259. Extensions of the 6-notes Blues scale to four 7-notes scale that keep the 1-1-3 four-notes subscale

The Blues 6-notes scale is in semitones intervals the 1-1-3-2-3-2 or 2-1-1-3-2

or in steps of diatonic scale 7-1-1#-3-4#

If we want to tune a portable Celtic harp with levers for sharps it could be repeating a note e.g.

a#-b-c-d#-e#-f-g#-a# or in steps of a 7-notes diatonic scale 6#-7-1-2#-3#-4-5#-6#

If we want to keep the 1-1-3 invariant which is the ancient Greek chromatic tetrahord (4-notes subscale) known as parachromatic tonal  , then the possible extensions to 7 notes are the

1) 1-1-3-1-1-3-2 Which is nothing else than the Byzantine parachromatic scale
It  contains the 5-notes pentachord subscale   2-1-1-3 known as Samba

The Byzantine parachromatic scale is called also inverse Persian or  Purvi Theta scale.

E.g. as steps of a diatonic scale 6-7-1-1#-3-4-4#-6. or in c major a-b-c-c#-e-f-f#-a

If we want to tune a portable Celtic harp with levers for sharps it could be e.g.

c-d#-e-f-g#-a#-b-c

2) 1-1-3-2-2-1-2 , which contains the 5-notes pentachord subscale   2-1-1-3 known as Samba. It is  made from the samba pentachord and the diatonic tetrachord 2-2-1.

E.g. as steps of a diatonic scale 6-7-1#-2-3-4-4#-6 or in notes of c major a-b-c#-d-e-f-f#-a

3) 1-1-3-2-1-2-2 . Again it contains the the 5-notes pentachord subscale   2-1-1-3 known as Samba

E.g. as steps of a diatonic scale 6-7-1-2-3-4-4#-6 or in notes of c major a-b-c-d-e-f-f#-a

4) 1-1-3-2-3-1-1 , or  as steps of a diatonic scale 7-1-1#-3-4#-6-6#-7 or in notes of c major b-c-c#-e-f-f#-a-a#-b It is as symmetric as the Byzantine (double) parachromatic scale. Actually it is made from the samba pentachord 1-1-3-2  (or  by cyclic permutation 2-1-1-3 ) and its inverse  2-3-1-1.

258 WHY PROFOUND IMPROVISATION IS A TRIPLE BALANCE MEDITATION IN 2/3DS INDEPENDENT FROM THE MUSICAL INSTRUMENT

WHY PROFOUND IMPROVISATION IS A TRIPLE BALANCE INTERNAL ACTIVE MEDITATION IN 2/3DS INDEPENDENT FROM THE MUSICAL INSTRUMENT!

Improvisation produces beautiful music and gives deep satisfaction as it requires deep internalisation of the musical composition process.

There mainly 3 centers that are involved in the process of musical improvisation

1) The skill and conveniences of the fingers and geometry, tuning etc of the musical instrument

2) The internalized memories of musical listening that have become feeling-habits

3) Our mental images of musical-theory conceptual tools (like chords, intervals , scales , rhythms etc)

Now if one of these control or abilities centers over-dominates the other two some rather undesired effects occur in the improvised music

1) If the skill and convenience of the fingers in the instrument drives are mainly when improvising music , then a rather narrow type of music may be produced depending on what our knowledge of the  instrument allows. In addition each time we try to improvise, our fixed skills on the instrument tend to repeat so much that the resulting music is repetitively boring. This is what happens to skilled instruments players that do not have sufficient or do not create new musical theoretic concepts

2) When out listening memories and listening habits mainly dominate much our improvisation, then we tend to repeat known small pieces of melodies or harmonies and the richness of the new musical sound is not occuring.

3) When our mental musical theoretical and conceptual tools dominates when improvising, we may fall in the trap of creating very interesting new concepts of music which nevertheless are not well sounding and do not trigger familiar feelings of our musical habits therefore are not grasped at least initially as beautiful music.

It is only when our improvisation is a triple balance of a triple improvisation that the resulting music is beautiful and satisfying musical creation. And the triple improvisation is a triple improvisation in FINGER-ACTIONS, FEELINGS AND INTELLECTUAL THINKING.

