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Tuesday, November 5, 2019

280. IMPROVISATIONAL SONGS THAT THEIR CHORD PROGRESSION IS A REPEATING CYCLE OF CHORDS

(This post has not been written completely yet)

VECTORS, WAVES AND SPIKES
The identification and method of composition of them is based on the next concepts

1) As melody it has 3 layers (Simplicial submelody of the harmony, melodic arpeggio , diatonic chromatic arpeggio or ostinado)
2) Within each chord, it has 
2.0) A single note from the simplicial submelody
2.1) A projected and simplified melodic arpeggio
2.2) The full diatonic chromatic ostinado, which consists from
a) Diatonic chromatic maxima VECTORS
b) Diatonic chromatic RIPPLES or waves or cycles or oscillations
c) SPIKES (jumps with intervals higher than 2nd)

THERE ARE HUNDREDS OF DIFFERENT SONGS ON THE SAME CHORD-CYCLE  AND THOUSANDS OF DIFFERENT IMPROVISATIONAL SONGS ON THE SAME CHORD-CYCLE.

(see also post 17 and 29 , 145 ,148, 150)

THE ANCIENT MUSICAL THEORY SIMPLE DESCRIPTION OF RAPSODY MUSIC STIL LIVING IN THE AEGEAN ISLANDS LIKE THAN OF CRETE IN GREECE :

Such music was created in ancient times it  is mesmerizing with complicated melodic lines but in reality very simple musical description.

For example for Aegean islands (Greece) improvisational folk melodies (mandinades) condylies) with violin or Lyra, the next factors prevail.

1) "Poetic meters" over the same note sometimes notes up to 8 notes. The density of the notes is high. E.g. with 4 notes per  measure-bar and a beat of 80-100 bars per minute gives a tempo of 320-400 beats-notes per minute.

3) Straight vectors ascending or descending usually of 4 or 5 notes so as to reach a new chord neighborhood.

2) Mainly waves by intervals of 2nds (chromatic) inside intervals of 3rds (melodic, either standing or ascending descending, and usually inside a chord  so as to reach the neighborhood of a new chord. The simplistic sub-melody of such a waving melody is essentially an arpeggio of the underlying chord.


A) THE UNDERLYNG CHORD OF THE SONG IS ONLY ONE AND IS A POWER  CHORD AT ROOT POSITION OF SAY A DIATONIC SCALE (ALTHOUGH IN ANCIENT TIMES THEY DID NOT HAVE THE CONCEPT OF A  7-NOTES SCALE BUT ONLY OF A 4-NOTES SCALE THE  TETRACHORD WHICH WAS A SCALE SPANING ONLY AN INTERVAL OF 4TH INSTEAD OF AN INTERVAL OF 8TH, THUS POWER CHORD WOULD BE THE ROOT POSITION ON THE TETRACHORD). 

SINGLE CHORD IMPROVISATION: We may as well alternate the root chord of a scale as power chord (only an  interval of 5th) with melodic themes (of 3 or 4 notes and inside  a three-chord or tetrachord ) based on each of the  the 3 notes of the root 3-notes or 4 notes chord and translated or inverted melodically by intevals of 3rd across the 3 or 4 notes of the roor chord. 
E.g. in  the Dorian mode of the C diatonic sacle and with an harp,  here


MANY CHORDS-CYCLE  IMPROVISATION: We do the same as with the one chord for each chord of the chord-cycle. with melodic themes (of 3 or 4 notes and inside  a three-chord or tetrachord ) based on each of the  the 3 notes of the underlying  3-notes or 4 notes chord and translated or inverted melodically by intevals of 3rd across the 3 or 4 notes of the roor chord. We may sure thatthe melodic centers are notes of the underlying chord. At the chord transition one of the previous three-chords or tetrachords of the melodic theme becomes the bridge between the 2 consecutive chords and we constinue as before.  

