₃-G₃-C₄-E₄-G₄. INTERVALS (8-5-4-3M-3m) or in semitones (12-7-5-4-3 )

1-1'-5'-1''-3''-5''

For a 12-string guitar it would be

C2:C₂-C3C₃-G3G₃-C4C₄-E4E₄-G4G₄.

It is the overtones from the 1st till the 6th.

A 2nd version of the 1st overtones tuning  is starting from the 2nd overtone till the 8th omitting the 7nth overtone thus

C2-G2-C3-E3-G3-C4 INTERVALS (5-4-3M-3m-4) or in semitones (7-5-4-3-7 ) in numbered steps of the diatonic scale 1-5-1'-3'-5'-1"

Therefore it supports the ancient isocratic accompanying of melodies with only one power chord.

Overtone tunings that are open tunings have been used in songs by folk musician Joni Mitchell and by rock guitarist Mick Ralphs of Bad Company; these open overtones-tunings select their open notes from the first six partials of their overtone sequence on C or G. For open tunings, the open strings and the frets are each associated with a major-chord, which is played by strumming the open strings or the strings after they have been barred at one fret with one finger, greatly simplifying major-chord playing. For each such open or barred chord, the overtones reinforce the bass note, increasing the guitar's volume of sound and resonance. In an open overtones-tuning, adjacent strings that differ by a third interval can be tuned in just intonation, resulting in greater consonance than thirds in equal temperament.

Another advantage is that the guitar now is a bit more than 4 octaves compared to 3 plus octaves of the standard tuning. Also the three strings C2, C3 C4 give an easy coverage of 3 octaves and any scale in it once we learn in in the first string it is the same in the other two!

The higher 3 strings C₄-E₄-G₄. ar  major chord in normal position , and are part of the Harmonic-melodic tuning discussed in post 90 and 164. They support 3 shapes of major and minor chords 2 shapes of diminished and 1 shape of augmented triad chords by using at most 3 frets.

The strings 2-3-4 (counting 1 from the highest) are as the 3 highest strings of a standard tuning of guitar. They also support  3 shapes of major and minor chords 2 shapes of diminished and 1 shape of augmented triad chords by using at most 3 frets.

The strings 3-4-5 as a power chord p5 as in 3-courses Bouzouki. Therefore it supports the ancient isocratic accompanying of melodies with only one power chord.

The strings 4-5-6 are again an inverted form of power chord.

Therefore it supports the ancient isocratic accompanying of melodies with only one power chord.

ROOT/POWER CHORD/ ROOT MAJOR CHORD/CHORD PROGRESSION IMPROVISATION METHOD.

We notice that the intervals escalate  from 8 to 5 to 4 to 3M and finally 3m. This is also an organizational structure of melodies in C major mainly in the ancient mode of isocratic harmony and played mainly across a single string..

1) At first melodies within an interval of 8 accompanied with a single note the root C.

In general we may also have a melodic theme starting at the first note of string and ending at its other end note , in other words one octave. Then translate , invert and mutate it by playing it on another string and by the tuning all strings are only 3 notes , in intervals of 8, 5, 4, 3M, 3m apart, thus plenty many variations! All themes and variations are isocratically accompanied by the root of the scale C (or interval C-G).

2) Then  melodies within an interval of 8 accompanied with a pair of notes at different octaves that are  the root C.

2) Then  melodies within an interval of 7  accompanied with a power chord 1-5-1'of 3 notes C3-G4-C4

Again in general we may also have a melodic theme starting at the first note of string and ending at 7 fret note , in other words one 5th. Then translate , invert and mutate it by playing it on another string and by the tuning all strings are only 3 notes , in intervals of 8, 5, 4, 3M, 3m apart, thus plenty many variations! All themes and variations are isocratically accompanied by the power chord 1-5-1'of 3 notes C3-G4-C4

3)  Then  melodies within an interval of 4  accompanied with a power chord 1-5-1'of 3 notes C3-G4-C4

Again in general we may also have a melodic theme starting at the first note of string and ending at 5th fret note , in other words one 4th. Then translate , invert and mutate it by playing it on another string and by the tuning all strings are only 3 notes , in intervals of 8, 5, 4, 3M, 3m apart, thus plenty many variations! All themes and variations are isocratically accompanied by the power chord 1-5-1'of 3 notes C3-G4-C4

4) Then melodies within the arpeggio or vector-chord of  a chord 1-3-5 (see post 159) accompanied by the major chord 1-3-5 C major

Again in general we may also have a melodic theme starting at the first note of the chord 1-3-5 C major of a string and ending 7th frets higher, in other words one 5th or vector-chord . Then translate , invert and mutate it by playing it on another string and by the tuning all strings are only 3 notes , in intervals of 8, 5, 4, 3M, 3m apart, thus plenty many variations! All themes and variations are isocratically accompanied by the major chord 1-3-5 C major.

