182. SIMPLE RULES OF INTERVALS FOR COMPOSITION OF BEAUTIFUL MELODIC THEMES

We will formulate rules of combinations of intervals of 1,2,3,4,5,7 semitones  (Intervals of 2 of 3 of 4 or of 5 as it is used to say). Such rules are used to compose beautiful melodic themes or improvise inside a  vector-chord (see also post 159) .


(3,4)
1) Combination of intervals of 3, in othre words of 3 or 4 semitones

We combine the 3+4=7 mostly as it gives arpeggios of minor major chords ans rarely the 3+3=6 and 4+4-8 that give arpeggios of diminished and augmented chords.

We also alternate the 3+4 with the 4+3 as so it  mainly in the chords of a diatonic scale.


(3,4-5)
2) Combination of intervals of 3, in other words of 3 or 4 semitones and intervals of 5 in other words of 7 semitones.

We combine by alternating them around the 5 : 3-5-4 and 4-5-3, 4-5-3-5-4 etc

(3,4-7)
3)  Combination of intervals of 4, in other words of 5 semitones and intervals of 5 in other words of  7 semitones


Similarly for the 7 : 3-7-4 and 4-7-3, 4-7-3-7-4 etc

(5-7)
4)  Combination of intervals of 4, in other words of 5 semitones and intervals of 5 in other words of  7 semitones

We alternate 5 and 7 : 5-7-5 etc

 (5-5)
5)  Combination of intervals of 4, in other words of 5 semitones


We avoid repetitions of 5

6)  (7-7)
Combination of intervals of 5, in other words of 7 semitones

We allow up to 3 repetitions  of 7 7-7 , 7-7-7

(1,2-3,4)
7) Combination of intervals of 3, in other words of 3 or 4 semitones and intervals of 2 in other words of 1 or 2 semitones

We combine 1 freely with 3, 4  1-3, 1-4 as it gives intervals of minor 3 and of 4 that exist in arpeggios of major minor chords.

(1,2-5)
8) Combination of intervals of 4, in other words of 5 semitones and intervals of 2 in other words of 1 or 2 semitones

We  combine only 2 with 5 2+5 =7, 5+2=7  as it gives intervals of 5 that exist in arpeggios of minor and major chords.


(1,2-7)
9) Combination of intervals of 4, in other words of 5 semitones and intervals of 2 in other words of 1 or 2 semitones

We combine freely the 1, 2 with 7  1+8= 2+7=9 as it gives intervals of 6 that exist in arpeggios of (inverted) minor and major chords.

10) (1,2-1,2)

We combine freely 1-2 and 2-2 as it gives intervals of 3 of the major minor chord arpeggios

181. THE (C2:C2)-(G2:G2)-(B3:B3)-(D3:D3) (5-3M-3m) OR (D3:D3)-(A3:A3)-(D3:D3)-(F4:F4) (5-4-3m) OPEN TUNING FOR 4-COURSES INSTRUMENTS

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, in other words, harmonic and melodic improvisation is required in percentages of 40%-60% for a 4-courses instrument, the most probably 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)  THEY ARE OPEN Dm and G tunings respectively!


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}

<sub>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

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 the 5-5 part and also in the 4-5 part, and also it allows for isocratic tuning.


By permuting the melodic tuning for 4-courses instruments, 3m-3M-3m  which is an open tuning we get the 5-6m-5 which is again open tuning but with intervals of 5. IT IS AN OPEN TUNING

E.g. 

A2-E3-C4-G4 OPEN TUNING FOR Am7

or 

E2-B3-G4-D4  OPEN TUNING FOR Em7

180. The panduri-tambouras (F2:F2)-(D3:D3)-(A3:A3)-(E4:E4) (6M-5-5) tuning of a 4-courses instrument.

It is a combination of tuning that requires intervals of 3 or inverted by 6, that give easy major-minor triads and at the same time the tuning by 5's (or Bouzouki 5-4).

For a 4-courses instrument like Bouzouki etc it can be with a slight inversion in the lower triad chords E.g.