The triple improvisation is

1) An improvisation of new shapes and patterns on the skill of the fingers that play the instrument

2) An improvisation in our nervous system, on new synthesis of musical memories and stored musical feelings which is new but also familiar. And this is a process not on the instrument but on our internalized musical memories and feelings.

3) An improvisation of new combinations of musical-theoretic concepts that give a simple center to organize our improvisation. And this is a process not on the instrument neither on our musical habits of feelings but on our intellect and mental images of theoretical concepts.

For those that play many instruments with strings or winds, the parts 2) and  3) are indispensable tools for simplification and learning as the do not depend on the instrument!

As the inner two parts of this meditation may have their own timing and flow, the improvisation must follow and combine these separate timings: 1) Of the fingers abilities, 2) of the speed of shaping of the emotions 3) of the speed of the flow of intellectual musical conceptual tools.Therefore fastness might be impressive finger-skill but may not correspond to a deep satisfying musical creation. 

As 2/3 of the improvisation is internal rather than external on the musical instrument, we may say that an improvisation is a type of TRIPLE ACTIVE MEDITATION.

257. MAINLY (1/2 OF THE TIME) MELODIC (ALTERNATING MAJOR-MINOR 3RDS) IMPROVISATION "WALKING" WITH CHROMATIC DECORATIONS (OSCILLATIONS BY 2NDS) IN DIATONIC SCALES

MAINLY (1/2 OF THE TIME) MELODIC (ALTERNATING MAJOR-MINOR 3RDS) IMPROVISATION "WALKING" WITH CHROMATIC DECORATIONS (OSCILLATIONS BY 2NDS) IN DIATONIC SCALES

There is a type of improvisation where the  main and most often (at least 1/2 of the time) size of steps in the Improvisational "walking" is the intervals of 3rds in other words "meloding walking" , and in particular alternating major and minor 3rds. Then about 1/3 of the time we move with chromatic steps of intervals of 2nds, and particular when going up or down we oscillate around a note with an interval of 2nd (chromatic embellishments) and less often (less than 1/3 of the time) with harmonic intervals in other words  intervals of 4ths, 5ths or larger than 8ths.

This type of improvisation works well in diatonic scales where there is maximum number of triad chords made from alternating intervals of major-minor 3rds. On the other had in chromatic minor scale (harmonic minor, double harmonic minor, melodic minor , parachromatic etc) the "walking" with intervals of 2nds is more convenient as there not many triad major or minor chords .

Such type of improvisation is quite often in folk Irish music or early New Orleans jazz. This is the cae also with Andes improvisational folk music with Zampona pan-flutes.

Such improvisation are to be contrasted with the usual "improvisational walking" e.g. of Stephane Grappelli which is mainly with steps by intervals of 2nds.

Similarly improvisational counter-melodies in Greek folk Bouzouki music which are mainly with steps by intervals of 2nds.

The keys to a nice flow of improvisation as expressed in many cultures folk music are 

Simplicity in the harmony (triads of harmonic pairs of chords) 
Simplicity in melodic themes 
Simplicity in rhythmic variations of the melodic themes and repetitions

256. THE TRIAD OF CHOICES WHEN IMPROVISING A MELODY

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), The relevant theme variation here is inversion

2) The  quantitative  triad of the character of the move :Chromatic (2nds) , Melodic (3rds) ,Harmonic (4th, 5ths or more than 8ths). The relevant theme variation here is expansion-contraction

3) The rhythmic pattern of repetitions or translations . The relevant theme variation here is translation.

The keys to a nice flow of improvisation as expressed in many cultures folk music are 

Simplicity in the harmony (triads of harmonic pairs of chords or triads of chords or only a pair of chords or a single power-chord)
Simplicity in melodic themes 
Simplicity in rhythmic and pitch variations of the melodic themes and repetitions


IF THE CENTRAL  ENTITY IN HARMONY IS THE TRIAD CHORD THE CENTRAL ENTITY IN MELODY IS THE MELODIC THEME AND IN PARTICULAR THE OVERSIMPLIFIED VERSION OF SIMPLE MELODIC MOVE BY AN INTERVAL AS  TRACED IN SIMPLIFIED WAY BY THE SIMPLICIAL SUBMELODY.

