291. HEXATONIC SCALES FOR HARMONICA ALTERNATIVE TUNINGS AND 2-CHORDS IMPROVISATIONS

HEXATONIC SCALES FOR THE HARMONICA

(see also post 215 and 364) 

THESE 2-CHORD HEXATONIC HARMONICAS DESCRIBED HERE ARE NOT DESIGHNED SO MUCH TO PLAY ALL POSSIBLE MELODIES ON A SINGLE HARMONICA BY BENDING AND OVERBLOW BUT TO MAKE EASY IMPROVISATION ON HEXATONIC SUBSCALES OF  THE SCALES DIATONIC, HARMONIC MINOR, 7-NOTES BLUES (INVERSE HARMONIC MINOR) , DOUBLE HARMONIC MINOR, MELODIC MINOR ETC SUCH 2-CHORDS IMPROVISATIONS ARE COMMON IN CUBA AND LATIN JAZZ FOLK MUSIC, GREEK ISLANDS MUSIC, IRISH MUSIC ETC

MOST OF THE HEXATONIC TUNINGS IN THIS DISCUSSION HAVE A SINGLE CHORD AT THE BLOW ROW AND ANOTHER SINGLE CHORD AT THE DRAW ROW.
ACTUALLY ANY TWO SUCCESIVE CHORDS IN THE DIATONIC SCALE (E.G. 7DIM-1M, OR 4M-5M, 3M-4M, 5M-6m , 6m-7dim) CAN BE USED FOR AN APPROPRIATE  TWO-CHORD HEXATONIC TUNING HARMONICA.
THUS WE WILL HAVE THE NEXT 6 TYPES OF CHORD PAIRS IN THE HARMONICA WHICH ARE CHORDS IN DIATONIC CHROMATIC RELATION

M=MAJOR m=MIOR d=DIMINSIHED
n=number of semitones that the roots are apart

IONIAN/MYXOLYDIAN: M2m

DORIAN: m2m

FRYGIAN: m1M

LYDIAN: M2M

AEOLIAN: m2d

LOCRIAN:d1M

But we also present many other non-diatonic chromatic pairs that involve also augmented chords and a re met in the harmonic minor (which apears also in the overtone sequence)  double harmonic minor, melodic minor (which apears also in the overtone sequence)  etc

E.G. 

m2M (Erik Satie hexatonic of the harmonic minor hptatonic)

M2dim (hexatonic from melodic minor)

m1m

M3m

M1M (Hexatonic from the harmonic minor)

aug2M

dim1m

m6m

aug3aug

dim1aug

etc

I  have ordered in Seydel company and play all of the next harmonicas of diatonic gendre  chromatic gendre and enharmonic gendre hexatonic sub scales of  the diatonic scale of the harmonic minor scale and invererse harmonic minor scale (Blues 7-tonic scale ) and when I will find time I  will upload sound files with improvisations of them. Of course I think it is much cheaper instead of ordering so many custom 2-chords hexatonic harmonicas as below, to just tune the digital harmonica Lekholm DM48 which I also have and it is fun to try these tunings and easy improvisations on them 

ALL OF THE HEXATONIC TUNING  IN THIS DISCUSSION HAVE A SINGLE CHORD AT THE BLOW ROW AND ANOTHER SINGLE CHORD AT THE DRAW ROW.

ACTUALLY ANY TWO SUCCESIVE CHORDS IN THE DIATONIC SCALE (E.G. 7DIM-1M, OR 4M-5M, 3M-4M, 5M-6m , 6m-7dim) CAN BE USED FOR AN APPROPRIATE  TWO-CHORD HEXATONIC TUNING HARMONICA.

THUS WE WILL HAVE THE NEXT 6 TYPES OF CHORD PAIRS IN THE HARMONICA WHICH ARE CHORDS IN DIATONIC CHROMATIC RELATION (the roots are separated by an interval of 2nd) 

e.g. if the 7-notes diatonicscale is the C-D-E-F-G-A-B-C in semitones 2-2-1-2-2-2-1  then

M=MAJOR m=MIOR d=DIMINSIHED

1,2,3 etc =number of semitones that the roots are apart

1) IONIAN/MYXOLYDIAN: M2m       C-D-E-F-G-A-C in semitones 2-2-1-2-2-3 and over the Blow-draw 2 chords Cmajor Dminor

                                             or  G-A-B-C-D-E-G and over the Blow-Draw 2 chords Gmajor Aminor (also called Celtic minor hexatonic)

2) DORIAN: m2m                D-E-F-G-A-B-D in semitones 2-1-2-2-2-3  and over the Blow-Draw 2 chords Dminor-Eminor (also called Celtic major hexatonic)

3) FRYGIAN: m1M             E-F-G-A-B-C-E in semitones 1-2-2-2-1-4  and over the Blow-Draw 2 chords Fmajor-Eminor (also a hexatonic version of the 

                                              akebono 5-notes scale)

4) LYDIAN: M2M                     F-G-A-B-C-D-F  in semitones 2-2-2-1-2-3  and over the Blow-Draw 2 chords Fmajor-Gmajor (also called an alternative 

                                             version of Celtic major scale)

5) AEOLIAN: m2d                  A-B-C-D-E-F-A  in semitones 2-1-2-2-1-4  and over the Blow-Draw 2 chords Aminor-Bdim 

6) LOCRIAN:d1M                     B-C-D-E-F-G-B  in semitones 1-2-2-1-2-4  and over the Blow-Draw 2 chords Bdim-Cmajor (also called enharmonic major) 

See also posts 274 and  225.

THE HEXATONIC SCALES DESCRIBED BELOW FOR THE HARMONICA THAT CREATE TWO ONLY CHORDS ARE AS WELL APPLICABLE FOR T HE CELTIC HARP WITH LEVERS. WE ONLY HAVETO REPEAT ONE NOTE ON THE NEXT STRING. AGAIN TWO ONLY CHORDS ARE CREATED (BU EVEN AND ODD STRINGS EXCEPTTHE REPETIONS) AND IMPROVISATIONS CAN BE CARRIED IN THE CELTIC HARP AS WELL.