(E2:E2)-(C3:C3)-(G3:G3)-(D4:D4)  (6M-5-5)

OR

(F2:F2)-(D3:D3)-(A3:A3)-(E4:E4)   (6M-5-5)

(if used to tambouras or mandolin)

Or if we are used to Bouzouki (which is also open D minor)

(F2:F2)-(D3:D3)-(A3:A3)-(D4:D4)   (6M-5-4)

The only reasons that one would prefer the later from the former is that the (A3:A3)-(D4:D4)  allows for easy two notes chords by intervals of 3. Nevertheless, it loses its uniformity for solos in the higher 3 strings, and also some major-minor triads on them playable at 2 or 3 frets. Personally, I would prefer the

(F2:F2)-(D3:D3)-(A3:A3)-(E4:E4)   (6M-5-5)

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   -5-5 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 in the  -5-5 part .

3) It is uniform tuning for melodies to shift among the strings in the   -5-5 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 very easy and symmetric in the higher 3 strings

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 in the lower 3 strings.

6) It allows strumming only 

179. THE AMAZING IONIAN-AEOLIAN-MIXOLYDIAN PANDURI-TAMBOURAS E2-G2-B3-D3-A3-E4 3m-3M-3m-5-5 TUNING . SLIGHT MODIFICATION OF THE HARMONIC TUNING OF THE 6 or 12 STRING GUITAR AND OUD

(SEE ALSO POST 90 AND 164) 

A2-C2-E3-G3-D3-A4  3m-3M-3m-5-5 (privileged scale C major)

or 

B2-D2-F#3-A3-E3-B4  3m-3M-3m-5-D (privileged scale D major)

(For 53 cm scale length children guitars)

ALSO NOTICE THAT THE ISOCRATIC INTERVALS OF 5 THAT ACCOMPANY FAST DANCING FREE MELODIES ARE THE A2-(C2)-E3  , C2-(E3)-G3, G3-D3-(A4) THAT ARE THE IONIAN  AEOLIAN  AND MIXOLYDIAN MODES  C MAJOR SCALE.

For the oud and for a standard 66 cm scale length guitar one tone lower is more appropriate

G2-Bb2-D3-F3-C3-F4

with privileged scale the  Bb major or 

F#2-A2-C#3-E3-B3-E4

with privileged scale the  A major or 

E2-G2-B3-D3-A3-D4

with privileged scale the  G major or 

for a 12-string guitar it can be the tuning

(E2:E2)-(G2G2)-(B3:B3)-(D3:D3)-(A3:A3)-(E4:E4)  3m-3M-3m-5-5

OR

(D2:D2)-(F2F2)-(A2:A2)-(C3:C3)-(G3:G3)-(D4:D4)  3m-3M-3m-5-5



Because of the part 3m-3M-3m is has plenty of many major minor triads that can be played with 1-2 frets only

And because of the part -5-5 it allows for the old isocratic with an interval of 5 playing of fast melodies. 

It can be considered also a minor triad panduri in lower 3-strings consecutive higher  at an interval of minor 3 of a 3-courses Tambouras.


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   -5-5 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-3m or  -5-5 part .

3) It is uniform tuning for melodies to shift among the strings in the   -5-5 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 very easy and symmetric

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 4-lower strings or per  3-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 like Bouzouki etc it can be wit a slight inversion in the lower triad chords E.g.

(E2:E2)-(C3:C3)-(G3:G3)-(D4:D4)  (6M-5-5)

OR

(F2:F2)-(D3:D3)-(A3:A3)-(E4:E4)   (6M-5-5)

(if used to tambouras or mandolin)

Or if we are used to Bouzouki (which is also open D minor)

(F2:F2)-(D3:D3)-(A3:A3)-(D4:D4)   (6M-5-4)

The only reasons that one would prefer the later from the former is that the (A3:A3)-(D4:D4)  allows for easy two notes chords by intervals of 3. Nevertheless, it loses its uniformity for solos in the higher 3 strings, and also some major-minor triads on them playable at 2 or 3 frets. Personally I would prefer the

(F2:F2)-(D3:D3)-(A3:A3)-(E4:E4)   (6M-5-5)

178. THE MANDOCELO-OCTAVE-MANDOLIN TUNING OF THE 6 OR 12-STRING GUITAR

This is the next tuning

For the 6-string guitar

Bb1-C2-G2-D3-A3-E4


Or for the 12-string guitar the


(Bb1:Bb1)-(C2:C2)-(G2:G2)-(D3:D3)-(A3:A3)-(E4:E4)




The -(C2:C2)-(G2:G2)-(D3:D3)-(A3:A3)- is a mandocello, while the

(G2:G2)-(D3:D3)-(A3:A3)-(E4:E4) is an Octave mandolin


The  main advantages for 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

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. Of course, this already occurs in the alternating minor-major interval of 3 tuning (A2:A2)-(C3:C3)-(E4:E4)-(G4:G4)-(B4:B4)-(D4:D4).

