226. PERCEIVING THE STANDARDLY TUNED 6-STRING GUITAR AS TWO INSTRUMENTS: A BASS AT THE LOWER 4 STRINGS AND A BARITONE UKULELE AT THE HIGHER 4 STRINGS. THE TRIAD-CHORDS OF THESE BASS AND UKULELE. .

We have mentioned before the power that the triad-chords have in playing and unlocking the full fretboard of an instruments like ukulele, Bouzouki, Bass etc

We apply it here in understanding the standard tuning of the 6-string guitar as an hybrid of a bass (at the lower 4 strings) for bass-melodic -lines and baritone ukulele at the higher 4 strings for easy and plenty many triad-chord shapes.

225. THE GENEALOGY OF 7, 6 ,5, NOTES SCALES THAT CONTAIN THE POWER-5 CHORD AND ARE MADE FROM TETRACHORDS OF A 4TH AND PENTACHORDS OF A 5TH. THE CHROMATIC, DIATONIC AND ENHARMONIC GENDRES

In ancient Greece according to Aristoxenos, there were 3 musical gendres , the diatonic , the chromatic and enharmonic which were also tetrachords  (total length an interval of 4th)  and pentachords (total legth an interval of 5th and consisting from an initial or final tone and a tetrachord as before) and by combing a tetrachord with a pentachord they got various   7-notes scales inside an octave . In other words the 7-notes scale was of the form Tetrachord1+2+tetrachord2 , in which case it was called two "divorced" tercahords or Tetrachord1+tetrachord2+2 in which case it was called two adjoint tetrachords.  1) the Diatonic  was balanced feelings (that eventually after more than 1 thousand years resulted to the 7-notes diatonic scale, and a simplified rounding of their tetrcahords to a single one was the 2-2-1 and most probably all permutations of it )  the 2) Chromatic  was sad feelings (that eventually after more than 1 thousand years resulted to the 7-notes harmonic minor and double harmonic minor scales, blues scale etc , And a simplified rounding of their tetrachords to a single one was the 3-1-1 nd most probably all permutations of it  ) and 3) the enharmonic  was happy feelings (used major 3rd intervals and a simplified rounding to a single one was the 4-(1/2)-(1/2)) and most probably all permutations of it )  and has many similarities with the Japanese 5-notes scales like the Akebono with interval structure 4 - 2 - 1 - 4 - 1 e.g. at the mode 2-1-4-1-4  e.g. A B C E F A. (See e.g. the video https://www.youtube.com/watch?v=vv7CO-nVFj8 ) 

In Ancient Greece, Byzantine and middle east, the 7-notes scales were created by combining 4-notes (tetrachords) that have total length an interval of 4th and 5-notes (pentachords) that have total length and interval of 7th. In this way all  such 7-notes scales contain the power-5 chord 1-5-1' (e.g. C3-G3-C4).

The representation of such tetrachords and pentachords can be with the sequence of intervals in semitones. Thus to find all of them is in mathematical terminology to find all partitions of 5 in ti 3 numbers (having sum 5) and all partitions of 7 in to 4 numbers (having sum 7).

The solutions is the next

ALL 6 TETRACHORDS

DIATONIC GENDRE (FAMILY)

(containing only 2 and 1)

2-2-1  syntono major  , Ionian/mixolydian (known also as Rast/Tsargiak/Mahour)

1-2-2  syntono minor  , Phrygian/Locrian (known also as Qurdi)

2-1-2   minor, Dorian/Aeolian (known also as Bousselik/Nichavent/Ousak)

CHROMATIC GENDRE (FAMILY)

(containing 3)

1-3-1   2nd chromatic  (known also as Hijaz)

1-1-3    parachromatic tonal

3-1-1    1st chromatic

ENHARMONIC GENDRE (FAMILY)

1/2-1/2-4
1/2-4-1/2
4-1/2-1/2

ALL 20 PENTACHORDS

All pentachords contain a single power-5 chord that power-5 chord which is defined by the end-notes of the pentachord.

