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Friday, January 31, 2020

292. METHOD OF SINGLE INSTRUMENT IMPROVISATION BY ALTERNATION OF CHORD- VARIATIONS WITH MELODIC THEMES-VARIATIONS ON A STRING INSTRUMENT WITH A SCALE MARKED ON THE FRETBOARD OR ON A DIATONIC HARP , WINDS,HARMONICA ETC. LONGITUDINAL CHORDS

  METHOD OF SINGLE INSTRUMENT IMPROVISATION BY ALTERNATION OF  CHORD- VARIATIONS WITH  MELODIC THEMES-VARIATIONS  ON A STRING INSTRUMENT WITH A SCALE MARKED ON THE FRETBOARD OR ON A DIATONIC HARP , WINDS,HARMONICA  ETC. IMITATION ASSIMILATION, INNOVATION.
LONGITUDINAL CHORDS 


IT IS  ESPECIALLY  EASIER AND  RICHER AT THE MELODIC TUNING OR 2ND OVERTOME TUNING (SEE PSOT 301)  BY ALTERNATING MINOR-MAJOR 3RDS OF THE 6-STRING GUITAR AS IN POST 90. 

At  that tuning there is a very rich scheme of triad-chords on all inversions on every 3 consecutive strings and the chromatic, melodic harmonic relations of the chords ate directly geometrically visible on the fretboard. The wheel of chords by 4ths has 4-different ways to play it on thsi tuning. But as it is with triad-chords  which is the most rich way we may substitute it with melodic-chromatic relations. Between the triad-chords we play melodic improvisatinal lines.


(See also post 102)

IMITATION ASSIMILATION, INNOVATION.

THIS METHOD BECOMES EASY, FOR 3 OR MORE STINGS INSTRUMENTS (TENOR GUITAR, UKULELE, BOUZOUKI, OUD , SAZ, MANDOLIN, VIOLIN , CELTIC DIATONIC HARP  ETC) WHEN A SINGLE PRIVILEGED DIATONIC (OR CHROMATIC SCALE) IS MARKED ON THE FRETBOARD. ALSO ONOTHER DIATONIC INSTRUMENTS LIKE FLUTE, PANFLUTE, CHALUMEAU CLARINETT SAXOPHONE HARMONICA ETC. THE MELODY IS IMPROVISATIONAL GOING UP OR DOWN AND THE ALTERNATED CHORDS ARE CHORDS AS TRIADS OF MARKED NOTES THUS OF THE DIATONIC SCALE AND ON THE LOCAL 3-STRINGS THAT INCLUDE THE MELODY STRING. IF IT IS A DIATONIC WIND INSTRUMENT THEN THE CHORD IS SUBSTITUTED WITH ITS ARPEGGIO . OF COURSE IT WORKS BEST FOR DIATONIC SCALES BECAUSE EVERY SUCH TRIAD IS A USUAL CHORD MINOR MAJOR OR DIMISHED. FOR CHROMATIC SCALES LIKE HARMONIC MINOR AND DOUBLE HARMONIC MINOR THE CHORDS ARE LESS COMMON. 

IT IS IMPORTANT TO REALIZE THAT THERE IS NO STRICT REQUIREMENT THAT THE CHORD JUST BEFOR OR AFTER THE INTERMEDIATE MELODIC IMPROVISATION FITS HARMONICALLY AS ACCOMPANYING CHORD OF THE MELODY. BUT IT CAN OF COURSE. THUS THIS CONCEPT OF IMPROVISATION WHICH IS MAINLY FR A SINGLE INSTRUMENT IS A WIDER CONCEPT THAT THE USUAL CHORD ACCOMPANIED IMPROVISATIONS

We continue the discussion of the post 82, about chord-independent and unaccompanied melodies  composition and improvisation.

Studying some of the musical pieces of Bach for solo instruments (e.g. 

