323. THE BEST WAY TO LEARN THE FRETBOARD OF ANY OPEN (OVERTONES) TUNING.

See alo post 13 for learning the fretboard ofthe guitar

When having many string instruments it is more wise to have different tunings too. Especially if we utilize a digital (midi controller) fretbaord that supports practically any tuning, it is a need to have a unified and efficient way to learn fast the fretboards of any tuning and in particular open (overtone) tunings that sound better and have an umderlying unity in their pattern.

THE BEST WAY TO LEARN THE FRETBOARD IN ANY OPEN TUNING (E.G, OVERTONES TUNINGS OR E.G. THE  TUNING IN THE POST   ) IS BY CONCEIVING THE FRETBOARD AS OF A DIATONIC INSTRUMENT, MARK THE DEFAULT PREFERED DIATONIC SCALE ON THE FRETBOARD, AND LEARN THE 3-NOTE CHORDS NORMAL FORMS (ON 3 CONSECUTIVE STRINGS) IN THIS SCALE AND TUNING.

THEN FIGURE OUT THE BASIC 3 INVERSIONS OF A TRIAD CHORD (EQUIVALENT TO THE DEA-SYSTEM) AND CORRESPOND TO EACH INVERSION D, OR E OR A,  THE MODE OF THE DIATONIC SCALE THAT IT GIVES. 

THEN LEARN THE MINOR CHORDS HARMONIC TRIPLET OF CHORDS AND MAJOR CHORDS HARMONIC TRIPLET OF CHORDS OF THE DIATONIC SCALE WITH ANY CONVENIENT INVERSION ON THE FREBOARD.

I use this method to play all over the fretboard on the next tunings. Because an open tuning is a chord, all the tuning below have almost isomorphic placements of harmonic triads of minor or major chords of the diatonic scale with their 3 inversions around each normal form triad chord of the diatonic scale on the fretboard. We will enlarge with diagrams on it.

I have usually the next tuning on my string instruments

1) Standard guitar tuning and ukulele (Venezolano cuatro) tuning 4-3M-4

2) Cavaco (Brazilian  cuatro)  tuning 4-3M-3m

3) 1st overtones tuning 5-4-3M-3m-4 (as in post 191 and 301) for 6 strings, or less

4) Troll or Black mountain or Calico open tuning 5-4-3M on 4 (courses) strings instruments (see post 301)

5) Inverted  ukulele tuning   5-6m-5 on 4 (courses) strings instruments as in post 308

6) 5th overtones open tuning 4-3M-3m-4-5 as in post 301, for 6 strings or less
For less than 6 strings we keep the higher part of the tuning so as to have the interval of 5th at the two highest notes E.g. for 4 strings it would be 3m-4-5

7) 6th overtones tuning 5-4-3M-4-5 as in post 301, for 6 strings or less. It is a balanced tuning  as far as major-minor triads is concerned and it has also the very interesting inverse  4-5-6m-5-4 . 

8) The alternating minor-major 3rds of harmonic guitra tuning 3m-3M-3m as in post 164 for 6 strings or less and in particularthe panduri tuning 3M-3m for 3-course string instruments 

We enlrage more on this.

322. THE BASIC CHROMATIC TRIPLET OF CHORDS OF ANY MODE OF THE DIATONIC SCALE

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

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

Besides the basic harmonic triplets (in other words a sequence of 3 chords X1,X2,X3 so that X1-X2 , X2-X3 are harmonic relations od chords, in other words chords that their roots differ by an interval of 4th (5th)) , there are also the chromatic triplets (in other words a sequence of 3 chords X1,X2,X3 so that X1-X2 , X2-X3 are chromatic relations od chords, in other words chords that their roots differ by an interval of 2nd). BOTH  ARE BASIC TYPES OF TRIPLETS. In other words with the 3 CHORDS OF THE TRIPLET WE CAN ACCOMPANY ANY MELODY IN THE DIATONIC SCALE. WE CANNOT HAVE THIS PROPERTY OF BEING HARMONICALLY A BASE OF 3 CHORDS FOR MELODIC TRIPLETs (in other words a sequence of 3 chords X1,X2,X3 so that X1-X2 , X2-X3 are melodic relations of chords, in other words chords that their roots differ by an interval of 3rd) 

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

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


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

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

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

We may compare the basic chromatic triplets with the basic harmonic triplets (see also post 222)

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


Besides these 2 types of basic triplets we have also a 3rd type X1 X2 X3 , where X1-X2 is a chromatic relation and the X2-X3 is an harmonic relation or vice versa. We may call them the mixed
basic chromatic-harmonic triplets. E.g.  the basic triplet that is used sometimes in blues 1M 2m, 5M , is such as 1M-2m have chromatic relation while 1M-5M harmonic relation.

To convert a basic harmonic triplet to another chromatic or mixed basi triplet we utilize correspondences where we correspond each of the 3 main major chords of the diatonic scale with their lower minor relative and the 5M7 with the 7d. Therefore

2m<->4M
3m<->5M
6m<->1M
7d<-> 5M7

The same arguments may apply for the chromatic tonality where some of the mnor chords become major and some of the major chords minor. E.g. We have the harmonic triplet (3M7, 6m ,2m ) of the frygian mode and the harmonic triplet (7M7-3M7-6m) of the Locrian mode which are combined with the more standard harmonic triplets of the diatonic tonality of the dorian mode (2m-5M7-1M) or the myxolydian mode (5M7-1M7-4M) .