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 ) 

DIATONIC GENDRE: CIRCULAR TUNING FOR THE 6-NOTES CELTIC MINOR SCALE

We may also notice that the 6-notes scales are favored for a harmonica, as the periodicity in the circular tuning is per octave and not per 2 octaves as in 7-notes scales. A good example is the Celtic minor 6-notes scale ( in semitones 2-2-3-2-2-1). This scale is used also for the hundpans   and hang drums.  The example is in the next table of tunning for the case of D root. The blow row is only the chord I and the draw row only the chord ii. The Celtic minor is the maximal harmonic 6-notes scale, in the sense that it is a 6-notes scale with the maximum number of standard chords. In the same way that a 7-notes diatonic scale is a maximal harmonic 7-notes scale in the sense that it is a 7-notes scale with a maximum number of standard chords (see the article https://simplerguitarlearning.blogspot.com/2018/08/117-small-7-notes-diatonic-scale-and.html  )

 An example is  in the next  table of tunning for the case of D root.
MOST OF THE HEXATONIC TUNINGS IN THIS DISCUSSION HAVE A SINGLE CHORD AT THE BLOW ROW AND ANOTHER SINGLE CHORD AT THE DRAW ROW.
ACTUALLY ANY TWO SUCCESIVE CHORDS IN THE DIATONIC SCALE (E.G. 7DIM-1M, OR 4M-5M, 3M-4M, 5M-6m , 6m-7dim) CAN BE USED FOR AN APPROPRIATE  TWO-CHORD HEXATONIC TUNING HARMONICA.

Stil another mode of it is the next where at blowing is the major chord and at draw is the minor. In the example table below we are in t he G major scale.

On the other hand the sequence 2-3-2-2-2-1 (e.g.  C-D-F-G-A-B) IS NOT A CYCLIC PERMUTATION of the 2-2-3-2-2-1 or 1-2-2-3-2-2 or 3-2-2-1-2-2 and it should be  considered a different scale than the Celtic 6-notes (minor) not a different mode of it. It could be  called maybe Celtic 6-notes major, because both the blow-row chord and the draw-row chord are major chords!  But it can also be considered a Hexatonic version of the melodic minor  2-1-2-2-2-2-1.  It may be also called 1st harmonic hexatonic as it appears as the notes of the first 11 overtone harmonics. The indication 1st is becaouse the 7nth harmonic e.g. at root C is between Bb and B , so the first choice gives this  hexatonic while the 2nd choice the 2nd harmonic hexatonic which is the 2-2-1-2-4-1 as we shall see later in the enharmonic gendre.

MOST OF THE HEXATONIC TUNINGS IN THIS DISCUSSION HAVE A SINGLE CHORD AT THE BLOW ROW AND ANOTHER SINGLE CHORD AT THE DRAW ROW. Below is the table of such a tuning for a harmonica starting from D, and not C but with the same interval structure  2-3-2-2-2-1. And there is alo the inverse of this scale with interval structure 2-1-2-2-2-3 E.g. again derivable from  the 7-notes C major mode of the diatonic scale , but now we omit C. Thus D-E-F-G-A-B-D . I believe the previous discussion  completely clarifies the distiction between a scale and its modes.

The Byzantine culture absorbed the musical culture of Ancient Greece, that used mainly not 7-notes scales but 4 and 5 notes scales of total length an interval of 4th or 5th (called tetrachorda). The names of the modes Ionian, Dorian, Phrygian , Lydian etc were originally different 7-notes scales in the Byzantine empire relevant to the places in Greece that were mostly used, that when the European culture after Bach absorbed them in the 12-notes equal tempered system, thet altered them, and they ended to become  different modes of the one diatonic scale and not different scales.

The inverse of the Celtic major, which is the 2-1-2-2-2-3 has one minor chord at the Blow row and one minor at the draw row. Here the tuning table at the G major scale as 2m-3m

Hexatonic scales as the above at various modes of them are used not only at modern handpans but also at chinese Bahu flutes.


CHROMATIC GENDRE: BLUES - COUNTRY 6-NOTES MAJOR SCALE AND THE 7-NOTES BYZANTINE PARACHROMATIC SCALE.

According to the wikipedia (https://en.wikipedia.org/wiki/Blues_scale), a 6-notes version of the major country-blues  scale is e.g. the 
C, D, D♯/E♭, E, G, A, with interval structure 2-1-1-3-2-3. Or if we prefer a root at D, then  D-E-F-F#-A-B-D. While if we prefer the root A it will be A-B-C-Db-E-Gb-A or 6-7-1-2b-3-5b-6 We notice that we utilize the 2b and 5b blue notes of the diatonic scale only in place of the 2 and 5 and we omit the 4 note. Below is the table for a harmonica with such a tuning.

On the other hand historically the Byzantine emptire was utilizing many 7-notes scales, not possible to include in the Bach equal tempered 12-notes chromatic scale. But 3 chromatic sacles of them are possible more or less to include, Two of the chromatic such scales are the harmonic minor (e.g. from the A natural minor we derive the harmonic minor by giving a sharp at G, thus  A B C D E F G# A , with interval structure 2-1-2-2-1-3-1) and the double harmonic minor (an additional sharp to d  thus  A B C D# E F G# A ,  with interval structure 2-1-3-1-1-3-1). They  where used mainly in religious hymns in the Churchs. But the 3rd such chromatic scale was used mainly in the Emperors palace and other cosmic events and was called parachromatic (see e.g.  http://www.huygens-fokker.org/docs/modename.html    http://www.huygens-fokker.org/scala/ ). The Byzantine parachromatic scale is called also inverse Persian or  Purvi Theta scale. The part 2-1-1-3 is also known as samba pentachord in arabian culture, while the part 1-1-3 is known since ancient Greece time as the tonal tetrachord of the chromatic family. The interval structure of  the parachromatic Byzantine scale is 2-1-1-3-1-1-3 . When assumed to start from the 6th note (Aelolian mode), 6-7-1-2-3-4-5-6 , to derive the Byzantine parachromatic we only need to convert 2 to 2b and 5 to 5b which means 6-7-1-2b-3-4-5b-6 .Thus starting from D , it would be D, E, F, Gb ,A, Bb, B , D While if we prefer the root A it will be A-B-C-Db-E-F-Gb-A  or 6-7-1-2b-3-4-5b-6. We notice that we utilize the 2b and 5b blue notes of the diatonic scale only in place of the 2 and 5 .  We may observe that it is a 7-notes version of the Blues scale, and a tuning table for a harmonicas at the D4- major 6-notes Blues-country scale and a D4- parachromatic 7-notes scales are given below. (see also article https://simplerguitarlearning.blogspot.com/2019/06/235-parachromatic-byzantine-overtone.html ) The blues major scale is derived from the Byzantine parachromatic 6-7-1-2b-3-4-5b-6. by omitting the  4 note , thus 6-7-1-2b-3-5b-6 with interval structure 2-1-1-3-2.
On the other hand if we assume the Byzantine parachromatic to be  a major scale and we start from the ionian mode of a diatonic scale  1-2-3-4-5-6-7-1, or A, B, C♯, D, E, F♯, and G♯. then the Byzantine parachromatic would be  1-2-3b-4b-5-6b-7bb-1'  or A-B-C-Db-E-F-Gb-A. And to derive the major blues scale we simply omitt  the 6b, or A-B-C-Db-E-Gb-A  (in semitones 2-1-1-3-2-3).