BWV 1013 - Partita in A Minor for Solo Flute  https://www.youtube.com/watch?v=Datoqxx-biwwe may be inspired for the next method of unaccompanied improvised soloing:


IMITATION ASSIMILATION, INNOVATIION.

The melody is like a man wandering-walking in a town, who spends much time at squares and garden of the town that his is exploring. The squares and garden  are the chords, played in the solo , preferably a single chord spanned in two octaves, At this time of the soloing the emphasis is on the harmony. But when continuing till the next "garden or square"   then the emphasis is on the melodic themes and their affine structure dynamics (see post 97 and 101). How much time is spent in "gardens" ( chords) or "street-walking" (transition melodic themes) is a matter of choice of the improviser. If the melody is unaccompanied, then at the same time the chord progressions is improvised in this way. 

When spending time within a "garden" or "square" in other words within a chord the best idea is to have the chord in 4-notes form e.g. like a with 7nth or with 6th, and in the current octave or in the next. Then start the melody at a note of the chord and end it again at a note of a chord in this or the next octave. For example we may compose the melody from 3-notes micro-themes, the first and last inside the  chords and the middle possible outside the chords.  Since the chord has 4-notes and the scale  7 notes the passing or transient notes are only 3, less than the 4 of the chord, therefore, any such melodic theme fits harmonically to this chord.

Here is an example :

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

And another example

https://www.youtube.com/watch?v=rZWOKDwzzZ8

For more details see post 102.

IMITATION ASSIMILATION, INNOVATION.

The melocic part of the improvisation shoud have symmetries or in other words a structure of simple melodic theme, with its variations.

0) An affine pattern of the melody which is independent of a realization in  a mode or in a scale (see post 97)
1) Reflection to a horizontal axis (time)
2) Reflection to a  vertical axis (pitch)
3) Point symmetry to a time point
4) Pitch translation
5) Recursive pitch waving ascending or descending.
6) Cyclic or balanced behavior   in ascending-descending.
7) Dilation on the size of intervals (waved changing of the 3 melodic densities or speeds). Usually the melody starts with low melodic speeds or densities , accelerates to higher speeds or densities and then decelerates again to lower speeds or densities, as is also the motion of bodies in dancing.
8) Statistical types of symmetries.


The improvisation method of post 293 can be adopted to apply here too.


 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 may use as duration an independent duration that no chord is playing.  During the rest ofthe time there is strumming of the chord or a chord 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.


LONGITUDINAL CHORDS:

IF THE INSTRUMENT IS NOT SUPPORTING AT ALL OR WELL AN HARMONIC SIMULTENEOUS OF ITS NOTES PLAYING OF A CHORD (LIKE A VIOLIN ,  LYRA  OCTAVE MANDOLIN, FLUTE, PANFLUTE, CLARINET, SAXOPHONE, ETC) THEN THE NEXT SUBSTITUTION TECHNIQUE APPLIES AS IN POST 262.

The concept of 5-fold scale-closure of atriad chord and melodic improvisation on it ,is the binding entity  of the rhythm-melody-harmony in the improvisation at least at one layer of complexity.

The fivefold is the concept of longitudinal-chord , e.g. on single string, as contrasted to the concept of transversal-chord of many strings simulteneously. 


The 5-notes (pentachord or 5-fold) methods of improvising over a triad chord with violin, lyra , panflute and Celtic harp. 

The "arpeggios" inside such a 5-fold may be called ROTATIONS or PERMUTATIONS ofthe 5-fold.


As we have mentioned before too, a criterion if a piece of melody is fitting to an underlying or accompanying chord is if at least 50% of the time of  the melody the notes of the chord are sounding. This is not the only criterion. Let us call it the 1st criterion. Actually this is a rather strict criterion. Another more loose criterion that we call here the 2nd criterion is that the intervals created by the notes oft he melody and the chord are more than 50% intervals of 3rds 4ths, 5thsor 8ths and larger rather than intervals of 2nds.