THE DIATONIC FAMILY
(containing only 2, and 1)

2-2-2-1       Major Lydian    Contains a major chord (known also as Natzi/Zaouil)
2-2-1-2        Major Ionian/Mixolydian    Contains a major chord.(known also as Rast/Mahour)
2-1-2-2       Minor Dorian    Contains a minor chord (known also as Bousselik/Nichavent)
1-2-2-2       Minor Frygian/Aeolian    Contains a minor chord (known also as Qourdi)


THE CHROMATIC FAMILY
(containing  3 )

1-1-3-2
1-1-2-3
1-3-2-1   Contains a major chord and a diminished chord
1-2-3-1   Contains a minor chord and a diminished chord
1-2-1-3   Contains a minor chord and a diminished chord
1-3-1-2   Contains a major chord and a diminished chord (known also as Hijaz)
3-2-1-1    Contains  a diminished chord
2-3-1-1
3-1-2-1   Contains a major chord and a diminished chord
2-1-3-1   Contains a minor chord and a diminished chord (known also as Nevesser/Nikriz)
3-1-1-2   Contains a major chord (known also as Saz-kar)
2-1-1-3   Contains a minor chord (known also as Samba)


THE ENHARMONIAN GENDRE (FAMILY)
(containing  4 )

1-1-1-4   Contains a minor chord
1-1-4-1
1-4-1-1
4-1-1-1   Contains a major chord


By combining a treachord and a pentachord we get a 7-notes scale. We remind the reader that in this book by scale we mean a sequence of notes giving an octave and all cyclic permutations of them are considered the same scale but also 7 different modes of it.

As a rough estimation of an upper bound on the number of the scales of this genealogy we calculate that if x is the number of different such scales then x<=6*20*2*2=480, because we will combine 6 tetrachords with 18 pentachords thus 6*20=120 such combinations, but also combining first 18 pentachords and then 6 tetrachords will give twice as many, thus 6*2*20=240 . And by taking also the inverse order on all notes of them at most  6*20*2*2=480 scales. Of course some of them will turn out to be simply modes (cyclic permutations ) of some previous or next, thus 480 is an upper bound not an exact number.

In this way we can get the next scale

1) The diatonic
2) The harmonic minor
3) The inverse of the harmonic minor
4) The Neopolitan minor scale
5) The inverse of the Neopolitan minor  scale
6) The double harmonic minor
7) The melodic minor
8) The double melodic minor or Arabic scale or Neopolitan major
9) Parachromatic Byzantine scale (1-1-3-2-1-1-3)
10) Inverse parachromatic Byzantine
11) Debussy's 7-tonic (2-1-1-1-1-3-3) .
etc

Modes of the above 1-8 scales include the Byzantines minor and Byzantine double minor , Hungarian minor, Gypsy major and minor, Rast scale, Nikriz scale, Hitzaz scale, Hitzaskar scale , Nihavent scale, Neveser scale, 7-notes Sambach scale, Ousak scale , Qurdi scale , kartzigiar scale etc


Some japanese folk scales

Also arabic scales (projected in the Bach equally temperament  12-notes chromatic scale ) under the names  Shouzinak , Housam, Shegiach , Moustaar  , Persian or todi theta scale, the Enigmatic scale,
Debussy's 7-tonic (2-1-1-1-1-3-3) etc
 etc

See also post 21.

And many more beautiful scales that are not known with any name!

In ancient Greece according to Aristoxenus the tetrachords where 6 and of 3 generations.

They divided the semitone in to 6 equal segments, or the octave in to 72 segments or the pure 4th in to 30 segments.

Then the tetrachords were the next (the integers are Aristoxenus segments)

ENHARMONIC  GENDRE

3-3-24  or semitone/2 -- semitone/2 --2 tones

CHROMATIC GENDRE

Soft 4-4-22  or 1/3 tone 1/3 tone  22 segments

4.5 -4.5 -21


tonal   6-6-18  or 1 semitone 1 semitone 3 semitones

DIATONIC GENDRE

uniform  6-9-15 

syntono  6-12-12

Now two tetrachords make a scale of an octave in two ways 

The disjunctive way  = tetrachord+1tone+tetrachord=5+2+5 semitones=12 semitones

Or the adjoint way = tetrachord+tetrachord+1 tone=5+5+2 semitones=12 semitones

E.g. syntono+1tone+syntono=diatonic scale lydian mode
or syntono+syntono+1tone=diatonic scale Locrian mode

or tonal+tonal+1tone=6-6-18-6-6-18-12 which is a mode ofthe by now known as inverse persian todi theta scale 
The same with the tonal+1tone+tonal.

etc

See also post 227


For reasons of completeness we enumerate here the trichords which are of length an interval of 3rd.