The major blues scale e.g. D major Blues scale might be supposed to be used for improvisations of 12-bars blues on  the D major scale, as it can also be also derived from the major D pentatonic by adding   a  blue note 3b which will make it 6-notes scale. E.g. the blues major D scale D, E, F, Gb ,A, B , D, (in semitones 2-1-1-3-2-3) whould play over the chords Dmajor D-F#-A,  (D-Gb-A),  A major A-C#-E, or A major with 6th A-C#-E-Gb and G major G-B-D. Obviously some notes  would creare a dissonance, but it may be considered part of the chromaticity of  the Blues major scale improvisation. Similarly the D major blues could be used to improvise over the C major and G major 12-bars blues.

CHROMATIC GENDRE: MORE  6-NOTES SCALES THAT ARE  BEAUTIFUL FOR HARMONICAS. COMBINING PARTS OF THE PENTATONIC  WITH CHROMATIC PARTS.

MOST OF THE HEXATONIC TUNINGS IN THIS DISCUSSION HAVE A SINGLE CHORD AT THE BLOW ROW AND ANOTHER SINGLE CHORD AT THE DRAW ROW.
ACTUALLY ANY TWO SUCCESIVE CHORDS IN THE DIATONIC SCALE (E.G. 7DIM-1M, OR 4M-5M, 3M-4M, 5M-6m , 6m-7dim) CAN BE USED FOR AN APPROPRIATE  TWO-CHORD HEXATONIC TUNING HARMONICA.

We noticed in the previous post that the Blues-country scale with interval structure 2-1-1-3-2-3, (and any cyclic permutation of it, is still the same scale although a different mode of it) sounds partially as the pentatonic scale 2-2-3-2-3 and partially with chromatic part 1-1-3 which was identified as the ancient Greek tonal tetrachord of the chromatic family. By writting the Blues scale in a different 5th mode of it (cyclic permutation) makes it more clear: 2-3-2-1-1-3 . The 2-3-2 part is inherited from the pentatonic scale 2-2-3-2-3 and the 1-1-3  is the ancient Greel tonal tetrachord of the chromatic family (that exist also in the Byzantine emperor parachromatic 7-notes scale). Such scales may be obviously be used in Gypsy jazz, but in ordinary western jazz too.

Other parts of the pentatonic sacle are also the 2-2-3, 

1) Thus we may discover the next hexatonic scale that should sound similarly 2-2-3-1-1-3 and it is not a different mode of the Blues-country scale. In the tables below we show this tuning , when starting from the root D .  Thus D-E-F#-A-Bb-B-D. It is still a 6-notes version of the Byzantine parachromatic scale of the previous post but different from the Blues-country scale, still sounding in a similar way. 

2) There are the invesres of course of the previous hexatonic scales a) the inverse ofthe Blues-country in the mode 2-3-2-1-1-3, which is the 2-3-2-3-1-1 (after inverting and taking a cyclic permutation of it). b) The inverse of the  2-2-3-1-1-3, which is the 3-2-2-1-1-3 ((after inverting and taking a cyclic permutation of it). We write them always so as to separate the pentatonic part, and the chromatic part.

3) If we combine now the pentatonic part 2-3-2 (of the Blues scale) with the chromatic part 1-3-1 (which exists in the harmonic minor) we get a hexatonic scale 2-3-2-1-3-1, that sounds partially as pentatonic and partially as chromatic (harmonic minor). It is a 6-notes version of the harmonic minor scale,perfect for harmonicas that favor in the cyclic tuningthe heaxtonic scales. Some times it is also called the Erik Satie hexatonic scale. (See e.g. the video https://www.youtube.com/watch?v=okU96j6ThIM&t=8s )We give below the tuning table when starting from the root D. And of course there is the inverse of it again which is not a different mode of it. D-E-G-A-Bb-C#-D.

4) If we combine now the pentatonic scale part 3-2-2  with the chromatic part 1-3-1 (which exists in the harmonic minor) we get a hexatonic scale 
3-2-2-1-3-1, or at a different mode as  2-1-3-1-3-2  that sounds partially as pentatonic and partially as chromatic (harmonic minor). It is a 6-notes version of the Neapolitan scale 2-1-3-1-1-2-2 (e.g. from D it would be D-E-F-G#-A-Bb-C-D), perfect for harmonicas that favor in the cyclic tuning  the hexatonic scales. We give below the tuning table when starting from the roor D thus D-E-F-G#-A-C-D , with interval structure at the mode 2-1-3-1-3-2 .  It is over the chords Dm-Caug. This 6-tonic scale is also a hexatonic scale of  the 7-notes extension of the Blues scale 3-2-1-1-3-2  which in semitones it is  the 2-1-2-1-1-3-2 e.g. C-D-Eb-F-Gb-G-Bb-C. And of course there is the inverse of this neapolitan again which is not a different mode of it and in semitones it is the 2-3-1-3-1-2 and it is also a hexatonic version of  the 7-notes  scale 2-2-1-1-3-1-2 (e.g. C-D-E-F-Gb-A-Bb-C). This hexatonic scale e.g.  C-D-F-Gb-A-Bb-C is over the chords Fmajor and Gb augmented. On the other hand what is considered a 7-notes blues scale (see e.g. https://en.wikipedia.org/wiki/Blues_scale ) the 2-1-2-1-3-1-2 (which is actually the inverse harmonic minor scale) e.g. C-D-Eb-F-Gb-A-Bb-C , has a 6-notes version 1-2-1-3-1-4 or in adifferent mode the 2-1-3-1-4-1 e.g. Eb-F-Gb-A-Bb-D-Eb which is over the chords Ebm and Dm. Similarly an alternative 6-notes version of the latter 7-notes blues scale (and  also inverse harmonic minor) is the  C-D-Eb-F-Gb-A-C or in semitones  2-1-2-1-3-3 and over the chords Cdim and Dminor.

ALL 7 HEXATONIC SCALES FROM THE 7 MODES OF THE 7-NOTES BLUES SCALE (OR INVERSE HARMONIC MINOR SCALE)

Some og these hexatonic scales of the inverse harmonic minor are also hexatonic scales of the diatonic scale or the melodic minor or the double harmonic minor!