1) GENERAL METHOD Now if we utilize only 5 notes of the full chromatic 12-notes scale 3 of which are the notes of the triad chord X, then if we improvise a melody M which in the average stays about equal time to these 5 notes then according to the 1st criterion this melodic improvisation M fits the chord X. We call this the 5-notes methods of improvising over a triad chord.

2) THE CHROMATIC INSTANCE In particular, these 5 notes maybe the closure of the chord (see post 183 CLOSURE OF A CHORD OR VECTOR-CHORD VERSUS ARPEGGIO OF A CHORD FOR IMPROVISING OVER A CHORD) or vector-chord of the chord. This is a rather chromatic method of improvising over the chord it is best when the improvisation over a chromatic minor scale. As we mentioned if we improvise a melody M which in the average stays about equal time to these 5 notes then according to the 1st criterion this melodic improvisation M fits the chord X.

3) THE MELODIC INSTANCE Another method is the melodic method of  extending the chord X by a3rd lower of the root note and a 3rd higher of the highest note.  We make sure that the extended 3rds together with the inner 3rds of the chord are laternating major-minor 3rds E.g. if the triad chord is the major C-E-G, then we extend to the A-C-E-G-B, If the triad chord is the minor A-C-E we extend to the F-A-C-E-G. As we mentioned if we improvise a melody M which in the average stays about equal time to these 5 notes then according to the 1st criterion this melodic improvisation M fits the chord X.


In addition for every such chord or chord transition we may have a morphological rhythmic pattern E.g. A1 B1 B2 B3 or A1 A2 A3 B1 , which shows how the melodic theme is repeated or varied by translation inversion contraction/expansion and rotation-mutation.

In post 103. (HOW TO CREATE MELODIES FROM A CHORD PROGRESSION 2/2: THE CHORD-LOCAL 7-NOTES SCALES OF A CHORD PROGRESSION AND THE MELODIC THEMES VARIATIONS THAT THEY DEFINE) we combined the chromatic 5-notes neighbourhood of the chromatic instance and he  melodic instance and we created the 7-notes local neighborhood scale of a chord and hopefully of the chord progression.



MODES OF A SCALE AS LONGITUDINAL CHORDS AND AS A METHOD OF MIDDLE-SCALE /MICRO-SCALE MELODIC THEMES IMPROVISATION AND VARIATIONS FOR NON-POLYPHONIC INSTRUMENTS THAT DO NOT SUPPORT CHORDS.

We have discussed already in post 262 (also post 92) , how the 5-notes scale-closure of 3-notes chord, can serve as sub-scale for improvisations under tis chord,

We may apply this idea to power chord e.g. c-g-c'  , which spans an octave , and consider as 5-fold closure of thispower chord the notes (in the example) c-e-g-a-c'  or  c-e-g-b-c'

Furthermore , even for a triad chord like the c-e-g, we may extend the concept to 2 alternative hexatonic scale, that can serve as space for melodic improvisation under this chord,
a) the c-d-e-f-g-a-c'
b) the c-d-e-f-g-b-c'

(see also post 92  )
Again because the notes of the chord c, e,g, c' are more than the notes outside the chord a melodic improvisation which spends time uniformly distributed among the notes, is a melody that is accompanied by the chord.

But also we may apply the rule that for a melody to be acompanied by a chord it is adequate that at least 50% of the time it is occupied by notes of the chord. (see post 111 , and 138 )
This rule was applied when we had improvisation in a diatonic scale, accompanied by the root-chord ofthe scale. (see post 138)

Or in general improvisations of any mode of the diatonic scale, accompanied by the chord of the first note of the mode.
(see also post 222 about the modes of the diatonic scale as triads of chords)
Here we claim that the harmony of each mode ofthe diatonic scale is the chord of its first note. So we have the next 7-cases

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

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

Therefore , instead of the five notes c-d-e-f-g. as sub-scale fitting the chord c-e-g, we may take all the major-mode 7-notes c-d-e-f-g-a-b-c'  
It may be considered after all as a chord with 2nd, 4th, 6th and 7nth!