Based on the above, the themes in the simplicial sub-melody as simple moves are of two polarities up (+) or down (-) and of three sizes Chromatic (symbol C) by intervals of 2nds, Melodic (symbol M) by intervals of 3rd and Harmonic (symbol H) by intervals of 4th, 5th, 8th or higher. Then the progression of the simplicial melodic themes in the song will have a symbolic form like E.g.

H(+)M(-)H(-)M(+)C(-)M(+)H(+).......etc

The translation/transposition  of a simplicial melodic theme retains its cahracter as chromatic , melodic or harmonic.
The inversion of a simplicial melodic theme inverses the + to - andthe - to +
The expansion/contraction of a simplicial melodic theme e.g. an expansion changes a chromatic to a melodic or harmonic and a melodic to an harmonic. A contraction changes an harmonic to a melodic or chromatic and a melodic to a chromatic.


MAINLY MELODIC IMPROVISATION WITH CHROMATIC DECORATIONS
There is a type of improvisation where the  main and most often (at least 1/2 of the time) size of steps in the Improvisational "walking" is the intervals of 3rds in other words "meloding walking" , and in particular alternating major and minor 3rds. Then about 1/3 of the time we move with chromatic steps of intervals of 2nds, and particular when going up or down we oscillate around a note with an interval of 2nd (chromatic embellishments) and less often (less than 1/3 of the time) with harmonic intervals in other words  intervals of 4ths, 5ths or larger than 8ths.

Such type of improvisation is quite often in folk Irish music or early New Orleans jazz. This is the cae also with Andes improvisational folk music with Zampona pan-flutes.

This type of improvisation works well in diatonic scales where there is maximum number of triad chords made from alternating intervals of major-minor 3rds. On the other had in chromatic minor scale (harmonic minor, double harmonic minor, melodic minor , parachromatic etc) the "walking" with intervals of 2nds is more convenient as there not many triad major or minor chords .


Such improvisation are to be contrasted with the usual "improvisational walking" e.g. of Stephane Grappelli which is mainly with steps by intervals of 2nds.

Similarly improvisational counter-melodies in Greek folk Bouzouki music which are mainly with steps by intervals of 2nds.

When making a melodic improvisation the triad of choices are the next 3 (similar to the triad of choices in chord-progression improvisation  of making  a chord transition which is chromatic melodic or harmonic. The mutation or rotation may be considered  a 4th decision but it essential a restart of the previous process.

1) TRANSLATE UP OR DOWN THE MELODIC THEME, CHROMATICALLY, MELODICALLY OR HARMONICALLY 

2) INVERT THE MELODIC THEME CHROMATICALLY, MELODICALLY OR HARMONICALLY

3) EXPAND-CONTRACT THE MELODIC THEME WITHIN THE SCALE.

4) ROTATE IMPROVISATIONALLY IN PLACE OR CREATE A NEW MELODIC THEME (MUTATION) IN PLACE , OR UP OR DOWN BY AN HARMONIC INTERVAL (4TH OR 5TH) OR INTERVAL LARGER THAN AN OCTAVE.

255. THE Gm7 MINOR (Bb AEOLIAN MODE) TENOR GUITAR AND CORRESPONDING BARITONE OR TENOR UKULELE AND BOUZOUKI

THE PREFERENCE OF THE B FLAT SCALE

It seems that in various cultures there is a systematic preference of the Bb major scale and its minor mode G in various chromatic versions natural G minor, harmonic G minor, double harmonic G minor, etc

1) Most of the old centuries folk Greek songs (dimotika) seem to be ton Bb scale

2) Most of the Greek rebetika seem to in G chromatic minors  and D chromatic minors

3) The natural scales of Trumpet and clarinet is in Bb.

4) It seems that early new Orleans Jazz (that utilizes trumpet and clarinet) is in Bb scale (e.g. see Tuba skinny https://www.youtube.com/watch?v=wk64II0TGCk )

What is the real reason? Difficult to say. But the next video finds the reason on the pineal gland the the link of the soul to the body https://www.youtube.com/watch?v=8vP72lFnrDk

Thus a guitar with privileged scale  the Bb instead of the standard G major would be advantageous to play such music.