For  alternative basic chromatic triplets of the chromatic tonality (that corresponds to the harmonic minor and double harmonic minor) we have the triplets (we notice that thsi type of chromatic tonality gives for the basic chromatic triplets, cases of 2 major chords and one minor, thus the major chords are dominating!)


IONIAN MODE: 7M-1M-2m
DORIAN MODE: 1M-2m-3M
FRYGIAN MODE: 2m-3M7-4M
LYDIAN MODE: 3M-4M-5M
AEOLIAN MODE: 5M-6m-7M
LOCRIAN MODE: 6m-7M-1M

321. THE TECHNIQUE OF GHOST CHORDS IN CREATING MELODIC LINES ACCOMPANIED BY A CHORD AND THE NOTES OF A SECOND OR 3RD GHOST CHORD AT AN INTERVAL OF 2ND , 3RD OR 4TH CLOSE TO IT

THE TECHNIQUE OF GHOST CHORD IN CREATING MELODIC LINES ACCOMPANIED  BY A CHORD BY UTILIZING THE NOTES OF THAT CHORD AND THE NOTES OF A SECOND GHOST CHORD AT AN INTERVAL OF 2ND OR 3RD OR 4TH CLOSE TO IT (CHROMATICALLY OR MELODICALLY  OR HARMONICALLY RELATED  CHORD)

We have discussed in other posts (see e.g. post 92 ,103 ,104, 183 and 364) the concept of chromatic or diatonic closure of a 3-notes chord  or vector chord and how we can create melodic lines accompanyed by this chord with notes also from the other notes of the closure oft he chord.

Here we modify a little this technique and instead of utlizing the closure of a chord (e.g. instead of utilizing the [CM]=c-d-e-f-g, which is the closure of the chord CM=c-e-g in the C major diatonic scale) we utilize  the neigbor chord  Dm=d-f-a or Bdim =b-d-f.  We may call it ghost-chord. But very often this  chord is the next or the previous in the chord-progression of the song. We may also use 2 ghost chords the first a 2nd away and the second a 3rd away in t he same direction. In this way at each note ofthe initial chord is shapeb a threechord (3notes subscale). 

It may even better be a relative chord (roots a third apart) in other words in a melodic relation to the basic chord, or a chord that the root is a 4th or 5th away, in other words in harmonic relation with the original.  Obviously if the ghost chord is in melodic relation with the original, we utilize melodic themes inside three-chords over the notes ofthe original chord. If the ghost chord is in harmonic relation with the original, we utilize melodic themes inside tetrachords over the notes of the original chord. It is instructive of course to notice which tetrachords appear between the current chord and the ghost chord (see post 364).

The most obvioys choice of the ghost chord is  the previous or next chord from the current in the chord progression. and the 2nd ghost chord thr relative chord a 3rd away in the same direction. 

Each order of notes in normal position of  the two chords (1st, 2ns, 3rd etc) define corresponding intervals (di-chords) , three-chords and tetrachords , where the melodic  themes take place. (See also  post 364). 

It is quite obvious that when the ghost chord has a melodic relation (roots at a distance of interval of 3rd) the melodic themes are easier harmonized with the current chord because the 2 of the three notes ofthe three-chord are most often already inside the current chord.

In order to have that the final melodic theme will be still harmonizable by the initial chord (in the example the C major) it is required a timing and rhythm that gives at least 50% of the time of the melodic line to be of the notes of  the initial chord.

This technique sounds even better if in the chord progression of the song, the previous or the next chord of the Cmajor is the  Dm or the Bdim. But this is not necessary in general.

It is obvious that this technique can be used when we want the melodic line to be accompanied by 2 or 3 chords as in post 313 , we just apply it for each part of it that it is accomapnied by one of t he 2 or 3 chords.

We should remark that for hexatonic-scales harmonicas, that the blow row gives one chord and the draw raw another chord thiw techniques occurs naturally as we improvise in the harmonica, but we stay longer in the blow row or longer in the draw row.

We may create such nice loops, of 2  chords and parallel melodic themes with arpeggiator application in ipad like chordion, dot melody, arpeggist , fugue machine, ioniarics polyrhitmic arpeggiator etc (see post  12 )

320. THE UBIQUITOUS MIDI CONTROLLER MOGEES TRIGGERED FROM SOUNDS BY ANY EVERYDAY SUROUNDING OBJECT

An astonishing and brilliant idea to create a completly  any-hardware midi controller is the idea of MOGEES.

https://www.youtube.com/watch?v=RGbyFxw3-pY

The astonishing part of the experience in playng with the Mogees is that the human subconsious is tricked to think that the sounds listened are created by the hiting of simple surounding everyday objects (which of course would be a very nice bautification of our material world). 

This is not really the case. The microphone is not filtering the physical sound recorded by the little microphon neither it transforms it . It simply corresponds to it  ,arbitrarily and by user preset method ,other stored musical digital sounds or sample musical sounds.
It corresponds natural hitting sounds mainly to digital (mainly hitng ) sound. 
herefore because of the nature of natural surrounding objects sound as mainly hitting sound and the corresponding digital sound mainly of drums , percursions or metalophones , or string plucked instruments, the character of this midi controller is closer to percursion instrument or at best plucked string instrument.