Therefore we may identify that the  LONGITUDINAL CHORD=MODE of 7 notes, instead that the longitudinal chord e.g. of c-e-g is only the c-d-e-f-g. (see post  262 and post 292).

Therefore when improvising either as a single instrument (as in post 292 ) or with chord accompanying (as in post 294 ), and especially when our improvisation instrument is essentially not support polyphonic chords (like a flute, clarinet, saxophone, panflute, Lyra, violin, mandolin etc)
We may apply all we know and perceive about the role of chords in improvisation  to the Longitudinal chords-modes of the scale. So the effect of changing the chord, and also the hidden simplicity of the underlying chords-cycle is translated here as the hidden  simplicity of longitudinal-chords-modes cycle. The improvisaion at worse is of about equal time among the notes,but it is better if we spend more time on the notes of ofthe root-chord of the mode.

From this point of view the main 3-relations of the modes are
a) Chromatic : (the roots are in a diatance of 2nds or inverses
b) Melodic : (the roots are in a distance of 3rds or inverses)
c) Harmonic: (the roots are in a distance of 4ths or 5ths )

BECAUSE THE HARMONY OF THE CHORDS OF A MELODY IS A HIDDEN SIMPLICITY IT IS CRUCIAL IN MODERN MELODIC IMPROVISATIONS TO INDENTIFY THIS SIMPLICITY ON THE OBSERVABLES OFTHE MELODY.





1) THE CYCLE OF THE MODES AND THEIR 3-RELATIONS (CHROMATIC-MELODIC-HARMONIC) DEFINE THE MODULATIONS-TRANSLATIONS OF THE MICRO-MELODIC THEMES
THE MICRO-MELODIC THEMES   ARE MOST OFTEN CRATED OVER THE BASIC RHYTHMIC PATTERN. THEY MAY BE CONSIDERED IN DANCING SONGS AS PERCURSION INSTRUMENT.  USUALLY ARE MADE  FROM INTERVALS OF 2NDS (CHROMATIC-RHYRHMIC MELODIC MICRO-THEMES).  NEVETHELESS IN IRISH FOLK MUSIC EVEN THE MICRO-THEMES ARE FROM INTERVALS OF 3RDS OR 4THS/5THS (MELODIC-HARMONIC-RHYTHMIC  MICRO-THEMES). 
THEY ARE USUALLY WAVES AND EMBELISHMENTS AROUND SINGLE NOTES (OF THE UNDERLYING CHORD) AND START OR/AND END ON THIS NOTE
WE SHOULD DISCRIMINATE BETWEEN TRANSLATIONS OF THE MICRO-SCALE MELODIC THEMES WITHIN A MODE-LOMGITUDINAL CHORD (CALLED ALSO ROTATIONS) AND TRANSLATIONS AMONG MODES-LOMGITUDINAL CHORDS (CALLED ALSO MODULATIONS) .
THE MOST OBVIOUS TRANSLATIONS-ROTATIONS OF MICRO-THEME INSIDE A CHORD IS OF COURSE BY THE INTERVALS OF THE CHORD OT INVERSIONS OF IT, THSU 3RDS, 4THS/5THS.

A longitudinal-chord-mode should contain melodic micro-themes, that are translated, inverted, and mutated by changing mode (modulations) or moving inside the mode.