All of them are of the DIATONIC FAMILY

1-2

2-1

2-2 


OF SCPECIAL INTEREST IS THE 7-NOTE SCALE 2-2-1-2-1-2-2 E.G. C-D-E-F-G-G#-Bb-C WHICH IS DERIVED FROM THE FIRST 13 OVERTONES HARMONIC SERIES IN A NATURAL TRUMPET.   AND IT IS  CONSTRUCTED FROM THE 4-CHORD 2-2-1 AND THE 5-CHORD 2-1-2-2. IT IS THE MELODIC MINOR OR ACOUSTIC OVERTONES SCALE IF THE 7NTH HARMONIC E.G. IN C-D-E-F-G-G#-B-C  if we interprete the 7nth overtone as B rather than Bb. BUT It is the inverse 7-notes scale of the first 13 overtones e.g. in a string or natural trumpet C-D-E-F-G-G#-B-C if we perceive THE 7NTH HARMONIC AS   B


ALL 7-NOTES SCALES OF THE ENHARMONIC GENDRE BY COMBINING A DIATONIC TETRACHORD WITH AN ENHARMONIC PENTACHORD

2-2-1-1-1-1-4
2-2-1-4-1-1-1
2-2-1-1-4-1-1
2-2-1-1-1-4-1

1-2-2-1-1-1-4
1-2-2-4-1-1-1
1-2-2-1-4-1-1
1-2-2-1-1-4-1

2-1-2-1-1-1-4
2-1-2-4-1-1-1
2-1-2-1-4-1-1
2-1-2-1-1-4-1

ALL 6-NOTES (ENHARMONIC GENDER)  SCALES THAT CONTAIN THE POWER-5 CHORD AND AT LEAST ONE MAJOR 3RD INTERVAL

Many of  the irish melodies belong to such scales!

Because the power chord is contained, then there must exist an interval of 4th and an interval of 5th. If the interval of 4th contains a major 3rd then the only solutions are

4-1, 1-4 . Otherwise the interval of major 3rd must be contained inside the interval of 5th, and thus we have the 5-chords of the enharmonic gender


1-1-1-4   Contains a minor chord
1-1-4-1
1-4-1-1
4-1-1-1   Contains a major chord

In total we enumerate at first all such scales with 2 major 3rd intervals

1) 4-1-1-1-1-4
2) 1-4-1-1-1-4 
3) 1-1-4-1-1-4

If there is only one major 3rd interval (4 semitones) 

Then we combine the 1-4 , 4-1 with any 5-chord in the diatonic or chromatic gender

4) 1-4-2-2-2-1
5) 1-4-2-2-1-2
6) 1-4-2-1-2-2 
7) 1-4-1-2-2-2  
8) 1-4-1-1-3-2
9) 1-4-1-3-2-1 
10) 1-4-1-2-3-1
11)  1-4-1-2-1-3 
12)  1-4-1-3-1-2
13) 1-4-2-3-1-1
14) 1-4-3-1-2-1
15) 1-4-2-1-3-1
16) 1-4-3-1-1-2
17) 1-4-2-1-1-3 

18) 4-1-2-2-1-2
19) 4-1-2-1-2-2  
20) 4-1-1-2-2-2  
21) 4-1-1-1-3-2
22) 4-1-1-2-3-1
23)  4-1-1-2-1-3 
24) 4-1-3-1-1-2
25) 4-1-2-1-1-3 

Among these 25 scales we filter the combinationof diatonic 4-chords and only one major third
thus haveing the 7 diatonic-enharmonic hexatonic scales