Neverthless the idea is brilliant. The four free software applications that come in ipad and iphone with the mogees microphone (mogees play , mogees pulse , mogees keys , mogees maestro) are also very nice and creative, and can be used as an excellent method to practice musical improvisation and composition.

In the next video, we see how by combining the Mogees keys, with garageband we can improovise and compose music

https://www.youtube.com/watch?v=qc0P8KcVFhU


The improvisational composition here utilizes

1) A loop with drums
2) An improvised and recorded loop with bass
3) An improvised and recorded arpeggio loop (of 3 notes and translated in two places) with a melodic instrument
4) An improvised and recorded chord progression loop (here 2 chords only)
5) A finishing improvised and recorded arpeggio of  6 notes.













https://www.mogees.co.uk/

319. THE DIGITAL WHISTLE AND MIDI CONTROLLER WARBL

A peculiar and very intersrting digital wind instrument oriented to theIrish wistles and bag-pipes music is  the WARBL

https://www.youtube.com/watch?v=rCUeQ2b5Lzk&t=260s

I assess the new digital music instruments and software fromthe degrees of freedmon the allow to the player.

The warbl does not allow yet for any possible tuning of any note on any of its virtual holes=buttons, but the designer has written that he will consider it  in the future.

What I like in warble is that it is based on the simple fingering system ofthe irish whsitle of 6-front +1 thump hole which is also the universal smartest fingering system of all folk direct flutes among any continent.

Unfortunatly some digital wind instrumenst are based on the fingering system of the saxophone, or recorder , or clarinet, or Bohm flute which are not the smartest and most ergonomic possible for a wind instrument. But not the warbl. The Warbl is  based on the smartest posssible fingering system the irish whistle. Of course it supports other fingering systemsl ike that of recorder and native american flutes etc as well.

An interesting feature of the warbl is that the bending of the notes and partial holing is not supported by any sliding special button as in other digital wind instruments but by optical sensor by the distance of  the finger from the hole.

The current design state of the warbl (2020)  supports only 2 octaves with the tumb hole and 3 by utilizingthe right thumb and an additional button. But the designer has written that it will give it 3 octaves inthe future only with the left hand thumo button.

https://www.youtube.com/watch?v=6Azof-JJxLk

317. THE DIGITAL HARMONICA DM48

As far as I know till 2020 there is only one digital harmonica in the market and thsi si the

Swedish digital DM48 harmonica


https://www.youtube.com/watch?v=nwgIAFOnJVs&t=16s


I assess the new digital music instruments and software fromthe degrees of freedmon the allow to the player.

And on this the DM48 is an ecxellent score as it is the only digital wind instrument and midi controller that I know which allows for any possible tuning  on the holes a s blow and draw, plus slider shift.


I have configured it to my sensitivity and it is even more sensitive compared to the usual hardware harmonicas , with less impedance and plow pressure.

Because the DM48 is a midi controller triggering notes by the breath pressure , it is still an excellent tool for excercising the breath and having high emotional involvment while playing because of the breath.


https://www.youtube.com/watch?v=3ZpAqeLyiIs

316. THE SYLPHYO DIGIAL MULTI WIND INSTRUMENT

In my opinion one of the best digital wind instrument as midi controller is the SYLPHYO

https://www.youtube.com/watch?v=DCPS5wBcMB0

I assess the new digital music instruments and software fromthe degrees of freedmon the allow to the player.

Some of its advamtages over other digtal wind midi controllers is that it alloes for many different fingering systems which includes of course the simplest and universal one of irsh whistles and folk direct flutes like quenas, Xiao, shakhuhachi etc

What sylphyo unfortunately does not allow (but neither any single tube digital wind midi controlleras far as I know) is to set any possible note to any ofthe virtual "holes" or finger buttons.

It does allow though for plenty many different fingering systems of practiacally any known wind isntrumenst  at  any key.

Only the Swedish digital harmonica DM48 allwos it but it is not a single tube wind.

One of the best features of this SYLPHYO that I enjoy a lot is that it has a triple registry-thump key which is actually 5-fold and a allows forthe wind instrument taht you paly to have not 2 not 3 but 5 octaves while playing real tume.

Furthermore I enjoy a lot the easy design of sharps and flats which is simply by a single  (correspondigly ) button for all notes (like a pedal in orchestral harps) controlled by the little fingers.

Furthermore the slider that it has controlled by the right hand thump makes miracles in effects on the sounds.

Because the SYLPHYO is a midi controller triggering notes by the breath pressure and finger buttons, it is still an excellent tool for excercising the breath and having high emotional involvment while playing because of the breath.

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

315. THE DIGITAL FRETBOARD (MIDI/MPE CONTROLLER) ARTIPHON

In my opinion one of the best digitaL FRETBOARDS  midi controlers is the ARTIPHON, which is without strings

https://artiphon.com/

There are some digital guitars and midicontrollers in the market. E.g.  Jammy digital guitar the  https://www.youtube.com/watch?v=zR1nhH_CHNc which DOES have strings.

having strings is more natural when one wants to play guitar or other instruments like mandoline and ukulele etc, but they are not of much help when hewant to play violin, or winds, or saxophone etc.
At the latter cases the stribgless digital fretboard is mor convenient.