We create the micro-melodic themes usually from intervals of 2nds but sometimes from intervals of 3rds/4ths/5ths, within a mode and we translate and invert then either inside the mode-chord or by changing the mode by intervals mainly of 3rds, 4ths or 5th. (melodic, harmonic translations) and rarely by itervals of 2nds (chromatic translations)

2) THE MIDDLE-SCALE MELODIC THEMES ARE MAINLY FROM THE SIMPLICIAL SUB-MELODY AND REFLECT THE PATTERNSOF MODULATIONS (TRANSLATIONS) OF THE MICRO-MELODIC THEMES. THEREFORE THE CHORDS OF THE MELODY CAN BE TRACES EITHER AS SUBSCALES MODES-LONGITUDINAL CHORDS, OR AS SUBSETS OF TRANSLATIONS OF THE MICROMELODIC THEMES.
WHEN THE VIOLIN-LYRA  IS TUNED WITH OVERTONE TUNIGS LIKE 4-3M-3m (e.g. g-major: D4-G4-B4-D5  , OR f-major: C3-F4-A4-C4 OR c-major: G3-C4-E4-G4) then the strings are the Ionian, Frygian and Myxolydian modes,and trabsfering the micro-theme transversal onanother sring is always an interval of 3rd, 4th/5th thus easy to realisze the improvisation. Even if the violin-lyra  is tuned by 4-3M-4 (e.g.  g-major: D4-G4-B4-E5  , OR f-major: C3-F4-A4-D4 OR c-major: G3-C4-E4-A4) , by changingthe string we have transposition of the theme by 4th , or 3rd , and still is more or lesspossible and convenient. We may have the default diatonic scale of the violin-lyra marked on the fretboard, and usethe patternsof the 3-notes chords as patterns of the centers for translations ofthe micro-themes. If the instruments is flute, panflute, etc no such convenience,but still intevals of 3rd, 4th/5th are easy to visualize on the finger-holes. 

3) APLYING THIS TECHNIQUE OF MICRO-THEMES THAT ARE VARIED ACCORDING TO THE NOTES OF THE CHORDS AND THE CHORDS-TRANSITIONS AND ALSO INVERTED AND MUTATED AS WELL  IS CREATED AN ENDLESS STREAM OF SOLOING MUSIC WITH HARMONY AND RECOGNIZABLE THEMES. 


WE MUST NEVER FORGET THAT A FAST MELODIC INSTRUMENTAL PLAYING IS NOT ALWAYS THE BEAUTY IN MUSIC.

IN THE GOOD IMPROVISATION IT IS THE (USUALLY SLOW) FLOW OF THE EMOTIONS THAT MUST SHAPE THE KINETIC ACTION OF THE FINGERS ON THE INSTRUMENT AND MELODY AND NOT THAT  THE HABIT OF THE ACTION OF THE FINGERS ON THE INSTRUMENT AND MELODY THAT SHOULD SHAPE THE FLOW OF THE EMOTIONS!

HERE ARE MORE DETAILED IDEAS

MY PERSONAL APPROACH:

My personal approach to similar type of improvisation is as follows

HARDWARE  IDEAS

1) INSTRUMENT I utilize a 4-strings instrument instead of 3-stringsm although sometimes a 3-strings too. Of course I may use a 6-string instrument.

2) STARTING SCALE I chose a basic scale, usually the natural defoult scale of the instruent which is marked on its fretboard.

3) The TUNINGS are preferably overtones cuatro tunings thus cavaco cuatro or Swedish troll fiddle tuning. But I can also use the venezuala cuatro or ukulele (guitar tuning of 4 highest strings)

4) CHROMATIC TONALITY
Although I chose a diatonic scale, that is from 7 notes I involve also some or all of the 5 blue notes that result to all 12-notes of the musical universe. This is usually done in chords by convrting major to minor and vice versa E.g. a stanard chromatic extension ofthe chords of the diatonic scale is 3M instead of 3m and 7M instead of 7d. But also the minors  6m can become 6M when resolving to 2m and also the 3m to 3M when resolving to 6m, and the 2m to 2M7 when resolving to 5M. In addition we may suround each major chord with two dimisnsihed chords an interval of 2nd away, that resolve to them, in the same way that the 7dimished resolves to 1M.I have a composed collection of more than 800 chord progressions in tonality , chromatic tonality and general multitonality in which I can resort to improvise with melodic bridges metween the chords as in 10) and 11) below.