I have seydel harmonicas with these dtaitonic-enharmonic hexatonic scales

4) 1-4-2-2-2-1 (HEX ARABIC OR HEX NEAPOLITAN MAJOR 1M =inverse of 20) ) 
5) 1-4-2-2-1-2 (HEX MELODIC MINOR 1M-2d  inverse of 19))
6) 1-4-2-1-2-2 (HEX DIATONICENHARMONIC 1m-2d)
7) 1-4-1-2-2-2  (HEX AKEBONO-CRETAN 1M-7m)
18) 4-1-2-2-1-2 (HEX ENHARMONIC 1M-7d)
19) 4-1-2-1-2-2  (HEX HMIN ENHARM 1m-7d inverse of 5) )
20) 4-1-1-2-2-2  (HEX ARABIC OR HEX NEAPOLITAN MAJOR   1m)


Among these 25 scales we filter those that contain the 4-3, or 3-4 which is triad chord as with more harmonic sound

Major chord 4-3:

14) 1-4-3-1-2-1
16) 1-4-3-1-1-2
By cyclic permutation we may re-write them as 

14) 4-3-1-2-1-1
16) 4-3-1-1-2-1

Minor chord 3-4:
23)  4-1-1-2-1-3 
25) 4-1-2-1-1-3 

By cyclic permutation we may re-write them as 

23) 3-4-1-1-2-1
25) 3-4-1-2-1-1 


ALL 5-NOTES  SCALES THAT CONTAIN THE POWER-5 CHORD AND AT LEAST ONE MAJOR 3RD (4 SEMITONES)

This already mean that we know tow notes of the scale . The other 3 

1) All in the lower interval of 5th . Thus a 5-chord as above and then an interval of  4th or 5 semitones. 

1) 1-1-1-4 -5
2) 1-1-4-1-5
3) 1-4-1-1-5
4) 4-1-1-1 -5

2) All in the upper interval of 4th . Thus a 4-chord as above as as upper 3 notes and as lower notes the  3-4, 4-3 E.g.

5) 4-3-2-2-1 Known in this blog as the inverse maximal harmonic 5-tonic scale (see post 117  and 204 )
6) 4-3-1-2-2
7) 4-3-2-1-2
8) 4-3-1-3-1 
9) 4-3-1-1-3
10) 4-3-3-1-1

and

11) 3-4-2-2-1
6) 3-4-1-2-2
7) 3-4-2-1-2
8) 3-4-1-3-1 
9) 3-4-1-1-3
10) 3-4-3-1-1

3) 2 notes in the lower interval of 5th 

3-2-2, 2-2-3, 4-2-1, 4-1-2 , 2-1-4, 1-2-4, 3-3-1, 1-3-3, 3-1-3, 1-1-5, 5-1-1, 1-5-1

and one in the upper interval of 4th

2-3, 3-2, 1-4 , 4-1 Thus

11) 3-2-2-4-1
12) 3-2-2-1-4
13) 2-2-3-1-4
14) 2-2-3-4-1 Known also as Greek pentatonic 2-2-3-4-1 (known also as Raga Chitthakarshini)
15) 4-2-1-2-3
16) 4-2-1-3-2
17) 4-2-1-1-4
18) 4-2-1-4-1 known also as the Japanese  Hirajoshi 5-notes scale and In 5-notes scale and Iwato 5-notes scale and as Akebono 5-notes scale
19)  4-1-2-3-2
20) 4-1-2-1-4
21) 4-1-2-4-1
22) 2-1-4-2-3 known also as the Japanese  Insen 5-notes scale 
23) 1-2-4-2-3
24) 1-2-4-3-2
25) 1-2-4-4-1
26) 3-3-1-1-4
27) 3-3-1-4-1
28) 1-3-3-4-1
29) 3-1-3-1-4
30) 3-1-3-4-1
31) 1-1-5-1-4
32) 1-1-5-4-1
33) 5-1-1-1-4
34) 5-1-1-4-1
35) 1-5-1-4-1
36) 1-5-1-1-4

4) 1 note in the lower interval of 5th and 2 notes in the upper interval of 4th

thus 1-6, 6-1 and 1-1-1-2, 1-1-2-1, 1-2-1-1, 2-1-1-1, but none contains 4 , thus no new 5-notes scales.