I assess the new digital music instruments and software fromthe degrees of freedmon the allow to the player.

The artiphone has a significant degree of freedom, as at allows not only any tuning on the place of t he strings but also any tuning for each fret!

What no digotal fretbard allows yet till now is to set a tuning note for any frets which is not in  the 12 notes of the Westerm music universe but of any frequency at all (which would include ancient Greek scales, Byzantine scales, Arabic scales, Indish scales etc.

But at least aripohone allows for sliding among the frets.

https://www.youtube.com/watch?v=dHwiJTay6GI


This digital fretboard can save to anyone a lot of money in buying hardware traditioal instruments.
And as it can be even tuned fret-by-fret like a diatonic harp ,panflute , zamponia, or even harmonica it is an excellent musical instrument to learn improvisation.

314. IDENTIFICATION OF THE GREEK FOLK MUSIC SCALES "ROADS" OF REBETICA AS MODES OF THE HARMONIC MINOR ITS INVERSE AND THE DOUBLE HARMONIC MINOR.

According to Greek books , about the greek scales-modes called rembetiki roads (e.g. Manolis Michalakis Greek Folk music Combinations and Improvisations) these sacles-modes can be identified as follows:


Here we use the definition  that a scale is a sequence of notes making in total one octave and all cyclic permutations of it (which are simply different modes of it)

E.g. The major mode ofthe diatonic scale has interval structure

2-2-1-2-2-2-1

while the aeolian minor mode of it the interval structure

2-1-2-2-1-2-2

The A harmonic minor is the scale a-b-c-d-e-f-g#-a  (it has the 5th of the major mode raised by a sharp 5$ which is called the 1st blue note. See also post 245) In  intervals of semitones it is 2-1-2-2-1-3-1 and it has the characteristic 1-3-1 pattern
(https://en.wikipedia.org/wiki/Minor_scale#Harmonic_minor_scale)

OF SCPECIAL INTEREST IS THAT INVERSE OF THE HARMONIC MINOR 2-2-1-2-1-3-1  IS DERIVED FROM THE FIRST 13 OVERTONES OR HARMONIC SERIES OF A STRING OR NATURAL TRUMPET IF  THE 7NTH HARMONIC (E.G.  C-D-E-F-G-G#-B-C )  if we perceive the 7nth overtone as B rather than Bb (in reality it is somewhere in the middle)  AND SO IT  is the inverse 7-notes scale of the first 13 overtones  ON THE OTHER HAND THE MELODIC MINOR OR THE 7-NOTE SCALE 2-2-1-2-1-2-2 E.G. C-D-E-F-G-G#-Bb-C WHICH IS DERIVED FROM THE FIRST 13 OVERTONES HARMONIC SERIES IN A NATURAL TRUMPET IF WE PERCEIVE THE 7NTH HARMONIC AS Bb rather than B.   BOTH SCALES  ARE   CONSTRUCTED FROM THE 4-CHORD 2-2-1 AND THE 5-CHORD. 

The effect of this 5# blue note that dofferentiates the natural minor from the harmonic minor in the accoampanying chords is that the Em  (3m) becomes Emajor (3M).

While the A double harmonic minor is defined as the scale a-b-c-d#-e-f-g#-a. (it has the 5th of the major C mode raised by a sharp 5$ which is the 1st blue note but also the 2nd of the major C raised by a sharp which is the 2nd blue note).
(https://en.wikipedia.org/wiki/Double_harmonic_scale)
In  intervals of semitones it is 2-1-3-1-1-3-1 and it has the characteristic 1-3-1 pattern twice.

The effect of this extra 2# blue note that differentiates the harmonic minor from the double harmonic minor in the accoampanying chords is that in addition to that the Em  (3m) becomes Emajor (3M), the Bdimished (7dim) becomes also Bmajor (7major)


The inverse A harmonic minor is a scale starting from A and with inverse intervals structure to the harmonic minor in other words 1-3-1-2-2-1-2
e.g. a-bb-c#-d-e-f#-g-a

The effect of the blue notes 1# and 4# in the accomanying chords is that  the  6minor becomes 6major , the 2m becomes 2major and the 5major becomes 5minor

1) A Nihavent= A natural minor=Aeolian mode of the C major diatonic scale.
Thus the Niavent is simply the Aeolina  mode 

2-1-2-2-1-2-2

A Nihavent : a-b-d-d-e-f-g-a


2) A Buselik=4th mode (Lydian mode) of the inverted A harmonic minor 
Thus the Buselik is the 4th mode ofthe inverted harmonic minor.

If  the harmonic minor is the 2-1-2-2-1-3-1, the inverted harmonic minor is the 1-2-1-2-2-1-2 and the 4th mode of it is the 2-2-1-2-1-3-1.

A Buselik: a-b-c#-d-e-f-g#-a           

The effect in the accompanying chords is that the a minor (6minor) becomes amajor (6major) besides that the 3minor becoming 3major.