And as 4-strings (or 4-double strings) tenor guitar version this Bb major scale tuning would be

(from lower pitch to higher)      F3-Bb3-D4-G4

it is an open Gm7 tuning.

The next 3 pictures are from a baritone ukulele tuned in this way. 
A baritone ukulele  usually has scale length of 48 cm, which for the E4 string of the standard guitar is about the note A4.
 Actually I have subtracted the second double string from the higher 3 pairs of strings and have left it only to the lower pitch pair of strings to make the sound more sweet.

An ordinary tenor size with 4-double strings ukulele can also have very well a Bb major or G minor tuning as follows

There is also the Bb major or G minor tuning as follows

(F2:F4 Bb2:Bb4, D3:D4, G3:G4)

or 

(F3:F4 Bb3:Bb4, D3:D4, G3:G4)

4-DOUBLE STRINGS TENOR GUITAR (GUITAR-LELE)

(The range is about the vocal range of a female contralto singer)

A tenor guitar  has scale length usually 58 cm which is about the F#4 at the E4 string of the standard guitar. 

With the nylon strings the G minor or Bb major tuning  in other words 

(F2:F4, Bb2:Bb3, D3:D4, G3:G4) 

is supported as follows:

So for the G4 of the 1st pair, I use an E4-guitar nylon string. For the G3 of the 1st string I use an nylon G3-string of the guitar. For the D4 of the 2nd pair, I use a nylon B3-string of the guitar. For the D3 of the 2nd pair, I use a nylon D3-string of the guitar. For the Bb3 of the 3rd pair, I use again a nylon G3-string of the guitar. For the Bb2 of the 3rd pair, I use a nylon A2 string of the guitar. For the F4 of the 4th pair, I use a nylon A4-string of the tenor ukulele . And for the F2 of the 4th pair I use a nylon E2-string of the guitar. 

This (F2:F4, Bb2:Bb3, D3:D4, G3:G4)  tuning is supported also with usual guitar metal strings

So for the G4 of the 1st pair, I use an E4-guitar metal string. For the G3 of the 1st string I use a metal G3-string of the guitar. For the D4 of the 2nd pair, I use a  B3-string of the guitar. For the D3 of the 2nd pair, I use a metal  D3-string of the guitar. For the Bb3 of the 3rd pair, I use again a metal G3-string of the guitar. For the Bb2 of the 3rd pair, I use a   A2 string of the guitar. For the F4 of the 4th pair, I use a  E4-string of the guitar . And for the F2 of the 4th pair I use a  E2-string of the guitar.

Of course we may as well have this Bb or G minor tuning with single strings

(F3, Bb3, D4, G4)

Such a Bb tuning can very well apply to the 2/3 children 6-string guitar of about 58 cm too, with the full 6-string version

(G2, C3, F3, Bb3, D4, G4)



As alternative the Bb tuning can be in the normal position open Gm7 tuning

G3-Bb3-D4-F4

Which can very well apply for a Bb 4-single strings Bouzouki

 The above 4-course Bb guitar can be extended to 6-courses or 6-strings Bb guitar as in post 273.

THE UKULELE-BOUZOUKI-PANDURI TUNING on 6-strings

This tuning sometimes is used in the instrument Dobro too.

We apply the 3M-3m-4-3M-4  tuning in intervals

This is best realizable in shorter an 2/3 or 1/2 children guitar :

The F3-Bb3-D3-G4  part is a 4-string Greek Bouzouki or a ukulele in Bb major

The Bb2-X-F3-Bb3 part is a 3-string Greek Bouzouki in Bb major

The Eb2-Bb2-F3 is a low tambouras or saz with privileged scale the Eb major.

Some further advantages of this Bb 6-string guitar tuning are 

1) At the 4 higher strings all the chord-shapes and chords of the standard guitar can be played without any note missing. Thus we reduce all well-known guitar chord playing in the higher 4-strings

2) Nevertheless, in the lower 3 strings, it plays also the 2-frets triad-chords of 3 strings of a panduri

3) In the 5th 3rd 2nd strings it plays all the tunes of a Greek 3-strong bouzouki, including the isocratic with two strings playing as drone an interval of 5th Thus it combines playing with ancient tunings that require strings tuned at  intervals of 5th (melodies orientation) and more modern tunings (chords or harmonic orientation)

4) It is an open minor 7nth or major 6th tuning.