For the next steps I will enlarge more in the subsequents paragraphs

CHORD-BASED IDEAS

IMITATION ASSIMILATION, INNOVATION.

5) I improvise on major-minor lternations of HARMONIC CYCLES
with bridging the chords small melodic themes too.

6)  I improvise on major-minor lternations of CHROMATIC  CYCLES (like Andaluzian cycle)
with bridging the chords small melodic themes too.

7) I improvise on ISOMORPHIC CYCLES OF CHORDS (X1-X2-X3etc) with (Y1-Y2-Y3 etc) Most often of chromatic sequences that are melodic or harmonic isomorphic . I bridge them with small melodic themes too.

8) 2-VOICES AMBIGUITY REVEALED
I ascend or descend  a mode of the scale with 2-voices simulteneous notes intervals of 3rds. The ambiguity of  them is that they can be part of a minor or dimished chord  (sad feeling) or a major chord (happy feeling).  So 1st I play the 2-voice interval andthen I reveal it as major ot minor chord depending on the mood and to if I am ascending or descending.

MELODIC THEMES BASE IDEAS


9) SMALL MELODIC THEMES VARIATIONS
The idea here is to start with short and rythmic melodic themes and apply the 3 basic variations , like translation (chromatic, melodic, harmonic) inversions and mutations. The structure of the melodic themes may mimic the chords accompanying a melody. Instead of chords here we may have an isokratic a drone  or intermittently  repeating melodic theme , which may be an "arpeggio" of the closure of a chord, and over this we add sequentially a higher octave melodic theme that is varied and evolves.

MIXED CHORD AND MELODIC THEMES IDEAS

10) "WALKING THROUGH PARTS OF  A  TOWN", FLUID-CHORD-TRIADS or 2-VOICE ACCOMPANYING OF MELODY.

This idea is very old idea  in ancient folk music before the era of classical music when complicated melodies where accompanied by power chords that are essentially 2-voices chords. It is an idea also similar to the next below at 11) except that instead of alternating standard 3-voices chords with melodic themes, we  are struming or arpeggiating on a single triad which is not standard major or minor and so that it is constantly changing at each note of the melodic themes so that the 2 lower notes are rather stable and are used as 2-voice chord which accomnies the 3rd note which is changing faster and is usually the higher.

11) "TRAVELING AMONG AND WITHIN TOWNS"

This is a generic type of improvisation where I improvise "randomnly"  with melodic themes that are translated , inverted and mutated mainly within the diatonic scale, but at their standing notes (melodic centers) I apply arpegiation or struming of the close local major or minor/diminishd chord which fits to the melody at that time. The choices are only 2-3 at each time. Here the metaphor for the melodic themes is traveling and the metaphor for chords is "town"


12) OVERTONES VERTICAL GATES
This applies especially well in overtones tunings and of course on the full 6-string 1st overtones tuning. I improvise horizontally with melodies and at the standing note a cross-over vertically at the local overtones "gate" which is of course an extended overtones arpeggio of a major or minor chord.




OF COURSE IN THE 4TH GENERATION DIGITAL  MUSIC  MAKING THAT KNOW  IS BEEN BORN, THE ABOVE METHOD OF ALTERNATION OF CHORDS (ARPEGGIATED) AND MELODY CAN BE VERY WELL PLAYED WITH SOFTWARE THAT CREATES MUSIC CALLED ARPEGGIONOME (for iOs ) OR ARPIO (for Android) by Alexander Randon. (https://www.linkedin.com/in/alexandernaut/) Furthermore withother less automated softare like the ThumbJam we can still make such improvisations ina very efficient ,easy and beatifull way.


Thursday, January 30, 2020

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, BCDEF, and Gthen 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.

Friday, January 24, 2020

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.

Thursday, January 23, 2020

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.

Friday, January 10, 2020

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!