7-NOTES BLUES SCALE C-D-Eb-F-Gb-A-Bb  (or in semitones 2-1-2-1-3-1-2) also inverse harmonic minor scale, with chords 

Cdim, Dminor, Ebminor, FMajor, Gb augmented , A diminished , Bb major

4.1) 1st mode C-D-Eb-F-Gb-A-C    (or in semitones 2-1-2-1-3-3)  based on the 2 chords Cdim-Dm

4.2) 2nd mode  D-Eb-F-Gb-A-Bb-D   (or in semitones 1-2-1-3-1-4)  based on the 2 chords 

Dmin-Ebmin (hexatonic caval double harmonic minor too)

4.3) 3rd mode Eb-F-Gb-A-Bb-C    (or in semitones 2-1-3-1-2-3)  based on the 2 chords Ebmin-Fmajor (Erik Satie hexatonic scale)

4.4) 4th mode F-Gb-A-Bb -C-D-F    (or in semitones 1-3-1-2-2-3)  based on the 2 chords 

Fmajor-Gbaug ( inverse hexatonic neapolitan )

4.5) 5th mode  Gb-A-Bb-C-D-Eb-Gb   (or in semitones 3-1-2-2-1-3)  based on the 2 chords 

Gbaug-Adim

4.6) 6th mode A-Bb-C-D-Eb-F-A    (or in semitones 1-2-2-1-2-4)  based on the 2 chords Adim-Bbmajor (hexatonic enharmonic major, or hexatonic Locrian mode) 

4.7) 7th mode  Bb-C-D-Eb-F-Gb-Bb   (or in semitones 2-2-1-2-1-4)  based on the 2 chords 

Bbmajor-Cdim (Hexatonic melodic minor too)

ALL 7 HEXATONIC SCALES FROM THE 7 MODES OF THE 7-NOTES HARMONIC MINOR SCALE .

Some og these hexatonic scales of the inverse harmonic minor are also hexatonic scales of the diatonic scale or the melodic minor or the double harmonic minor!

7-NOTES HARMONIC MINOR  SCALE A-B-C-D-E-F-G#-A  (or in semitones 2-1-2-2-1-3-1) with chords                               Aminor-Bdim-Caug-Dminor-EMajor-FMajor-G#dim-Aminor

4.1) 1st mode A-B-C-D-E-F-A   in semitones 2-1-2-2-1-4  based on the 2 chords 

Amin-Bdim  (Aelian diatonic too)

4.2) 2nd mode B-C-D-E-F-G#-B  in semitones 1-2-2-1-3-3  based on the 2 chords Bdim-Caug 

4.3) 3rd mode C-D-E-F-G#-A -C in semitones 2-2-1-3-1-3  based on the 2 chords Caug-Dminor (Neapolitan Hexatonic too)

4.4) 4th mode  D-E-F-G#-A-B-D  in semitones 2-1-3-1-2-3   based on the 2 chords Dminor-Emajor (Erik Satie hexatonic)

4.5) 5th mode  E-F-G#-A-B-C-E  in semitones 1-3-1-2-1-4  based on the 2 chords 

Emajor-Fmajor  

4.6) 6th mode F-G#-A-B-C-D-E-F   in semitones 3-1-2-1-2-3  based on the 2 chords 

Fmajor-G#dim  

4.7) 7th mode   in semitones 1-2-1-2-2-4  based on the 2 chords 

G#dim-Amin  (hexatonic enharmonic minor)

FROM THE 7-NOTES MELODIC MINOR THE HEXATONIC SUBSCALES NOT COVERED BY THE PREVIOUS ARE THE NEXT

E.g. let the 7-notes melodic minor A-B-C-D-E-F#-G#-A in semitones 2-1-2-2-2-2-1 and chords

m-m-aug-M-M-m-d the next are additional hexatonics

C-D-E-F#-G#-A-B-D in semitones 2-2-2-2-1-3 and 2 chords Caug-Dmajor

B-C-D-E-F#-G#-B  in semitones 1-2-2-2-2-3 and 2 chords Bminor-Caug

F-G#-A-B-C-D-F#  in semitones 2-1-2-1-2-4 and 2 chords F#minor-G#dim

5) If we start with the double harmonic minor, e.g. from A, it is A-B-C-D#-E-F-G#-A  which has interval structure  2-1-3-1-1-3-1 , we may derive an appropriate hexatonic which contains a part ofthe pentatonic scale ,which here is the 3-2-3. The resulting scale  is the 3-2-3-1-2-1, or in a different mode the 2-1-3-2-3-1. Starting from the root D it is D-E-F-G#-Bb-C#-D.  At Blow it is Bb major and at Draw it is C#minor 
The mode 1-2-1-3-2-3 e.g. F# G ABb C# D# would give at the Blow row a single minor chord F# and at the Drow row  a major  chord D# . 

Again we may discover different hexatonic scales from the double harmonic minor like the 
2-1-3-1-4-1 E.g. E-Gb-G-Bb-B-Eb-E , which as harmonica has at Blow a minor chord (here Eminor) and the draw again a minor chord one semitone lower (here Ebminor). Again because of the two minor chords one semitone apart the sound is with tesmion and neither the blow chord neither the draw chord resolves it better.
For Gm -F#m the scale would be G-A-Bb-C#-D-F#-G and for Dm-C#m it would be D-E-F-G#-A-C#-D. 

There are also similar hexatonic scales that are  symmetric like  3-2-1-3-2-1 or 3-1-2-3-1-2 or 1-2-3-1-2-3. The latter when placed to an harmonica tuning it gives at the blow row a single chord and at the draw row again a single chord E.g. A-Bb-C-D#-E-F#-A. 

ENHARMONIC GENDRE: MORE HEXATONIC SCALES FOR HARMONICAS : UTILISING AKEBONO 5-NOTES SCALE

MOST OF THE HEXATONIC TUNINGS IN THIS DISCUSSION HAVE A SINGLE CHORD AT THE BLOW ROW AND ANOTHER SINGLE CHORD AT THE DRAW ROW.
ACTUALLY ANY TWO SUCCESIVE CHORDS IN THE DIATONIC SCALE (E.G. 7DIM-1M, OR 4M-5M, 3M-4M, 5M-6m , 6m-7dim) CAN BE USED FOR AN APPROPRIATE  TWO-CHORD HEXATONIC TUNING HARMONICA.