2-1-4-1-4

224. THE 7 BASIC IMPROVISATIONAL EXERCISES ON A WIND

The 6 basic improvisational exercises on a whistle or  transverse flute or quena (rim blown flutes) or winds with reeds are the next 6


1) Correct covering of holes and scale fingering

2) Overtones awareness and octaves crossing

3) Ornamentations (Cuts or hammers, double cuts, slides (rolling or bends), vibratos, etc)

4) 2,3,4,5 etc Translations (tails or Alankaras)

5) Rotations (or permutations, including arpeggios of chords in 2 octaves and power chords too in 2 octaves and arpeggios or permutations or rotations of vector intervals of 3rd (trichords), 4th (tetrachords) and 5ths (pentachords).

6) Inversions (in pitch or rhythm of small musical themes.

7) Improvisations restricted in a pentachord (as in post 225) and over 3 chords.

We enlarge more on them.  But the next 18+7 videos are very instructive too



A) 18 Videos by Phil (Kerry whistles) 

https://www.youtube.com/watch?v=SQq2dbN5Xsk&list=PLiYGJiKPn5B3RN_xjtQ6ZktWFAg4HWv7Z&index=18


B) 7 Videos by Das (flute maker)

https://www.youtube.com/watch?v=7Ox55nMD9RE

223. MINORIZATION-MAJORIZATION AS A UNIQUE HARMONIC TRANSFORMATION (NEGATIVE--POSITIVE HARMONY) MODULATIONS VERSUS TRANSPOSITIONS OF MELODIES AND HARMONIES

Here it is described why and how the transformation of a song from a major mode diatonic scale to a minor mode diatonic scale (and vice versa) is not just an ordinary change of mode among the 7 possible modes of the diatonic scale (e.g. from the ionina to the aeolian) but a  unique harmonic and melodic transformation.

In the nxt video this transformation from a  major mode to the minor mode (but also as scale modulation) is described under the term negative harmonics.

Do you know beautiful songs written in a Aeolian or minor mode of a diatonic scale? Then try the positive harmony, in other words transform them melodically and harmonically to a major mode and make them happier.

https://www.youtube.com/watch?v=qHH8siNm3ts&t=168s


TRANSCRIPTIONS:
We must discriminate between the concept of transposition transcription  of the  melody and harmony of a song from that of modulation transcription .  A transposition transcription preserves the intervals among the notes of the melody and types of chords and it is played on higher or lower pitch. But a modulation transcription does not preserves the intervals among the notes of the melody neither the types of the underlying chords as it is "translating within the scale" and not within the 12-notes chromatic scale, the melody and its chords starting from a different note of the scale (different mode). Both though require that all the melody (or song) is written in a single scale (or mode) and the transcription is another scale or mode of equal number of notes. 

222. THE 7 MODES OF A DIATONIC SCALE AS TRIADS OF CHORDS

We cannot stress much the importance of triads of chords (but also of notes intervals and scales) in improvisation.

A good application is to realize that as a diatonic scale is characterized as chords on the wheel by 4ths by its 3 chords on the steps 1M, 4M , 5M  (harmonic triplet of chords) ,  OR 7d 1M 2m (chromatic tripler of chords) the same can apply for the modes of the diatonic scale.

The chords of a mode of a diatonic scale at the steps 1,4,5 (or 7,1, 2) of it characterize its mood.

For example for the mixolydian mode of the diatonic scale from C ,(G, A, B , C, D, E, F, G) the chords at the steps 1,4 ,5 are the G, C, Dm) thus the 1, 2, 5 or I, ii, V of the original ionian and are the base of blues jazz.


Based on this perception, the 7 modes of the diatonic scale have the following chord triads:

(that is chords on their 1st 4th and 5th step, and we symbolize by m=minor M=major d=diminsihed.
Based on this perception, the 7 modes of the diatonic scale have the following chord triads:

(that is chords on their 1st 4th and 5th step, and we symbolize by m=minor M=major d=diminsihed.