5) It has two intervals of 8th (2nd-5th, and 3rd-1st strings) and one interval of 5th (6th-4th strings) which allows for nice isocratic improvisations.

6) It has chord triads with all 3 inversions in all 4 rows of consecutive strings 1st-2nd-3rd (Ionian mode) , 2nd-3rd-4th (Aeolian mode) , 3rd-4th-5th ( Ionian mode) , 4th-5th-6th (Ionian mode) 

We should mention though that this improvement is not as advantageous as the fully melodic-harmonic guitar tuning described in post 90. The only reason we describe the current tuning is that it preserves the 2/3 of the learned guitar on the standard tuning while it allow for more chord triads and advantages described above. 

254. THE PANDURI TUNING AND OTHER ALTERNATIVE TUNINGS OF SAZ

5) And I have converted a saz (https://en.wikipedia.org/wiki/Ba%C4%9Flama 79 cm scale length)  to an Harmonic Threechord (with tuning   G3:G4, B3:B3, E3:E4:E4  or F3:F4, A3:A3, D3:D4:D4.

Notice that the highest string E4 is octaved one octave lower by E3, while the lowest string G3  is octaved by one octave higher.  This instrument  has a very fine and sweet sound and can be played with the most swell and easiest way compared to the other conversions, because of 

1) the narrow width of the neck 

2)  very low height of the (movable) frets 

3) very low tension of the strings 

4) very small diameter of the strings of such instruments. 

I consider this instrument a divine sound and easiness  when playing it!

Of course I have set the movable frets only to the 12-tone equal temperament  Bach scale and have get rid of the other additional movable frets. 

We notice that the rule ofthe octave strings in the pairs is that of teh half-baritone. In other words in the high triple string E3:E4:E4, the octave string E3 is lower, while in the lowests pair G3:G4, the octave string is the G4 which is higher. The main notes are the (G3, B3, E4).

Again an important advantage of this tuning of the 3-groups of strings Saz is that all the three inversions of a major or minor chord exist as triads (3-notes chords) as the shapes of the guitar chords D, A, E, inherited on the 3-pairs of strings only. (see DAE system post 3). So for any solo that one plays, he can quickly try a major or minor chord in one of the above 3-inversions or shapes that contains the particular note of the melody (even as root of the chord shape). The simplicity of an instrument when it is adequate harmonically and melodically ,sometimes can contribute as  major factor for easy and fruitful improvisation.

Finally other optimal tuning are the harmonic tuning that is alternating intervals of major and minor thirds, that make a 3-notes chord (see also Harmonic tuning of the guitar in post 90 ) Here it would be 

G3G4-B3B3-D4D4D4 or G3G4-Bb3Bb3-D4D4D4 or A3A4-C4C4-E4E4E4 or 

A3A4-C#4C#4-E4E4E4 etc  Such tuning has the highest density per a number of frets of major or minor triad chords.


Some Russian bass or alto Balalaikas have such tuning inherited from Russian (gypsy) guitar open tuning

PANDURI TUNING FOR SAZI (IN THE RANGE OF TAMBOURAS AND BOULGARI)


These tunings have less range than the tunings by 5ths , but also other advantages that we describe here

These PANDURI tunings are not only mainly for playing arpeggios and simplicial submelody, when another ,usually wind , instrument is playing the solo but advantageous, as we explain below when the Saz is playing solo too.

For solos, the tunings below have the characteristic that we can easily-readily play the 2nd or 3rd voice on the other 2 strings. In addition as the strings are  close and differ only at an interval of 3rd, and as most melodies have a span of 1-2 octaves, then all of the  melody  can be played in  one only of the 3 strings (courses) which is quite intuitive in its linear pitch order, as in harp or panflute (except here chromatically not diatonically).

This tuning is the open G major chord or F major chord.

G2G3-B3B3-D3D4D4   or F2F3-A3A3-C3C4C4  

Because the D3D4D4 course of strings has two D4 it sounds like D4 finally rather than like D3! So the final sound is like G2-B3-D4.