B) THE SOLOING IS ANY REPEATING PROGRESSION OF SHORT RYTHMIC MELODIC THEMES WITHIN A TETRACHORD WHICH  IS USUALLY  THE 1-2-2 IN SEMITONES THUS THE FRYGIAN TETRACHORD AT THE 3RD POSITION OF A  DIATONIC SCALE WITH UNDERLYING POWER CHORD AT THE ROOT POSITION OF THE TETRACHORD OR THE 3RD POSITIONOF A MODERN 7-NOTES DIATONIC SCALE. (SOMETIMES ALTERNATING WITH ANOTHER TETRACHORD E.G. THE IONIAN TETARCHORD AT ROOT POSITION OF THE 7-NOTES DIATONIC SCALE , AND IN ANY CASE THE ACCOMPANYING CAN BE ALSO BY THE POWER CHORD AT THE ROOT POSITION OF THE 7-NOTES DIATONIC SCALE IN INSTEAD OF THE 3RD POSITION OF THE DIATONIC SCALE)


THE MORE COMPLICATED BUT NOT  ALWAYS MORE ENLIGHTENING DESCRIPTION WITH MODERN SCALES AND CHORDS: 


We may create such nice loops, of 2 or 3 or more chords and parallel melodic themes as "dolphin words"  with arpeggiator applications in ipad like chordion, dot melody, arpeggist , fugue machine, ioniarics polyrhitmic arpeggiator , touchscaper etc (see post  12 )
We must notice that many application create looping melodic themes that are any sequence of notes, which allows for the loop to be acctually a repeating sequence of smaller melodic thems M1 M2 M3 ...Mn  (or "dolphin words")  one for each chord  C1 ,C2 C3,...Cn ofthe cycle of chords.
We may also utilize chord sequencers or chord progressions sequencer applications

The symbols here mean M=major m=minor ,  dim=diminished , aug=augmented, the numbers 1,2,3,4,5,6,7 are the steps of a diatonic scale (ionian mode).


E.G.

1) 1M


2) 5M7->1M


3) 6m->1M



4) 1M->4M->5M->1M    (Cretan matinodies, kondilies) 
or only 1M (3rd note) ->1M->5M7(5th note)->1M (3rd note)
or only 1M (3rd note) ->1M->1M->1M (3rd note)
e.g. as order of notes in a diatonic scale 
3 3 3 4 3 5 5 5 4  2 3 4 5 5 3
as rhythm from 15-syllables poetry
(1M         )
10010100
(5M7)1M
1001  010
(combination of poetry rhythms of anapestik  100 with trochaic 10 )
In addition to  rhythm, scale and chord progression we need also the statistical profile of the progression of the simplical melodic themes (see post 282) so as to determine the local style of the particular improvisations.
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.


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



Dolphin words (=abstract order patterns of melodies) are beatifully composed with the arpeggiator




5)  5M7->1M7->4M   (Jazz, Celtic folk)


6) 2m7->5M7->1M    (Blues)


7) OTHER TRIAD CYCLES 

One of the simplest cycle of chords is 3 consecutive chords in the cycles of 4ths.

E.g. in the C major diatonic scale

Dm->G->C  (Western Jazz)  (2m-5M-1M) (happy)

G->C->F  (Irish folk)  (5M- 1M- 4M) (happy)

Em->Am->Dm (Eastern folk and latin too)  (3m-6m-2m)  (sad)

E.g.

https://www.youtube.com/watch?v=BgS3zqzIpmU



Bdim->Em->Am  (Eastern Jazz) (7d-3m-2m)  (sad)

other combinations of major M, minor m, diminished d and augmented aug are

d-M-M  (happy)

aug-M-M  (happy)

aug-m-M  (sad)

aug-m-m  (sad)

M-m-m  (sad)

d-m-M (sad)

d-d-M (sad)

d-d-m (sad)

aug-aug-M (sad)

aug-aug-m (sad)

d-aug-M (sad)

d-aug-m (sad)

d-aug-d (sad)

aug-aug-d (sad)

etc

In the next video the next 4 triads are harmonizing the 4 known minor scales

5m->1m->4m =natutal minor (diatonic)