1. IONIAN  :  HARMONIC TRIPLET (1M, 4M, 5M)
2. DORIAN  : HARMONIC TRIPLET (2m, 5M, 6m)
3. PHRYGIAN : HARMONIC TRIPLET (3m, 6m, 7d)
4. LYDIAN: HARMONIC TRIPLET  (4M, 7d,1M)
5. MIXOLYDIAN: HARMONIC TRIPLET  (5M, 1M,2m)
6. AEOLIAN: HARMONIC TRIPLET (6m, 2m, 3m)
7. LOCRIAN: HARMONIC TRIPLET  (7d, 3m, 4M)

We may clasify them according the the major and minor chords

A.ALL 3 MAJOR CHORDS (ALL HAPPY) 

1. IONIAN  :  HARMONIC TRIPLET (1M, 4M, 5M)

B. 2 MAJORS AND ONE MINOR OR DIMINISHED CHORD (ALMOST HAPPY, ALMOST MAJOR)

4. LYDIAN: HARMONIC TRIPLET  (4M, 7d,1M)

5. MIXOLYDIAN: HARMONIC TRIPLET  (5M, 1M,2m)

C.  2 MINORS (OR DIMINISHED) AND ONE MAJOR  (LITTLE SAD,  ALMOST MINOR )

2. DORIAN  : HARMONIC TRIPLET (2m, 5M, 6m)

7. LOCRIAN: HARMONIC TRIPLET  (7d, 3m, 4M)

D. THREE MINORS OR DIMINISHED (ALL SAD) (ALL MINOR) 

3. PHRYGIAN : HARMONIC TRIPLET (3m, 6m, 7d)

6. AEOLIAN: HARMONIC TRIPLET (6m, 2m, 3m)

We may compare the basic harmonic triplets with the basic chromatic triplets (see also post 322)

1. IONIAN  :  CHROMATIC TRIPLET (7d, 1M, 2m)
2. DORIAN  :  CHROMATIC TRIPLET (1M, 2m, 3m )
3. PHRYGIAN : CHROMATIC TRIPLET(2m,3m, 4M)
4. LYDIAN:  CHROMATIC TRIPLET(3m, 4M, 5M)
5. MIXOLYDIAN: CHROMATIC TRIPLET (4M, 5M, 6m)
6. AEOLIAN:  CHROMATIC TRIPLET (5M, 6m, 7d)
7. LOCRIAN:  CHROMATIC TRIPLET (6m, 7d, 1M)



If we want an ordering of how much "minor" and "sad" or "anxious" is a mode and how much "major" and "happy" or "serene" is a mode based on the ordering d<m<M then we get the next partial ordering (non-linear ordering)

PHRYGIAN<AEOLIAN<DORIAN<MIXOLYDIAN<IONIAN

and

LOCRIAN<DORIAN

LYDIAN<MIXOLYDIAN

But the Locrian and Lydian are not comparable with all the others so as to put all of them in a linear order.

Here is a musicological old qualitative description of it, but the names are not the standard but an older version of them (e. mode V is referred in this table as Lydian , while nowadays is named Mixolydian). To realize about which mode is referenced we must look at the 2nd column with the latin numerals.

Based on this concept it is possible to define tunings  of an harmonica (see post 274 ) with these types of triads of chords so as to improvise with the corresponding harmony on each of the 7 modes!

221. UNLOCKING THE MELODIC AND HARMONIC IMPROVISATION BY UTILIZING TRIADS OF NOTES , INTERVALS , CHORDS AND 3-LEVELS STRUCTURE OF A MELODY

See also posts 217, 216, 214, 208 etc

We enlarge more on it below. It is a generalization of the concept of scale, as a diatonic scale can also be defined by a triad of major (or minor) chords consecutive on the wheel by 4ths.

The triads is the golden middle ground between the extreme simplicity of the one  note ,interval or chord and the more complex combinations of 5 or more notes , intervals or chords.

The simplicity of triad of factors for the melodic action is  mainly the next three factors

1) The triad of polarity (qualitative) of a melodic move (ascending, descending, rotating stationarily or isocratic)

2) The  quantitative  triad of the character of the move :Chromatic, Melodic ,Harmonic

3) The rhythmic pattern of repetitions (e.g. A1 A2 A3 B1)

We remind the reader that in posts 203 and 214 we described a 3-levels structure of melodies which we refresh here:

THE MELODIC IMPROVISATION IS A SEQUENCE OF "ROTATIONS". EACH "ROTATION" HAS THE NEXT 3-LEVEL  RHYTHMIC OR MORPHOLOGICAL STRUCTURE

THE 4 PARTS A1 A2 A3 BI STRUCTURE 

This structure is rhythmic morphological and comes as a pattern from the 15-syllable poetry.