3) A Hicaz  =5th mode (Myxolidian) of the D harmonic minor 
Thus the hicaz is the 5th mode of the harmonic minor

1-3-1-2-1-2-2

A  Hicaz: a-bb-c#-d-e-f-g-a   

The effect in the accompanying chords is that the   6minor becomes 6major and the 5major becomes 5minor       

4) E USSAK-KURDI=3rd frygian mode of the C diatonic scale
Thus the Ussak_Kurdi  is simply the 3rd Frygian  mode 
1-2-2-2-1-2-2

E Ussak: e-f-g-a-b-c-d-e



5) A NEVESER= 1st mode of the A double harmonic minor scale

2-1-3-1-1-3-1
Thus the Neveser is the 1st mode of the double harmonic minor as defined in this post 
(although it is the 5th mode of the double harmonic minor as the double harmonic minor is defined  in the wikipedia)

A Neveser:  a-b-c-d#-e-f-g#-a         

As we mentioned the effect in the accomanying chords is that the eminor becomes 3major and the 7dim becomes 7major

6) D NIKRIZ=4th mode (Lydian) of the A harmonic minor 
2-1-3-1-2-1-2
Thus the Nikriz  is simply the 4th mode (Lydian)  of the harmonic minor

D Nikriz:   d-e-f-g#-a-b-c-d        

As we mentioned the effect in the accompanying chords is that the 3minor becomes 3major

7) SAMBA is a 8 notes scale with interval structure 
2-1-1-3-1-2-1-1
e.g. fron A it  is a-b-c-db-e-f-g-g#-a

Notice that it is like the double harmonic minor  2-1-3-1-1-3-1 except is has both 5 and 5# notes. 
Actually it can be obtained from the 3rd mode of the double harmonic minor 3-1-1-3-1-2-1  by adding one note between the first and 2nd note: (1-2)-1-1-3-1-2-1=>2-1-1-3-1-2-1-1. So e.g. the A samba  a-b-c-db-e-f-g-g#-a  can be obtained so from the 3rd mode  F double harmonic minor  g#-b-c-db-e-f-g-g#
So the Samba is an 8-notes version of the 3rd mode ofthe double harmonic minor.
Thus the effect in the accompanying chords is that we have both the 3minor and 3major and also 7major instead of 7dim.

8) E HICASKAR (PIREOTIKOS) =5TH mode (myxolydian) of the double harmonic minor A 
1-3-1-2-1-3-1

E Hicaskar: e-f-g#-a-b-c-d#-e      

Thus the Hicaskar is simply  the 5th mode ofthe double harmonic minor scale as defined here

As we mentioned the effect in the accomanying chords is that the 3minor becomes 3major and the 7dim becomes 7major

9) E KARCIGIAR=5th mode (Myxolydian) of the inverse A harmonic minor  
2-1-2-1-3-1-2

E Karcigiar:  e-f#-g-a-bb-c#-d-e                                          

Thus the karcigiar is simply  the 5th mode of the inverse harmonic minor scale as defined here.

As we mentioned the effect in the accompanying chords is that the  6minor becomes 6major the 2m becomes 2major and the 5major becomes 5minor

10) A Neapolitan scale =a-b-c-d#-e-f-g-a

Interval structure  2-1-3-1-1-2-2. Notice that it has the 2nd blue not d# of the double harmonic minor a-scale without havingthe first blue note g#.

It is a 7 notes version of the 8-note samba scale

The effect on the accompanying chords is that the 7dim becomes 7major. 

313. COMPOSITION OF SIMPLE MELODIC THEMES ACCOMPANIED BY A TRIAD OF 3 CHORDS OR BY A PAIR OF 2 CHORDS

The following discussion is also a method to compose nice melodic themes directly with their underlying harmony.

We may create such nice loops, of 2 or 3 chords and parallel melodic thems with arpeggiator application in ipad like chordion, dot melody, arpeggist , fugue machine, ioniarics polyrhitmic arpeggiator etc (see post  12 )

We are used to simple melodic themes with one only underlying chord, and simple melodic themes that bridge two chords (usually harmonic pairs e.g. G7->C or 5M7->1M  see e.g. post 293 post 65, 69).
But here  we discuss furthermore simple melodic themes that span over 3 chords. E.g. 
6m->3M7->6m or 2m->3M7->6m  or 1M7-4M->5M7-1M etc

The reason that a minimum of 3 or at least 2 underlying chords are critical forthe melodic theme is that a diatonic scale is definable also by 2 or three of its chords. Eg, the C major is definable by the Cmajor F major Gmajor chords or onlythe Cmajor Gmajor chords. These are the harmonic type of basic triads of chords (e.g. 5M-1M-4M)  . But there area lso the chromatic type basic triads of  chords in a diatonic scale, that can accompany any melody (e.g. 7dim-1M-2m etc see post  222 )

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

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

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


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

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

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

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

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

We may compare the basic chromatic triplets with the basic harmonic triplets (see also post 222)

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

The same arguments may apply for the chromatic tonality where some of the mnor chords become major and some of the major chords minor. E.g. We have the harmonic triplet (3M7, 6m ,2m ) of the frygian mode and the harmonic triplet (7M7-3M7-6m) of the Locrian mode which are combined with the more standard harmonic triplets of the diatonic tonality of the dorian mode (2m-5M7-1M) or the myxolydian mode (5M7-1M7-4M) .