3) It is uniform tuning for melodies to shift among the strings.

4) The shift higher or lower vertical to the adjacent string or mutation of a melodic theme played horizontally on a string by an interval of 4 or 5 is very easy and symmetric

5) It supports 4 modes of the diatonic scale easily Ionian, Lydian, Mixolydian etc

If we consider the Bb1 very bass to play with an ordinary E2-guitar string then the next modification that eliminates it allows for a 3-courses bouzouki-like tuning at the higher 3 strings


(C2:C2)-(G2:G2)-(D3:D3)-(A3:A3)-(E4:E4)-(A3:A3)

Another way to sweeten the Bb1 is to add in the pair the 2nd string one octave higher. So in total


(Bb1:Bb2)-(C2:C3)-(G2:G2)-(D3:D3)-(A3:A3)-(E4:E4)

or simply re-entrance

(Bb2:Bb2)-(C2:C2)-(G2:G2)-(D3:D3)-(A3:A3)-(E4:E4)

If the instrument is 4-courses than obviously, this tuning reduces to the Octave mandolin or mandocello tuning.

(C2:C2)-(G2:G2)-(D3:D3)-(A3:A3)

This tuning for 4-courses instruments that want to specialize to melodic improvisation more than harmonic improvisation seems to be the best.

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

(C2:C2)-(G2:G2)-(B3:B3)-(D3:D3)      (5-3M-3m) seems more appropriate.

177. 4 WAYS OF PLAYING: STRUMMING , HARMONIC IMPROVISATION , MELODIC IMPROVISATION , FINGER PICKING. THE APPROPRIATE TUNINGS AND INSTRUMENTS

There are 4 ways of laying the string instruments

1) Strumming  accompanying chords

2) Harmonic improvisation by more than 50% of the time triads or 4 ,5 notes chords alternated some  times by solos

3) Melodic improvisation by more than 50% of the time by soloing and some times alternating some intervals or chords

4) Finger picking which tries to incorporate equally isocratic bass, isocratic chords and solo with he same instrument.


ALL OF THEM REQUIRE ESSENTIALLY DIFFERENT INSTRUMENTS AND TUNINGS!


E.g.

1) Strumming is done very well with Ukulele, Charango, standard tuning 6-string and 12-string guitars and even 4-courses instruments that are the minimum requirement for 4-notes chords. There are even better tunings from the well known for this (e.g. the harmonic tuning of post 90 applied for 4-courses instruments or 3m-3M-3m versus the well known 4-3M-4) 

2) Harmonic improvisation requires large sounding body for the chords are best tuning is the 3m-3M-3m-3M-3m  versus the well known 4-4-4-3M-4 for 6-string guitar Or another example is the 3-string panduri tuned at an open major chord  3m-3M. Other appropriate tunings for 6 or 7 string guitars are the 3m-3m-3m-3m-3m-(3m) or 3M-3M-3M-3M-3M(-3M)

3) Melodic improvisation is done with instruments usually with deep although small area sounding body so that the single note sound more like "doggy" or "knock" and tunings that involve strings in intervals of 4 or 5. (See posts 160-175) Examples of instruments are violin, lyra, Russian pandouri, saz, Bouzouki, mandola, bass , puerto rican cuatro etc.
When the instrument is tuned uniformly in the strings by intervals of 4 then a span of the 4-fingers over consecutive frets will give when shifting from the last small finger to the next string and first index finger and interval of 2 .While when the instrument is tuned in all strings by intervals of 5 the same continuation motion in the fingers will give an interval of 3. This may explain partially why folk music (e.g. like Irish ) on  instruments tuned by intervals of 5 (e.g. mandocello) have more intervals of 3 compared to folk music (e.g. like puerto-rican  ) on  instruments tuned by intervals of 4 (e.g. like cuatro). 