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 (all possible major 3rd intervals were usually more than all possible minor 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 ) 

One natural way to derive a hexatonic scale is to require that part ofthe hexatonic scale  is either in the pentatonic or in the 7-notes diatonic. Thus here the two versions 2-2-2-1-4-1 and 2-2-2-4-1-1 may be obtained. In notes relevant to the D major scale  at appropriate modes are 1) 4-1-2-2-2-1 as D-F#-G-A-B-C#-D and 2) 1-2-2-2-4-1 as A-B-C#-F-F#-G-A
Below are tables of tuning for such harmonicas. The first of them has been called in post 204 the Cretan hexatonic 

Still one more hexatonic with rather familiar sound is the 2-2-1-2-4-1, which can  be obtained my omiting a note from the 7-notes diatonic scale E.g. C D E F G  B C. For the D major scale it would be D E F# G A C# D. 

It may be also called 2nd harmonic hexatonic as it appears as the notes of the first 11 overtone harmonics. The indication 2nd is becaouse the 7nth harmonic e.g. at root C is between Bb and B , so the 2nd choice gives this  hexatonic while the 1st choice the 1st harmonic hexatonic which is the 2-2-1-2-3-2, or Celtic maor that we discussed earlier.

 Its table is shown below when starting from C3. It is not harmonic not to play all possible songs in it (such would be  a cyclic tuning one) but to play melodies that are easily accompanied by two only chords the I=1Major, and viidim=7diminished (which sounds like the V7) as all the blow row is the 1major and all the draw ros is the 7diminshed.

THE CASE OF 2-2-1-2-4-1 OR 2ND HARMONIC HEXATONIC IS OF EXTREME IMPORTANCE AS IT PRODUCES HAPPY MUSIC 

E.G. FOR C MAJOR IT IS C MAJOR-Bdiminished AND IN NOTES C-D-E-F-G-B-C AS IN THE TABLE BELOW.

And there is also the very beatiful  2-2-1-4-2-1 that when tuned at an harmonic gives the Blow-row a minor chord and the draw-row a dimished chord.
Similarly the 2-2-1-2-1-4 or D E F#  G A Bb D which can be considered a hexatonic version of the G melodic minor.  

Other beatiful such scales that combine the Chromatic with the enharmonic gendre are the 
2-1-4-1-3-1. The Blow-row is a major chord and the draw-row another major chord one semitone apart. We give the tuning table below when starting from G3 as Hexatonic _enharmonic_harmonic_minor. The two major chords are D# and D. Because of the two minor chords one semitone apart the sound is with tesmion and neither the blow chord neither the draw chord resolves it better. We met the inerse of  thsi scale in the prevous discussion ofthe chromatic gendre andthe double harmonic minor.


More examples are symmetric hexatonic scales like the 1-1-4-1-1-4, or non-cyclic permutations of them like 4-1-4-1-1-1, and 4-4-1-1-1-1.

Another case is the pair of chords Blow=6m draw=5#dim E.g. in the G minor it is 

Blow=G Bb  D and Draw=A C F#, thus the hexatonic of the enharmonic gendre 2-1-2-2-4-1.

G A Bb C D F#   with the tuning table below. It is a hexatonic version of both the harmonic minor and the melodic minor.

It can be

More such scales are the 

 4-3-1-2-1-1
 4-3-1-1-2-1

 3-4-1-1-2-1
3-4-1-2-1-1 

And even more of them in post 225.

290. MODERN HARMONY COUNTERPOINT OF A NUMBER OF SIMULTENEOUS MELODIES

(This post has not been written completely yet)

 Generally speaking we may define in modern sense of harmony counterpoint of a number of  k melodies sounding simulteneously. We consider them acceptabke from the harmonic point of view if and only if the simulteneous intervals of all pairs of melodies from the k-melodies that are of intervals of 3rds and 5ths (or inversions) have total duration more than 50%  at a first basic  ranking and more than 80% at a more demanding  ranking , compared to those by intervals of 2nds. Here obviously the intervals of 3rds or 5ths (and inversions) are considered harmonic while those of 2nds chromatic and not much desirable.

See also the posts 102, 111, 138, 275 , 280 , 287, 102, 256, 257, 118, 128, 197, 183. 289.


In the next video of a New Orleans jazz band (Tuba Skinny) , we may observe some phenomena of  counterpoint of  least 4 parallel improvisational melodies at a ...storming level!



https://www.youtube.com/watch?v=HNcxDlbHMAQ&t=1795s

https://www.youtube.com/watch?v=ffXQ6qH3gwU&t=896s

https://www.youtube.com/watch?v=oRxfhyIO8wE&t=106s

 IMPROVISATION METHOD BASED ON  A SET OF CHORDS AND MELODIC LINES BRIDGING THE HIGHEST NOTES OF EACH OF THEM. APPLICATION WITH STRUMMING WITH CUATRO, CAVAQUINHO, UKULELE , HARMONICA VIOLIN, WINDS ETC

The application idea is that when the chord is realized with a voicing on the highest 4 (or all 4) strings , we create melodic lines on the highest string bridging the highest notes of two succesive chords. Because of a inherent phenomenon of the human sound perception , when we are strumming and chaning the chords with in-between such melodic lines, the musical perception clearaly heres a melody, which is that of the highest notes. If it was not the highest notes the melodic lines would be more often lost in listening in the strumming.
Such chord-bridging melodic lines use a last small part of the previous chord duration and a small initial part of the new chord duration. During the rest ofthe time there is strumming of the chord or a achord arpeggio or variations of small melodic themes inside the chord by intervals of 3rd or 4th/5th. Thus melodic-harmonic variaonions. While when bridging two succesive chords there may be melodic themes variations by intervals of 2nd 3rd or 4th/5th (thus chromatic-melodic-harmonic).
This technique utilizes the simplicity of the information of the set of chord and translates it it to a simple information about the partition of the types of variations of simple melodic themes with the time placement and duration of the chords.
With this technique we may create simplicial counter-melodies parallel to melody.

It applies verty easily when utilizing a chromatic harmonica (see post 274), but also a violin (especially marked at a particular diatonic scale, so that we can identify chord-triad  shapes on it after a convenient tuning) and finally also on a diatonic wind.

289. IMPROVISATION SYSTEM WITH THE SIMPLICIAL SUB-MELODY OF THE COUNTER-MELODY (THUS SIMPLICIAL COUNTER-MELODY) OF A SONG.

(This post has not being written yet completely)

See also post  102, 111, 138, 275 , 280 , 287, 102, 256, 257, 118, 128, 197, 183, 271, 290



Learning to improvise by singing over  any chord progression of a song.

The ability of this is after we have mastered improvisation as in post 288.