5m->1m->4M= Dorian minor (diatonic)

5M->1m->4M=melodic minor (chromatic)

5M->1m->4m=harmonic minor (chromatic)

https://www.youtube.com/watch?v=kobgAsDZxsw&t=125s

and of course

there are also the combinations

5M->1M->4M =ionnian mode , major (diatonic)

5m->1M->4M

5m->1M->4m

5M->1M->4m

If the triad is harmoni only at one pair we get also the triads

1M->2m->5M7  (blues)

1M->6m->5M7  

1M->3m->5M7  

4-CYCLES

8) 5M7->1M7->6m->4M  (Popular Pop)

(E.G. https://www.youtube.com/watch?v=eObM-tAgeG0&t=1273s )



9) 6m7->2m7->5M7->1M  (Pop music 50s)

(E.G. https://www.youtube.com/watch?v=gUNWjgaJEik&t=50s )


10) 6m->5M->4M->3M (Andalusian cadenza, part of the 1st chromatic tonal cycle as in 10))

(E.G.   https://www.youtube.com/watch?v=Li4izrMnd-I  or https://www.youtube.com/watch?v=2KE48jD5aVw  )

11) 3m->1M->6m->7M7 (flamenco pharaon or tonal 2nd chromatic 4-cycle)

E.g.    https://www.youtube.com/watch?v=BwDJ0e1fssw


12)   6m->4M->2m->3M7   (tonal 1st-chromatic 4-cycle)

E.g. https://www.youtube.com/watch?v=XgJFV5K3NLc


13)   1M->7M7>3m->5M7_1M   (tonal 2nd-chromatic 4-cycle)

14)  
1M->7M7>3M7->6m   (tonal 2nd-chromatic 4-cycle b)




15) CHROMATIC INVERSE OF HARMONIC RESOLUTION PAIRS: DIATONIC SCALE 
In the chords of a diatonic scale, , we may reverse chromatically by 4 or 5 chords any harmonic resolution transition of two chords and this is already a cycle of chords:

E.g,  5M7->1M ,which reversed chromatically as a cycle it is 

1M->7dim->6m->5M7  (or  with 5 chords 1M->2m->3m->4M-5M7)

similarly 

4M->3m->2m->1M7     (or with 5 chords 4M->5M->6m->7dim->1M7 )

and 

6m->5M->4M->3m7    (or with 5 chords  6m->7dim->1M->2m->3m7)

and 

2m->1M->7dim->6m7  (or with 5 chords 2m->3m->4M->5M->6m7)


16) CHROMATIC INVERSE OF HARMONIC RESOLUTION PAIRS : 1ST CHROMATIZATION OF DIATONIC SCALE:  In the chords of the 1st chromatic version of the  diatonic scale, , we may reverse chromatically by 4 or 5 chords any harmonic resolution transition of two chords and this is already a cycle of chords:

E.g,  3M7->6m ,which reversed chromatically as a cycle it is nothing else than the Andalussian cadenza

6m->5M->4M->3M

And also the next such cycles

1M->7M7->6m->5M7  (or  with 5 chords 1M->2m->3M7->4M-5M7)

and  similarly 

4M->3M->2m->1M7     (or with 5 chords 4M->5M->6m->7M7->1M7 )

and 

6m->5M->4M->3M7    (or with 5 chords  6m->7M7->1M->2m->3M7)

and 

2m->1M->7M7->6m7  (or with 5 chords 2m->3M->4M->5M->6m7)


17) MELODIC INVERSIONS OF HARMONIC RESOLUTION PAIRS. 1ST CHROMATIZATION OF DIATONIC SCALE:  In the chords of the 1st chromatic version of the  diatonic scale,  we may reverse MELODICALLY (in other words with chord transitions in relatives relation) by 4 or 5 chords any harmonic resolution transition of two chords and this is already a cycle of chords:

5M7->1M->6m->4M->2m->5M7

or 

5M7->1M->6m->4M->2m->7M7->5M7


18) 3M7->6m->5M7->1M  (4-cycle from 1st chromatic diatonic chord cycle, Andean Music)


5-CYCLES

19) 3M7->6m->2m7->5M7->1M  (5-cycle from 1st chromatic diatonic chord cycle)



20) 6m->2m->5M->1M->4M   (5-cycle ,Most popular Pop)

20.1)  1M->4M->3M7->6m->6M7->2m->1M (Scandinavian folk tunes)


6-CYCLES

21) 3m->6m->2m->5M7->1M->4M  (6-chords diatonic cycle)


22) 6m->2m->5M7->1M->4M->3M7  (6-chords 1st chromatic tonal chords in melodic (relatives) relations).

23) 1M->-6m->4M->2m->5M7->3m->1M  (6-cycle of melodic relations tonal chords)


7-CYCLES


24) 7dim->3m7->6m7->2m7->5maj7->1maj7->4maj7  ( 7-chords diatonic cycle))




25) 6m7->2m7->5maj7->1maj7->4maj7->7M7->3M7

(7-chords 1st chromatic diatonic cycle Jazz, Gypsy Jazz, Beethoven)


26)  6M7->2m7->5maj7->1maj7->4maj7->3M7->6m (Gypsy jazz)

In the next 7-cycles only one of the 3 minor chords or diminished is turned in  to a major chord

24.1)   5M7->1Μ->4Μ->7dim->3m->6M7->2m->5M7  (Scandinavian folk)

24.2)   5M7->1Μ->4Μ->7dim->3m->6m->2M7->5M7  

24.3)   5M7->1Μ->4Μ->7M7->3m->6m->2m->5M7  
24.4)   5M7->1Μ->4Μ->7dim->3M7->6m->2m->5M7  25) 7-chords melodic diatonic cycle (by relative chord transitions)

24.5)   5m7->1Μ->4Μ->7dim->3m->6M7->2m->5m7  (Scandinavian folk with 6M7 and 5m7)

6m->1M->3m->5M->7dim->2m->4M->6m


27) 7-chords melodic 1st chromatic diatonic cycle (by relative chord transitions)



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

28) 7-chords melodic 2nd chromatic diatonic cycle (by relative chord transitions partly mixed with harmonic relations)

1M->6m->4M->2m->7M7->3m->5M7->1M  (3melodic  2harmonic transitions )or


6m->1M->3M7->5M->7M7->2m->4M->6m (6melodic  1 chromatic  transitions )

or 

1M->7M7->3M7->6m->4M->2m->5M7->1M (2melodic  1 chromatic 3 harmonic transitions )
or


1M->6m->4M->2m->7M7->3M7->5M7->1M (4melodic  1 chromatic 2 harmonic transitions )

7-chords melodic-harmonic 2nd chromatic diatonic cycle


or

1M->3m->6m->4M->2m->5M7->3M7->1M (4melodic  1 chromatic 3 harmonic transitions )

or

1M->3m->6m->4M->2m->5M7->7M7->1M (3melodic  2 chromatic 2 harmonic transitions )

or

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

(0 melodic  3 chromatic 5 harmonic transitions )

or

1M->7M7->3m->3M7->6m->4M->2m (or 2M7)->5M7->1M 

(3 melodic  1 chromatic 4 harmonic transitions )

or

1M->4M->3M7->6m->6M7->2m (or 2M7)->5M7->1M 


(1 melodic  1 chromatic 5 harmonic transitions )

or

1M->4M->7M7->3m->3M7->6m-> 2M7->5M7->(5aug)->1M 


(1 melodic  1 chromatic 6 harmonic transitions )

or 

1M->7M7->3m->4M->3M7->6m->2m (or 2M7)->5M7->1M 


(0 melodic  3 chromatic 5 harmonic transitions )

or 

1M->4M->7M7->3M7->6m->2m (or 2M7)->5M7->1M 


(0 melodic  1 chromatic 6 harmonic transitions )

or 

1M->7M7->3m->4M->2m->5M7->3M7->(5aug)->1M


(3 melodic  2 chromatic 3 harmonic transitions)