176. THE IONIAN-LYDIAN-MIXOLYDIAN 3-BOUZOUKIs, 9-STRINGS TUNING 5-4-4-5-4-4-5-4 OF THE 12-STRING GUITAR for melodic improvisation accompanied by intervals of 5

This tuning again for melodic improvisation of the old centuries  where fast dancing melodies are accompanied by intervals of 5 (power chords) rather than modern triad chords (major-minor). When melodies are accompanied by isocratic intervals of 5 they are more free to move fast and in complicated ways inside the scale (changing modes e.g. from major to minor and other modes possibly fast) , without having to change their sounding simple accompanying harmony.

In this tuning compared to the previous in posts 160-175 , we abandon comply the requirement that there are in the strings possibilities for many easy major-minor triad chords with 1 or 2 frets. Instead we concentrate in the ability to accompany with the standard power chords of the diatonic scale which have roots in the I-IV-V of the diatonic scale (major mode), that is Ionian  mode, Lydian mode and Mixolydian mode. O r with the ionian mode of 3 different scales but consecutive in the wheel by intervals of 4 (or 5).

In addition we prefer the sound of the solo string to be from  single strings, while the accompanying interval of 5 from double strings. Therefore the tuning utilizes only 9 of the 12-strings of a 12-string guitar as follows

(G2:D3)-G2-(D3:A3)-D3-(A3:E4)-A3

Somehow this tuning is as if 3 Bouzouki of 3 courses (G-D-G) (D-A-D) and (A-E-A)  , or more exactly 3 Balalaikas.


As alternative, we can have the

(G2:G2)-D3-G3-(D3:D3)-A3-D4

(5-4-4-5-4)


or even 


(G2:D3)-D3-G3-(D3:A3)-A3-D4

Now we have only tow Bouzoukis, but we can also have the intervals of 3m, 3M on its last two strings.

If we want  also double strings for the solo then it should be

(G2:D3)-(G2G2)-(D3:A3)-(D3:D3)-(A3:E4)-(A3:A3)
or 

(G2:D3)-(G2G3)-(D3:A3)-(D3:D4)-(A3:E4)-(A3:A3)

Alternatively we may utilize the next slight variation of the tuning so that each triad of strings are not two interval of 5 but a genuine power chord .In other words not G2-D3-G2 but G2-D3-G3 

So in order to account for the existing strings and their tension the tuning fr this 9-string guitar from a 12-string guitar becomes

(D2:A2)-D3-(A2:E3)-A3-(E3:B3)-E4

OR

(C2:G2)-C3-(G2:D3)-G3-(D3:A3)-D4

(5-4-4-5-4-4-5)

                                                                          

Notice that the strings 

(C2:)-...-(G2:)-...-(D3:A3)-..

is already a mandocello

While the strings 

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

Also i  the mandocello (they are a 3-courses tambouras) but one octave higher.

and also that the strings (D3:A3)-D4 are already an Irish or Greek 3-courses Bouzouki. Similarly the  (G2:D3)-G3 and (C2:G2)-C3.

(Notice that the last 4 strings G3-(D3:A3)-D4 is already the Irish bouzouki in single strings , while the last 3 ,(D3:A3)-D4 the Greek 3-course Bouzouki. The range is from C2 of the cello and mandocello till the Bouzouki)

THE LATER TUNING ALLOWS TO PLAY IN MELODIES THE PARTS OF THE MELODIC THEMES OF INTERVALS OF 2 OR 3 HORIZONTALLY WHILE SΗIFT THE MELODIC THEME BY INTERVALS OF 4, 5 OR 8 VERTICALLY (FOR MELODIC THEMES MUTATIONS). IN TOTAL I FIND THIS TUNING VERY CONVENIENT FOR MELODIES IMPROVISATION.

EITHER WITH FINGERNAILS OF PLECTRUM ALL STRINGS CAN BE PLAYED SEPARATELY EVEN IF THEY BELONG TO THE SAME PAIR OF STRINGS

THIS TUNING ALLOWS ALSO FOR NORMAL FORM MAJOR-MINOR TRIADS USING ONLY 2 FINGERS  WITH ONLY 2 OR 3 FRETS (e.g.on the consecutive strings G3-D3-A3).

  ALTERNATIVES ARE AGAIN POSSIBLE E.G.

THE MANDOCELLO-OCTAVE-MANDOLIN TUNING


(C2:C2)-(G2G2)-(D3:D3)-(A3:D3)-(E4:E4)

(5-5-5-5)

OR THE CONSECUTIVE BOUZOUKIS


(D2:D2)-(A2:A2)-(D3:D3)-(A3:A3)-(D4:D4)

(5-4-5-4)