 Generally speaking at least 50% of the time the notes of the improvisation should belong to the underlying  chord.

Of course a more strict improvisation would be to require that 50% of the time the notes are notes of the underlying  chord and the rest of the time, notes between them, thus in the vector-chord or closure inside the diatonic scale, of the underlying chord. (e.g. if the underlying chord is  c-e-g, then the closure of the chord or the vector chord is  the c-d-e-f-g. Alternatively we may usea chord and one at chromatic relation to it as external notes, e.g. S major and d minor or C major and B diminsihed)

In this, we start with a song with its chord-grogression.  We use again the rule that that 50% of the time the notes are notes of the underlying chord and the rest of the time, notes between them thus in the vector-chord or closure inside the diatonic scale, of the underlying chord, or more generally notes of the diatonic scale that donot belong to the underlying chord.

The simplest idea is to go up or down in a linear pitch order of the notes of a diatonic scale, spending more time each time in the closure of the underlying chord and at least 50% on the notes of the underlying chord. Initially there is no need for waving and embelishments. Only a linear sequence that goes up or down from chord-closure to chord-closure depending on the underlying chord. We do not even need to know the chords of the chord-progression, as we will find them by shifting up or down and staying more time when the results is more harmonic. If it is a song, with its chord progression this actually would be a kind of simplicial submelody of a counter melody of the melody of the song. We may conceive it as a kind of  simplicial countermelody,  in the sense that it consists during  each underlying chord mainly from a single notes of the underlying chord,  thus certainly fitting harmonically to the melody of the song. Still another way to conceive this parallel improvisational melody is to think of it as simultaneously 1st 2nd and 3rd voice, but changing if  it is 1st 2nd or 3rd voice and mainly with hysteresis (counterpoint) following the underlying chords and their changes rather than the changes of the notes of the main melody.

See also posts 118, 128, 197, 183,  102, which contain more  ideas.
We remind the reader that two melodies sounding simulteneosuly may be assumed as fitting harmonically, if the duration of inervals of 3rd and 5th (and inversions) are more than 50%  at a first basic  ranking and more than 80% at a more demanding  ranking , of the total time compared to the duration of the interavals of 2nds. And the same with  a melody and a chord sounding sumulteneosuly. Or more generally we may defone counterpoint of k-melodies sounding simulteneously, if and only if the simulteneous intervals of all pairs of melodies that are of 3rds and 5ths (or inversions) have total duration more than 50%  at a first basic  ranking and more than 80% at a more demanding  ranking ,  compared to those by intervals of 2nds.

That is why when turning the singing improvisation to a melody of a musical instrument, it is more convenient to do so with, an harp, or a panflute, or an harmonica , then in general a diatonic instrument etc.

Of course as we excersise more, we learn to create small melodic themes instead of only one note, and then translate them or invert them chromatically, melodically or harmonically.

A practice that would implement the above in  easier way is

(See also post 271 about learning many instruments simulteneously utilizing simplicial submelody improvisation system and post 275 about whistling)

1) Download the song as an mp3 file , then open it in Audacity, and utilize its function of finding the chords.  
2) We look at the chord progression and try to identify the main  diatonic scale , from which it may deviate chtomatically. 
3) Then we choose the appropriate instrument that may diatonic at this scale or even chromatic. It may be a wind instrument like harmonica, flute, panflute, clariphone sax etc or it may be a bowed instrument like violin , metric-lyra celo-lyra (see post 264) or other stings instruments like cuatro, guitar, bouzouki, mandolin, mandola, etc. 
4) At first we whistle the simplicial counter-melody while the song is  playing paying attention mainly not the the melody but the underlying chord progression.
5)We may also record the whistling in the computer, while we listen in one only earphone and in one ear, the parallel song from the mobile or another computer. This may create an entereily new song and new melody and even different chord progression inspired and stimulated by the initial parallel song.  That is why a more likable way of the whistling melody should not be considred as a "mistake" but as a more likable melody of a new song, inspired from the initial.
6) Then we repeat the whistling simplicial counter-melody with the chosen instrument
7) If we are multi-intrument player, we rotate the instruments from the easiest to the more demanding (e.g. harmonica, then celtic harp, then chinese panflute, then marked scale cuatro, then fretted-lyra , then straight flute,  then clariphone or sax etc)  playing similar simplicial counter-melodies for this song. If we do that we try to identify ourself  with the simplicial counter-melody and consider that we actually we are player of a simplicial counter-melody for this song rather than aninstrument player that we learn  the particular instrument that we play). See also post 271.

A METHOD TO CREATE THEORETICALLY BUT ALSO PRACTICALLY SIMPLICIAL COUNTER-MELODIES:

 IMPROVISATION METHOD BASED ON  A SET OF CHORDS AND MELODIC LINES BRIDGING THE HIGHEST NOTES OF EACH OF THEM. APPLICATION WITH STRUMMING WITH CUATRO, CAVAQUINHO, UKULELE , HARMONICA VIOLIN, WINDS ETC

The application idea is that when the chord is realized with a voicing on the highest 4 (or all 4) strings , we create melodic lines on the highest string bridging the highest notes of two succesive chords. Because of a inherent phenomenon of the human sound perception , when we are strumming and chaning the chords with in-between such melodic lines, the musical perception clearaly heres a melody, which is that of the highest notes. If it was not the highest notes the melodic lines would be more often lost in listening in the strumming.
Such chord-bridging melodic lines use a last small part of the previous chord duration and a small initial part of the new chord duration. During the rest ofthe time there is strumming of the chord or a achord arpeggio or variations of small melodic themes inside the chord by intervals of 3rd or 4th/5th. Thus melodic-harmonic variations. While when bridging two succesive chords there may be melodic themes variations by intervals of 2nd 3rd or 4th/5th (thus chromatic-melodic-harmonic).
This technique utilizes the simplicity of the information of the set of chords and translates it it to a simple information about the partition of the types of variations of simple melodic themes with the time placement and duration of the chords.
With this technique we may create simplicial counter-melodies parallel to melody.

It applies verty easily when utilizing a chromatic harmonica (see post 274), but also a violin (especially marked at a particular diatonic scale, so that we can identify chord-triad  shapes on it after a convenient tuning) and finally also on a diatonic wind.

288. Method of Gradual learning of Improvisation by singing : At first within a chord and then on the basic 3 types of chord transitions: Chromatic, Harmonic., Melodic Finally on any cycle of chords. Parallel songs.

(This post has not being written yet completely)

See also post  138, 275 , 280 , 287, 102, 256, 257, 118, 197, 183.