It has 3 inversions triads for each major o minor chord but the normal form is the simplest. 


Such tuning (see also post 90 about the harmonic tuning of the guitar ) has the next advantages:

1) the highest density per a number of frets of major or minor triad chords in normal position .
2) They are easier for chords in normal position rather than for inversions(Compared to the standard tuning o 3-double strings bouzouki which is easier for chords in  inversions rather than in normal position).

3) The solos are in closer frets to the fingers and we do not need to shift the hand a lot to find the appropriate note.

G3G4-B3B3-D4D4D4 or G3G4-Bb3Bb3-D4D4D4 or A3A4-C4C4-E4E4E4 or A3A4-C#4C#4-E4E4E4 etc  Such tuning has the highest density per a number of frets of major or minor triad chords.

We give the  calculations of the right frets positions fora  saz  which has variable frets,of scale length 79 cm. We calculate the distance of each fret from the upper or lower end of the string (scale) , so that approximation errors are not added when realizing these positions. In these calculations the angle of the string relative to the surface ofthe fretboard is not included. If included the calculations might have very very small modifications. (For the formula for the  calculations see post 1) 

FRETBOARD DIMENSIONS	79	SCALE LENGTH IN CM
Number of fret	Lemgth from lower string end till fret	Multipler	Length from upper string end till fret
1	74.5661,	0.056125687	4.4339
2	70.3810	0.109101282	8.6190
3	66.4308	0.159103585	12.5692
4	62.7023	0.206299474	16.2977
5	59.1831	0.250846462	19.8169
6	55.8614	0.292893219	23.1386
7	52.7262	0.332580073	26.2738
8	49.7669	0.370039475	29.2331
9	46.9737	0.405396442	32.0263
10	44.3373	0.438768976	34.6627
11	41.8488	0.470268453	37.1512
12	39.5000	0.5	39.5000
13	37.2830	0.528062844	41.7170
14	35.1905	0.554550641	43.8095
15	33.2154	0.579551792	45.7846
16	31.3512	0.603149737	47.6488
17	29.5916	0.625423231	49.4084
18	27.9307	0.646446609	51.0693
19	26.3631	0.666290036	52.6369
20	24.8834	0.685019738	54.1166
21	23.4868	0.702698221	55.5132
22	22.1686	0.719384488	56.8314
23	20.9244	0.735134226	58.0756
24	19.7500	0.75	59.2500

253. SOME ALTERNATIVE TUNINGS TO PUERTO-RICAN CUATRO

The next pictures are from a Puerto-Rican Cuatro as 4-double strings instrument, with the previous tuning that makes it a guitar-lele.

We may utilize a E4 guitar string for the A4 of the A3:A4. We may utilize a D3  guitar string for the A3 of the A3:A4. We may utilize a  A2 or better for lower tension a D3 guitar string for the E3 of the E3:E4. We may utilize a B3 guitar string for the E4 of the E3:E4. We may utilize a G3  guitar string for the C4 of the C3:C4. We may utilize a  A2 guitar string for the C3 of the C3:C4. We may utilize a D3  guitar string for the G3 of the G3:G2. We may utilize a E2  guitar string for the G2 of the G3:G2. With the above choice of strings, and given that the scale length of this shorter guitar (baritone ukulele and the quatro with 48-52 cm scale length) is about at the A4 note of the e4 string of  a normal guitar, the strings are either exactly at the intended tension given the scale length or one note above or below the normal tension! 

Some advantages of this kind of tuning where in all the pairs  the two strings are one octave apart are the next  

1) it covers larger range of octaves than the tuning of an ordinary (tenor) ukulele! 

2) It also gives the opportunity with sufficient skill in the right hand fingernails, to play only the higher strings of each pair or only the lower strings of each pair moving therefore in two different octaves the same melody or harp-ism. 

3) Furthermore when singing, the instrument supports the voice in two octaves rather than one octave which makes singing more well supported by the instrument thus easier and more comfortable and accurate! 

While a tenor ukulele is about the range of a human mezzo soprano, and a charango-ukulele, about the range of a soprano human voice, the above tuning for a baritone ukulele or a Quatro it is about the range  Contralto human voice.