As each of the modes of the a diatonic is also definable and accomnied by an harmonic  triad of 3 chords, such melodic themes when using only chords from a diatonic scale and also the triad be  an harmonic triad of chords, then they will be also characterizable by the usual modes of the diatonic scale. Thus Ionian, Dorian, etc ..., Locrian type melodic themes over such an  harmonic triad of 3 chords.

The main characteristic of such  melodic themes, if the rhythm of changing chords is notmal,  is that they sound as if slow and interesting.

An excellent example is the well known song SUMMER TIME .https://www.youtube.com/watch?v=Q179VBna-_I

Other such examples a re the Bandola Llanera melodic themes, with usual chromatic tonality triplets the harmonic triplet (3M7, 6m ,2m ) of the Frygian mode and the harmonic triplet (7M7-3M7-6m) of the Locrian mode which are combined with the more standard harmonic triplets of the diatonic tonality of the Dorian mode (2m-5M7-1M) or the Myxolydian mode (5M7-1M7-4M) .

https://www.youtube.com/watch?v=l899uyxfL0s
The most common structure of such melodic themes is of course that they contain at least 3 long notes a1 a2 a3 so that each of the a2 a2 a3 belongs to the 3 accompanying chords X1 , X2, X3 correspondingly . In other words the a1 a2 a3 is the simplicial submelody version of the melodic theme. The rest of the notes of the melodic theme may very well belong to the diatonic closure of 5 notes of each of the underlying chords X1 X2 X3.

https://www.youtube.com/watch?v=qlrLHhpp8-E

It may be though that one of the 3 chords is hidden as accomnaying chord for the melodic theme in the sense of post 321, in other words one o the 3 chords is just utilized as chrpmatic transient notes ofthe melodic theme, and this hidden chord is of root and interval of 2nd close to one of the other 2 chords (chromatic relation).

Another very practical way to create  melodies accompanied by 2 only chords is to utilize harmonicas tuned to hexatonic scales that give in the blow and draw rows exactly these two chords (see e.g. post 291)

When such a simple melody is over a pair of chords, then it has two types of trinity polarity for the correlated emotions:
1) One based on its simplicial submelofy theme , which is if up (+) , if down (-) if horizontal (neutral 0) see e.g. post 114, 282
2) One based on the harmony of the accompanying pair of chords (X1,X2), which is if (major-major) then positive (+), if (minor-minor) negative (-), and if (minor-major) or (major-minor) neutral (0).


THE MISSING SIMPLICITY LAYER BETWEEN ONE NOTE OF A MELODY AND ITS UNDERLYING CHORD: THE PROGRESSION OF THE SIMPLICIAL MELODIC THEMES (DOLPHIN WORDS) OF A  COMPLICATED MELODY.

When listening to fast and complicated melodies e.g. in Gypsy jazz or in Irish reels or in Cretan kondilies (mantinodies), the subconscious perception of them perceives a betaifull simplicity which is not the harmony of the underlying chord. Where does it come from?

We have developed in these online notes the very useful concept of simplicial sub melody of a complicated melody. It may be identified from the durations of the notes (longer lasting note are correlated with the centers of the melody) but also from the notes of the underlying chord. Now because we extract and focus on the simplicial sub-melody of a complicated melody, the melodic themes of the simplicial sub-melody are the simplest possible this is "oriented intervals" or "vector intervals". We may call the simplicial melodic themes In other words intervals of two only notes that sound sequentially and not simultaneously with a specific order.

During a singly underlying chord we may have more than one such simplicial melodic themes. And they may be created on after its previous by some variation transformation like "translation" by an interval of 3rd or 5th or 8th  or "inversion" etc. This is very significant simplistic pattern of the ontology of the moves of the melody even during a sing;y underlying chord. We may have an increasing-ascending  progression of such simplicial melodic themes or oscillating-stationary  or decreasing-descending etc progression of such simplicial melodic themes. E.g. in Cretan Kondilies that have usually only two underlying chords (e.g. 1M->5M7->1M ) this progression during each chord (statistically determined rather than deterministically) defines the local style of the improvisational melody. E,g, 2 simplicial melodic themes for first 1M one for 5M7 and one back to 1M. In total 4 simplicial themes, the first 3 in a kind of variational repetition (translation or inversion) and one last and 4th closing one that may be mutated. Therefore the rhythm , and scale and underlying chord are not adequate to define the characteristic sound of such improvisations we need also the statistical profile of the progression of the simplical melodic themes.

In post  114, 231   such a progression of simplicial melodic themes has been called DOLPHIN WORD

This additional and missing simplicity layer in between the notes of a of a fast and complicated melody and its underlying chord has significance only when the melody is sufficient fast and complicated. This progression of simplicial melodic themes, together with the chord progression  , not only define the style but can be also an initial composition determination to be supplemented with an improvisational enhancement to the full melody when composing such songs. 

As alternative way to identify the style would be to use not the almost minimum number of chords to accompany it, but the maximum number of chords (usually of the diatonic scale) that can accompany it, and change them almost every beat. In this  way we define also an intermediate simplicity layer , between the notes of the  melody and the slow changing underlying chords, that can be lsos used both to define the style as well as to compose new ones.