1) Learning to improvise by singing over a single chord.

This phase is much like the slow melody improvisation , taht is used in meditation music and inner instrospection. It helpd to be slow, at first and even without rhytm or tempo at all. Then faster with arhythm. We aasume the chord as the root chord of a mode of the diatonic scale, and we improvise mainly inside the diatonic scale,  using all the 7 notes. But we may even use for short time any of the chromatic 5 notes, that would complete the 7-notes diatonic sacle, to the full 12-notes chromatic scale. Generally speaking at least 50% of the time the notes ofthe improvisation should belong to the root chord.

Of coure a more strict improvisation would be to require that 50% of the time the notes are notes of the root chord and the rest of the time, notes between them, thus in the vector-chord or closure inside the diatonic scale, of the root chord. (e.g. if the root chord is  c-e-g, then the closure of the chord or the vector chor is  the c-d-e-f-g.)

2) Learning to improvise by singing over a chord transition: Harmonic, Melodic, Chromatic.

Any chord transition , of any pair of chords of a diatonic scale, after converted to the minimal value would be either a major or minor  interval of 2nd , thus chromatic transition, or a major or minor interval of 3rd, thus melodic transition, or an interval of 4th or 5th, thus harmonic transition.

Again a rather strict improisation is  to require that 50% of the time the notes are notes of the root chord and the rest of the time, notes between them thus in the vector-chord or closure inside the diatonic scale, of the root chord.

3) Learning to improvise by singing over  any chord progression .

In this phase , we start with a cycle of chords of a diatonic scale which is repeating. We use again the rule that that 50% of the time the notes are notes of the underlying chord and the rest of the time, notes between them thus in the vector-chord or closure inside the diatonic scale, of the underlying chord, or more generally notes of the diatonic scale that donot belong to the underlying chord.

The simplest idea is to go up or down in a linear pitch order of the notes of the diatonic scale, spending more time each time in the closure of the underlying chordand at least 50% on the notes ofthe underlying chord. Initially there is not need for waving and embelishments. Only a linear sequence that goes up or down from chord-closure to chord-closure depending on the underlying chord. We do not even need to know the chords of the chord-progression, as we will find them by shifting up or down and staying more time when the results is more harmonic. If it is a song, with its chord progression this actually would be a kind of simplicial submelody of a counter melody of the melody of the song. See also posts 118, 197, 183,  102, which contain more  ideas.
That is why when turning the singing improvisation to a melody of a musical instrument, it is more convenient to do so with, an harp, or a panflute, or an harmonica , then in general a diatonic instrument etc.

Of course as we excersise more, we learn to create small melodic themes instead of only one note, and then translate them or invert them chromatically, melodically or harmonically.

4) PARALLEL SONGS: Learning to improvise by singing parallel to a familiar and likable song. The simplicial counter-melody (see post 289 )

Here is one of the most beatiful and insteresting parts of the gradual leraning process of improvisation: We put a likable and familiar song in our , mobile, or ipad, or lapto, or tablet, and we put only one earphone oin one ofthe ears,better on the left ear, which is simpler perception ofthe sounds, while we leave open our right ear. Then as the song progresses, we sing parallel to it. Here comes the most interesting part: WE FOLLOW OUR HEART FOR  OUR IMPROVISed MELODIC LINES AND NOT NECESSARILY THE HARMONY OR MELODY OF THE BACKROUND SONG. Most of the times we will follow the harmony (chord progression) of the song and in some time intervals a similar melody too, but if our feelings suggests we may deviate even from the harmony or rhythm of the songs to a completely different song of our own making! In this way we are not singing the background song but a completly different song, although we may return at some times to the harmony (chord progression) of the background song. Sometimes our own harmony and melody will turn out to be better than that of the background song. And this makes us fell beatiful as valuable composeres of new songs. The backround song has served only as insiring stimulation, for our own improvsed song!

287. IMPROVISATIONAL SONGS THAT THEIR CHORD PROGRESSION IS A SLIGHTLY CHANGING SEQUENCE OF REPEATING CYCLE OF CHORDS.

 See also post 280 about IMPROVISATIONAL SONGS THAT THEIR CHORD PROGRESSION IS A  REPEATING CYCLE OF CHORDS.

The most obvious slightly changing sequence of repataing cycke of chords is when the cycle of chords is a triangle.

E,g. From sad to joyful


3m->6m->2m  (repeated n-times) and then
5M7->6m->2m (repeated n-times) and then
5M7->1M->2m (Blues triangle repeated n-times) and then
5M7->1M->4M (repeated n-times)

Or

3m->6m->2m  (repeated n-times) and then
3m->6m->4M (repeated n-times) and then
3m->1M->4M (repeated n-times) and then
5M7->1M->4M (repeated n-times)

Or

3m->6m->2m  (repeated n-times) and then
3m->1M->2m (repeated n-times) and then
5M7->1M->2m (Blues repeated n-times) and then
5M7->1M->4M (repeated n-times)

Or

3m->6m->2m  (repeated n-times) and then
3m->1M->2m (repeated n-times) and then
3m->1M->4M ( repeated n-times) and then
5M7->1M->4M (repeated n-times)


Or

3m->6m->2m  (repeated n-times) and then
3m->6m->1M (repeated n-times) and then
3m->5M7->1M ( repeated n-times) and then
5M7->1M->4M (repeated n-times)

Or

2m->3m->6m  (repeated n-times) and then
5M7->3m->6m (repeated n-times) and then
5M7->1M->6m ( repeated n-times) and then
5M7->1M->4M (repeated n-times)

etc

286. HOW TO COMPOSE IMPROVISATIONAL INTRODUCTORY COUNTER-MELODIES TO A KNOWN SONG.

(This post has not been written completly yet)


The main idea is to apply the method below to a selected subset of chords of the chords of the song. Usually at thre "refren" or happier repeating part of  the song.

 IMPROVISATION METHOD BASED ON  A SET OF CHORDS AND MELODIC LINES BRIDGING THE HIGHEST NOTES OF EACH OF THEM. APPLICATION WITH STRUMMING WITH CUATRO, CAVAQUINHO, UKULELE , HARMONICA VIOLIN, WINDS ETC

The application idea is that when the chord is realized with a voicing on the highest 4 (or all 4) strings , we create melodic lines on the highest string bridging the highest notes of two succesive chords. Because of a inherent phenomenon of the human sound perception , when we are strumming and chaning the chords with in-between such melodic lines, the musical perception clearaly heres a melody, which is that of the highest notes. If it was not the highest notes the melodic lines would be more often lost in listening in the strumming.
Such chord-bridging melodic lines use a last small part of the previous chord duration and a small initial part of the new chord duration. During the rest ofthe time there is strumming of the chord or a achord arpeggio or variations of small melodic themes inside the chord by intervals of 3rd or 4th/5th. Thus melodic-harmonic variations. While when bridging two succesive chords there may be melodic themes variations by intervals of 2nd 3rd or 4th/5th (thus chromatic-melodic-harmonic).
This technique utilizes the simplicity of the information of the set of chord and translates it it to a simple information about the partition of the types of variations of simple melodic themes with the time placement and duration of the chords.
With this technique we may create simplicial counter-melodies parallel to melody.