5) Finally a chord progression by triads or tetrads on the last 3 or 4 strings ofthe tuning (major minor diminished augmented) alternated with melodic bridges among them.

THIS TUNING IS PROBABLY THE BEST TUNING I HAVE EVER ENCOUNTER WHEN THE REQUIREMENTS IN GUITAR PLAYING IS 80% HARMONIC IMPROVISATION AND 20% MELODIC IMPROVISATION .

Nevertheless for those that are used to the standard tuning guitar probably the tuning

Since the tuning is the first 6 overtones of a fundamental frequency,our subconscious feeling of sounds even as ultrasounds is much accustomed to such 6-notes chords!besides the overtones tuning is the

5-5-4-3M-4  (see post 219 and 220)

For a children's guitar of 58-59 cm scale length the tuning C₂-C₃-G₃-C₄-E₄-G₄. is feasible. But for standard 66-67 cm scale length guitar maybe the next two tunings are more feasible

_B2-B₃-F#₃-B₄-D#₄-F#₄.

OR 

_Bb1-Bb2-F₃-Bb3-D₄-F₄.

C2-C₂-C₃-G₃-C₄-E₄

For a 4-courses instrument like a bouzouki or ukulele or octave mandolin two relevant overtone open tunings tunings are the


C₃-G₃-C₄-E₄      or  C2-G2-C3-E3  OR  D₃-A₃-D₄-F#<sub>4

or     D2-A2-D3-F#3

5-4-3M

THIS IS USED ALSO IN SWEDEN AND SCANDINAVIA FOR THE 4-STRING VIOLIN AS OPEN a MAJOR CHORD TUNING AND IT IS CALLED TROLL (MAGICAL) OVERTONE TUNING</sub> 

and 

G₃-C₄-E₄-G₄.   or A2-D2-F#3-D₄.

4-3M-3m
Or 


C₂C₃-C3C3-E3E3-G3G3

8-3M-3m

THE 2ND OVERTONES TUNING FOR THE 6-STRING GUITAR AND OUD IS TO USE ALL THE 6 HARMONICS FROM THE 2ND TO THE 7NTH FOR THE 6 STRINGS OF THE GUITAR THUS IN INTERVALS 5-4-3M-3m-3M, OR IN NOTES FROM C2-G2-C3-E3-G3-B3
SEE ALSO POST 301.

190. TWO MULTI-OCTAVES SCALES MADE FROM INTERVALS OF 5THS AND 3RDS (OR 6THS)

The next two scales are made entirely from intervals of 7 semitones , in other words intervals of 5 and intervals of 3 or their complementary intervals of 6ths . They come from successive triad major or minor chords of 2 or 3 frets in the  uniform tuning by 5ths of string instruments. In addition these scales , when reduced to a single octave they give the diatonic scale.


1)   C2-G2-E3-B3-G4-D5-A6-F6-C8     6 OCTAVES

INTERVALS IN SEMITONES

7-9-7-8-7-7-8-7


2) C2-G2-B2-F3-A3-E4-G4-D5    3 OCTAVES


INTERVALS IN SEMITONES

7-4-7-4-7-3-7

Such scales can be used also for tuning of strings so as to give major minor triads with few only frets (2,3 frets) 

189. THE TRADITIONAL TUNINGS OF THE GREEK LUTE

The traditional tunings of the Greek Lute are


Main land and islands:  C4:C3-G3:G2-D4:D3-Α3:Α3  (Intervals as if of single strings (-4) (+5) (+5  ) IN SEMITONES  -5 +7 +7 (THUS TWICE RE-ENTRANCE TO LOWER)


The range is rather concentrated because of the re-entrance which gives a uniform sound in strumming and playing (unlike the octave mandolin or mandocello)








Creta: G3-D3-A3-E3    (Intervals as if of single strings -4  (+5)  (-4) ) IN SEMITONES  -5 +7 -5  (THUS  RE-ENTRANCE TO LOWER IN THE MIDDLE)



G3-D3-A3-E3  if we correct the re-entrance in the middle gives E2-A2-D3-G3 which is a 5-5-5 tuning  which is uniform in soling when changing strings.
The range is rather concentrated because of the re-entrance which gives a uniform sound in strumming and playing (unlike the octave mandolin or mandocello)



WE MAY COMPARE THESE TUNINGS WITH THE NEXT



If   both harmonic improvisation and melodic improvisation is required then the mixed tuning

(C2:C2)-(G2:G2)-(B2:B2)-(D3:D3)      (5-3M-3m) seems appropriate.