Examples of such progressions of simplicial melodic themes (or Dolphin words) are the next  (each vector-arrow is an oriented interval that fits to a single or more  underlying chord(s)).

Or

Or

Or

AS THE COMBINATION SIMPLICIAL MELODIC MOVES (ORIENTED INTERVALS) CREATE PATTERNS THAT ARE CALLED "DOLPHIN WORDS" , WE MAYS AS WELL CLASSIFY THE "SIMPLICIAL DOLPHIN WORDS" . The simplest such patterns are of course the 3: 1) THE CYCLE 2) THE ASCENDING SEQUENCE 3) THE DESCENDING SEQUENCE. They can be defined also by requiring that the Simplicail dolhin words are also the connected components of the melody. The mathematical topology that should be defined b th concept of "contact of a notea nd the melody so far " in order to define also the connected components . And the contact is  defined by 1) Loooking back  n-notes (e.g. n=4) 2) Assuming that the contact of the note and  of the previous melody so far  is broken if an interval larger than 2nd appears between the note and the last n-notes.

SEE ALSO POST 293

HERE THE PREVIOUS SIMPLICITY CAN BECOME COMPATIBE WITH THE SIMPLICITY OF THE HARMONIZING SET OF UNDERLYING CHORDS:

   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.

Dolphin words are beatifully composed with the arpeggiator

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

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

312. 2-DIMENSIONAL ISOMORPHIC LAYOUT OF NOTES BY ALTERNATING MAJOR-MINOR 3RDS: THE REMARKABLE ADVANTAGES IN IMPROVISING AND COMPOSING MELODIC VARIATIONS AND ACCOMPANYING CHORDS

See also post 90 about the relavant tuning in 6-string guitar.

The next photo of the ipad shows in the program Muzix pro (https://www.youtube.com/watch?v=qfvHNmO1GoQ&t=26s ) the diatonic Isomorphic layout by alternating 3rds, at the diatonic scale C major .

We notice that

1) Each row is by intervals of 2nds

2) Ecah colomn is by alternating major-minor intervals of 3rds.


The layout has the nice property that  vertically every 3 consecutive squares is a chord, either major minor or diminshed. That is why iti s an isomorphic layout as all chords ofthe same type have the same shape. Here it is even a strong isomorphic layout so that any chord of the diatonic scale in its normal position (1-3-5) has the same shape.



The advantages for melodic improvisation and chord accompanying   are the next


1) Horizontally, as the layout is by 2nds , the horizontal motion is good for melodic themes made by 2nds

2) If we want a 2nd faster speed of up or down in the melodic improvisation then we move vertically by 3rds, which as if utilizing a chord as a gate to move fast. 

3) If we want a 3rd faster speed of up or down in the melodic improvisation then we move diagonally by 4ths.

4) If we want to move by 5ths then we move vertically again but in the odd number of squares

5) Variations of an horizontal melodic theme is best if we shift one column up or down and repeat it (translation by a 3rd) or two rows up or down and repeat it: Translation by 5ths

6) When  stopping at acenter note oft he melodic themes that last longer, then the accompaying chord, is vertically 3 squares that has the melodic center not in the middle or at one of its two ends. We may even try the first and then if not very much desired sound we shift one up or one down.

The Musix pro application allows for fast by a visisble button to change  the scale or to have avaiable at 7 buttons  the 7 chords of  the scale. (here in the photo we have hide it).





MELODIC IMPROVISATION AND CHORD ACCOMPANYING WAS NEVER EASIER AND MORE MUSICALLY MEANINGFUL!



SOME RULES TO MAKE NICE MELODIC THEMES AND VARIATIONS OFTHEM ARE  THE NEXT

(See also Max Martns maths of  melodies in  post 311)

1) We choose as melodic theme a symmetric pattern (square, triangle , polygone etc) or part of it as basic melodic theme and from the shape (and since each chord is always , due to the isomorphic layout, a vertical segment of 3  consecutive squares) we make sure it is harmonzed and accompanied by 1, 2 or 3 chords.The symmetric pattern of the melodic theme should make visible also the simplified substructure of its simplicial submelody corresponding melodic themes (in other terminology "Dolphin word")

2) We variate it by translating it vertically , horizontally, diagonally etc But not only translating but also transforming it with affine (linear) transformations and even topological transformations as a type of mutations discussed also in 4).

3) We variate it by inverting its times sequetioanl order in its notes, or taking a rfkection of the shape , relative to an axis or point

4) We mutate it (if it is part of a connected symmetric shape) by taking complementary or other parts of the same connected symmetric shape (or if its a full connected symmetric shape by taking an alternative symmetric shape).

5) We go on and loop as above in 1) 2) 3) 4).

Because the beatiful melodies are reflected as beatiful geometric shapes,and the beatiful variations of them as beatiful geomotric motions and transformations, there is an open road to improvise amd compose an abundance of beatiful melodies with systematic symmetric structure in variatinosn ofthem and their  harmony. The quality of the image in is symmetries and transformations is reflected in the quality of the melody structure and its harmony. In thiw way light and sound merge.

I assume if Bach had this tool He would have composed even more and even more beatiful conterpoint musical pieces.