It applies verty easily when utilizing a chromatic harmonica (see post 274), but also a violin (especially marked at a particular diatonic scale, so that we can identify chord-triad  shapes on it after a convenient tuning) and finally also on a diatonic wind.

285. HOW IS IT POSSIBLE WHEN LEARNING AND REMEMBERING MELODIES TO REDUCE THEIR INFORMATION TO AS LITTLE AS THE INFORMATION OF ITS CHORD PROGRESSION? THE ROLES OF SIMPLICIAL SUBMELODY AND SIMPLICIAL MELODIC THEMES ("DOLPHIN WORDS")

(This post has not been written completly yet)
See also post 70 and post 282

Dolphin words are beatifully composed with the arpeggiator

Dot Melody of https://www.olympianoiseco.com/

https://www.olympianoiseco.com/apps/dot-melody/

Most musical instruments players, memorize their musical pieces, by just playing them sufficient many times, and letting the subconscious memorize them.

There are neverthless short notes about a melody that helps to remember it (especially when the target is an improvisation over the melody) which are not more complicated than the  chord progression which underlies the melody.

Here are hints for it

1) Determine and take note of the root of at least one main diatonic scale from which the melody may deviate and the melody has  maximal number of notes in it among other diatonic scales  (there may be more than one!) . 

2) Determine and take  a note of the parts A B C etc and repetion (loop) pattern of them

3) Determine initial-final note of  each melodic theme in the parts as it varies , as well as lowest and highest note of it and take a note of it attached to  the part

4) Determine and take a note of the longest central notes that define the simplicial submelody that should not me more than the chords of the chord progression

After all the above 4) aspects of  partial information about the melody , listen to it sometimes to refresh the memory about it, and then improvise on  it without changing the information that you took notes. Chose the best version that you feel better , and play it as your own version of the melody.

When creating improvisational variations, or remembering melodies that we must improvise, we must start from the simple and proceed to the more complicated.

And the simple in a song is the chord progression. The corresponding simplicity in the melody is the simplicial sub-melody as defined  in various types of it (melodic harmonic , chromatic etc) in previous posts.

The next level of simplicity is of course the progression of simplicial melodic moves or melodic themes as defined in post 282, which is also called the "Dolphin words".

Once these levels of simplicity are defined and remain invariant,  the rest of the variation  is creating connecting and transient notes, between them (the notes of the simplicial sub-melody and the notes of the simplicial move-themes) which can be quite arbitrary, without spoiling the compatibility of the  melody with the chord progression and which will create an improvisational variation of the melody. 

An excellent example is the well known song Petite Fleur by Sidney Bechet in G major scale.

We will utilize only the simplicial submelody not the simplicial melodic moves in this song .

The chord progression (simplified) is the next

C->B7->Em->F#->B7

C->B7->G->Am->G->Am->Em->F#->B7

C->B7->Em->F#->Em->E7->Am->D7->G

C->B7->Em->F#->Em->E7->Am->D7->G

A less simplified chord progression would be the next

C->B7->Em->F#->B7

C->B7->(D7)->G->Am->(D7)->G->(B7->Em)->Am->(B7)->Em->(C)->F#->B7

C->B7->Em->F#->(B7)->Em->E7->Am->D7->G

C->B7->Em->F#->(B7)->Em->E7->Am->D7->G

And with the simplicial sub-melody notes in parenthesis (one note per chord of the simplified chord progression) it becomes

C(c)->B7(b)->Em(g)->F#(f#)->B7(b)

C(c)->B7(b)->G(d)->Am(c)->G(b)->Am(a)->Em(g)->F#(f#)->B7(f#)

C(c)->B7(b)->Em(g)->F#(f#)->Em(e)->E7(d)->Am(c)->D7(c)->G(b)

C(c)->B7(b)->Em(g)->F#(f#)->Em(e)->E7(d)->Am(c)->D7(c)->G(b)

Now any convenient linking notes between those of the simplicial sub-melody that we feel we like to play within the rhythm will create an improvisational variation of the melody.

Other examples are in Cretan mandinodies (kondilies) . In such cases because the chord progressions is very short of two only chords, the successful layer of simplicity that will remain invariant is the simplicial melodic moves.

A METHOD T O CREATE THEORETICALLY BUT ALSO PRACTICALLY SIMPLICIAL COUNTER-MELODIES:

 IMPROVISATION METHOD BASED ON  A SET OF CHORDS AND MELODIC LINES BRIDGING THE HIGHEST NOTES OF EACH OF THEM. APPLICATION WITH STRUMMING WITH CUATRO, CAVAQUINHO, UKULELE , HARMONICA VIOLIN, WINDS ETC

The application idea is that when the chord is realized with a voicing on the highest 4 (or all 4) strings , we create melodic lines on the highest string bridging the highest notes of two succesive chords. Because of a inherent phenomenon of the human sound perception , when we are strumming and chaning the chords with in-between such melodic lines, the musical perception clearaly heres a melody, which is that of the highest notes. If it was not the highest notes the melodic lines would be more often lost in listening in the strumming.
Such chord-bridging melodic lines use a last small part of the previous chord duration and a small initial part of the new chord duration. During the rest ofthe time there is strumming of the chord or a achord arpeggio or variations of small melodic themes inside the chord by intervals of 3rd or 4th/5th. Thus melodic-harmonic variaonions. While when bridging two succesive chords there may be melodic themes variations by intervals of 2nd 3rd or 4th/5th (thus chromatic-melodic-harmonic).
This technique utilizes the simplicity of the information of the set of chord and translates it it to a simple information about the partition of the types of variations of simple melodic themes with the time placement and duration of the chords.
With this technique we may create simplicial counter-melodies parallel to melody.

It applies verty easily when utilizing a chromatic harmonica (see post 274), but also a violin (especially marked at a particular diatonic scale, so that we can identify chord-triad  shapes on it after a convenient tuning) and finally also on a diatonic wind.