2 lines in a 15-syllables poetry are divided to 4 parts A1 A2 A3 B1, each of the Ai having 4 syllables and the B1 3 syllables. Similarly here in the melody the A1 A2 A3 , B1 are of 2 measures.  Each of the A1 A2 A3 B1 contain at least one melodic theme. If we put the restriction that both the melodic theme and its variations are consisting from intervals that are 2nds in less that 1/3 (=33%) of the cases, then we get an "Irish" but also "south american", melodic/harmonic sound in the melody. The melodic theme of A1 is translated or inverted to that of the A2 and that of the A2 to that of A2. Finally the melodic theme of A3 is mutated to that of B1. The simplicial sub-melody has one note in each measure therefore two notes in each of the A1 A2 A3 B. These two notes signify a MELODIC MOVEMENT (VECTOR) which is the basis of an emotion.  If we superimpose the melody at the first two levels, the detailed improvisational notes of the melodic theme (1st level) and the melodic move or vector of the simplicial submelody (2nd level) we get a new musical entity and concept that we may call WAVING MELODIC VECTOR. The wavings are as in the 7 melodic themes patterns asin post 231. Another classification of them is that they are of 3 classes a) Chromatic (of length an interval of 2nd) b) Melodic (of length an interval of 3rd) c) Harmonic (of length an interval of 5th). The choice in the improvisation of one of these 3 classes is similar to the choice in a chord progression if the chord-transition will me chromatic , melodic or harmonic. Very often the wavings are of diminishing amplitude as we reach the melodic center-end note of it. This is very convenient to have in mind when we improvise because we think that we will move from a persisting note a (melodic center) to a persisting note b (melodic center ) in a scale but with improvisational waving way that we may change each time at willAll the melodic movements of the A1 A2 A3 B make a DOLPHIN WORD (as defined also in post 101, 114 ). Each part A (thus melodic move too) has an underlying chord. The chords of two parts like A1 A2 may be the same or different chords. The melodic move can be also a melodic triad (alternating major minor vector interval of 3rd as in post 208) . The Dolphin word of the "rotation" may be a closed polygon (e.g, triangle) of waving melodic vectors , so that the length of the melodic vector indicates also the length-interval of the waving melodic vector, which may also be the distance as musical interval of the middle notes of the underlying chords, of the melodic move.
This melodic polygone allows for simple and very concise, simple and visually beautiful  methods of writing the improvisation with not less information than the necessary but no more than a minimum too, so that each time we see the written paper and play the melody a different melody will emerge (mainly at the first layer/level of it) while still it will be "the same" song. 

When playing again such an improvisation the simplicial sub melody is repeated (thus the "rotation" A1 A2 A3 B or Dolphin word of it), but the other notes inside the measures that are embellishments may change. All together the "rotations" or Dolphin words make the total melodic phrases of the song. Therefore we have here at least a 3-level structures of the melody a) notes b) melodic moves c) "rotations" or Dolphin words,and in time it is 1, 2^3=8 (2 measures)  and 2^5=32 (A1A2A3B parts).

220. THE DOUBLE 4-STRINGS GREEK BOUZOUKI F2-bB2-D3-G3-B3-E4 (4-3M-4-3M-4) TUNING OF THE 6-STRING GUITAR OR OUD

See also post  and 200

The standard tuning of the guitar comes from a scale LIKE :

F2-Bb2-D3-G3-B3-E4-G#4-C#5-F5

So we may repeat the pattern 4-3M-4  D3-G3-B3-E4 of the standard tuning of the guitar to the

4-3M-4-3M-4  or F2-Bb2-D3-G3-B3-E4

We play this tuning as two 4-strings Greek bouzouki

The high  D3-G3-B3-E4  (4-3M-4) in G major

The low  F2-Bb2-D3-G3  (4-3M-4) in Bb major