With this musical instrument  the single unaccimpanied improvisation of  altrnating chord and melodus is  very well and efficient done! (see also post  102 THE METHOD OF UNACCOMPANIED IMPROVISATION BY ALTERNATION OF CHORDS VARIATIONS WITH SHORT MELODIC THEMES VARIATIONS and post 302. METHOD OF  IMPROVISATION BY AN UNACOMPANIED SINGLE DIATONIC INSTRUMENT OR  STRING INSTRUMENT WITH A SCALE MARKED ON THE FRETBOARD , BY SMALL MUSICAL THEMES AND PERPETUAL VARIATIONS BY TRANSLATION FROM S TRING TO STRING , INVERSION AND MUTATION.  and post 295. THE 3 MAIN TYPES OF IMPROVISATION AND  3 BASIC PRINCIPLES  )

311.MELODIC MATHS BY MAX MARTIN AND GERM-PATTERN SYSTEMS OF CREATING MELODIC THEMES AND MUTATIONS OF MELODIC THEMES AND RHYTHMS

 MELODIC MATHS BY MAX MARTIN AND GERM-PATTERN  SYSTEMS OF CREATING MELODIC THEMES AND MUTATIONS OF  MELODIC THEMES AND RHYTHMS

In the next videos one can see how melodic themes of notes  (but also of chords) and mutations of them plus repetitive combinations of them, can be created by keeping invariant an  initial germ-pattern or  melodic-seed of  interval shifts and pause (GERM PATTERN)  of a note (or chord) or  of  initial pattern of sequence of melodic themes of notes or chords after  seeminly random pauses (omittings) of the parts of the fixed pattern. 

See also post 312 about maths  in isomorphic 2-dimensional layouts of notes 

Melodic themes of notes can be considered and created also as repettitive combinations of a small set of interval-steps (pitch transformations) in a scale plus a pause wchich may be called MELODIC GERM . A melodic germ  as basic invariant can give many melodic themes with an internal affinity which can  be considered a system of muttations of melodic themes.

This process might be laso conceive as "arpeggiation"  of a muscal melodic theme that serves as germ-pattern of al the derived mutations of it.

Comparing the melody with a speaking language suggests the next correspondence

Let us correspond to each vowel a number of steps inteval shift insidea scale 

E.g. 

empty space=pause 

A=0 step

E= 1 steps

I= 2 steps

O=3 steps

OU=4 steps

Then the content of vowels of any phrase can be translated as a GERM-PATTERN for creating melodic themes as muttaions of this germ-pattern  (and latter also repettitive combinations of them)

See also post 106 about melodic seeds

AN INTERCATIVE MODE OF VARYING  MANUALLY ON THE TOUCHSCREEN  THE ORDER SHAPE ("DOLPHON WORD" ) OF MELODIC THEMES IS VERY WELL REALIZED WITH THE APPLICATION OSCILAB.   IT IS UTILIZIG ALSO A SUPERPOSITION OF 3 OSCILATIONS OF VARIOUS SHAPES AND CURVES

https://www.youtube.com/watch?v=_AiDOCG-Vdk

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


https://www.youtube.com/watch?v=sb3e4Mq6y3s


https://www.youtube.com/watch?v=w0-Ljf5gm4A


https://www.youtube.com/watch?v=Fc16Y1gKUDc



https://www.youtube.com/watch?v=w0-Ljf5gm4A



https://www.youtube.com/watch?v=Fc16Y1gKUDc

Applications like Sector (http://kymatica.com/apps/sector)   and Necklace  (https://apps.apple.com/us/app/rhythm-necklace-geometric-sequencer/id954669874  https://www.youtube.com/watch?v=ddWQU6Wo3v8 ) and Chronium
(https://www.youtube.com/watch?v=QYbi4rbMK88)

give in an intearctive way the remarkable ability to the user to variate the rhyhmic pattern  executed by a loop , in other words creating a continously changing or variating  polyrythm. The chronium also allows changingthe pitch and color of the beet as well

310. ISOMPORPHIC 2-DIMENSIONAL LAYOUTS FOR KEYBARDS STRING INSTRUMENTS TUNINGS AND SOFTWARE PADS FOR ARRANGING THE MUSICAL NOTESAND THEIR IPORTANCE IN IMPROVISING.

 ISOMPORPHIC 2-DIMENSIONAL LAYOUTS FOR KEYBARDS  STRING INSTRUMENTS  TUNINGS AND SOFTWARE PADS  FOR ARRANGING  THE MUSICAL NOTESAND THEIR IPORTANCE IN IMPROVISING.

THE TERM ISOMORPHIC REFERS TO THE CHORD-SHAPES THAT REMAIN THE SAME (ARE ISOMORPHIC) WHEN CHANGING THE ROOT NOTE AS LONG AS THE TYPE OF THE CHORD REMAINS THE SAME.

Isomorphic layouts: What they are and why they are awesome for your music

https://www.youtube.com/watch?v=ZczraF3dzU0&t=20s&fbclid=IwAR1bAiGG3HFPE9OciNXGPE5p_GD_L5AJaKXsabiypconKg_HYk_RAz5hR9s

See also post 164 for chromatic realizattion of the alternating 3rds such isimorphic layout by appropriate tuning on the fretboard of a guitar