Also

(C3:C3)-(G3:G3)-(B3:B3)-(D4:D4)



The 5 main advantages for HARMONIC AND MELODIC IMPROVISATION  of this tuning are:

1) It allows for the ancient isocratic accompanying of fast melodies with an interval of  5 by the two immediate lower strings of the string of the melody in the   5-3M part

2) The 2-octaves 7-notes scale by alternating intervals of 3 that shape the triad chords in a diatonic scale (called also melodic corridor or wheel by 3rds see post 94 and 79  )  have symmetric representations in this tuning either in the  3M-3m part .


4) The shift higher or lower by an interval of 4 or 5 vertical to  strings  which is usually a  mutation of a melodic theme played horizontally on a string  is feasible in the 5- part

5) It allows for both melodic improvisation with isocratic accompanying by intervals of 5 and harmonic improvisation with easy to play in 1 or 2 frets major-minor triads.

6) It allows strumming only on the 3-lower strings

It is probably the best optimal tuning when both harmonic and melodic improvisation is required in
percentages of 60%-40% for a 4-courses instrument .

But if conversely the requirements conversely in harmony and melody inother words harmonic and melodic improvisation is required in percentages of 40%-60% for a 4-courses instrument , the most probally the best tunig is the 5-5-5 (e.g. G2-D3-A3  or C2-G3-D4)

There is of course a minor version 5-3m-3M E.g.

(A2:A2)-(E3:E3)-(G3:G3)-(B3:B3)      (5-3m-3M)

In case we want to keep the 3-courses Bouzouki in it e.g.  D3-A3-D4 then the tuning should be

(D3:D3)-(A3:A3)-(D3:D3)-(F4:F4)      (5-4-3m)  or

(G2:G2)-(D3:D3)-(G3:G3)-(B3:B3)      (5-4-3M)


There are  also  overtone open tuning for 4-courses instruments (see post 191)

which are  the

For a 4-courses instrument like a bouzouki or ukulele or octave mandolin two relevant overtone open tunings tunings are the

C₃-G₃-C₄-E₄      or  C2-G2-C3-E3  OR  D₃-A₃-D₄-F#₄

_{or     D2-A2-D3-G3}

_5-4-3M
and 

G₃-C₄-E₄-G₄.   or A2-D2-F#3-D₄.

4-3M-3m
Or 

C₂C₃-C3C3-E3E3-G3G3

8-3M-3m

And also the 4-5-4 

D2-G2-D3-G3

which because of the 4-5 part it does have major-minor triads within 2-3 frets, and at the same time with the 5 part it allows for isocratic by 5th playing on the highest string.
It is also an open power chord tuning

and also the

4-5-5

D2-G2-D3-A3   which does have triads in thr 5-5 part and  also in the 4-5 part, and also it allows for isocratic tuning.

and 

5-5-4 

D2-A2-E3-A3

187 THE TRADITIONAL TUNINGS OF THE GREEK OUD AND 6-STRING GUITAR

The traditional tunings of the Greek Oud which is of 5 r 6-courses are

The Arabic tuning is

1) G2-A2-D3-G3-C4  (2M-4-4-4)   or D2-G2-A2-D3-G3-C4 (4-2M-4-4-4)

2) D2-E2-A2-D3-G3  (2M-4-4-4)

The Turkish tunng is


1) E2-A2-B2-E3-A3-D4   (4-2M-4-4-4)

2) E2-F#2-B2-E3-A3-D4  (2M-4-4-4-4)


We may compare it with the tuning of the Portuguese guitar (https://en.wikipedia.org/wiki/Portuguese_guitar ) which also has interval of 2M


D3-A3-B3-E4-A4-B4   (5-2M-4-4-2M)

and


C3-G3-A3-D4-G4-A4    (5-2M-4-4-2M)

or


C2-E2-G2-C4-E4-G4  (3M-3m-4-3M-3m)

186 THE 7 NOTES 2ND HARMONIC SCALE OF 3 OCTAVES AND THE CORRESPONDING TUNING OF STRING INSTRUMENTS

This 7-notes scale is of course the


B1-E2-A2-D3-G3-C4-F4-B4

and its span is 3 octaves when closing back to F.

The CONTRABASS , GUITAR BASS, PUERTO RICAN CUATRO etc are tuned in segments of this scale.

E.g. The Puerto Rican Cuatro has tuning


B3 B2♦E4 E3♦A3 A3♦D4 D4♦G4 G4

This tuning allows rather symmetric  representation also of the melodic-2nd harmonic 11-notes 4-octaves scale (of chords) as in post 184.