29) Small 4-chords melodic chromatic tonal cycle

1M->3m->5M->7M7->1M or



30) Small 5-chords melodic chromatic tonal cycle

1M->6m->4M->2m->7M7->1M  or

1M->6m->4M->2m->7M7->3M7->1M  

29) more than 7 chords:

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


31)  Other examples are , the next cycle of chords

 Bdim->Em->Am->Dm->G->C->F 


is a scale of chords of the simple type, that is a connected arc in the wheel of chords by 4ths, and the specifications of diminished, minor or major are set so that the particular scale of chords is also the chords of the major diatonic scale of notes!


Nevertheless we can alter that specification of the chords in which case more than one scale are produced:


B7->Em->A7->Dm->G7->Cm->F  or 


Bm7->E7->Am7->D7->Gm7->C7->Fm or 


B7->E->A7->Dm->Gm7->Cm->F  etc


Or 


B7->E(m)->A(m)->D(m)->G(m)->C->F


The E(m) means either major chord E or minor chord Em etc


The next scales of 7-chords have only two minor chords which complies with a desired ratio of minor chords not more than 1/3 of all chords


B7->E(m)->A(m)->D->G->C->F


B(m)7->E(m)->A->D->G->C->F


B7->E->A(m)->D(m)->G->C->F


B7->E->A->D(m)->G(m)->C->F


B7->E->A->D->G(m)->C(m)->F


B7->E->A->D->G->C(m)->F(m)



Or we may alternate minor major once at odd chords and once at even chords e.g.


B7->Em->A->Dm->G7->C->F->Bb->B7->E->Am->D7->Gm->C7->F->Bb->B7->E 
Larger scales are from 12-chords 


G#->C#->F#->B->E->A->D->G->C->F->Bb->Eb


or 



G#->C#->F#->B->Em->Am->Dm->G->C->F->Bb->Eb




Other simpler scales from chords are of 4 only chords e.g.



G->C->F ->Bdim7 etc


or 


G->C->F ->Caug(or G#aug) etc


or they can be based on wheel by 3rds and alternating minor major relative chords 

e.g. 

G->Em->C->Am->F >Dm->G etc



32) THE GENERAL PATTERN OF CHORD-CYCLES  WITH ALTERNATING CHORD-RELATIONS OF 
CHROMATIC-MELODIC ,CHROMATIC-HARMONIC , HARMONIC-MELODIC , HARMONIC-HARMONIC, MELODIC-MELODIC, CHROMATIC-CHROMATIC CHORD-TRANSITIONS.

This is a progressions X1->X2->X3->...->Xn  where the Xi->Xi+1  and Xi+1->Xi+2 is an alternation of chord relation and  transitions of the chromatic-melodic   , chromatic-harmonic,  melodic-harmonic,  chromatic-chromatic, melodic-melodic or harmonic-harmonic relations. 

Such constant alternating patterns of chord relations somehow determine also that the melodic themes (either within a single chord or within a chord transition), are structured and translated or inverted or expanded with similarly alternating intervals of 2nd, 3rd or 4th/5th. 






THE GENERAL PATTERN OF A CHROMATIC DOUBLE SCALE OF CHORDS 

Here is an alternative way to produce not harmonic scales of chords (based on the harmonic relation of chords) but chromatic scales of chords based on the harmonic relation of chords but which still involve the other two chord relations the melodic and the harmonic 


WE START WITH A CHROMATIC CADENZA OR ASCENZA  in semitones 2->2->1  or 1-3-1 or 1-3-1-1-3-1 in harmonic and double harmonic minor scales,   and we paralel chords rooted on such notes X1->X2->X3->X4 with chords 

Y1->Y2->Y3->Y4, such that the relation of Xi with Yi is either in a relation of being  relative chords (melodic relation of chords) or a 4th apart (harmonic relation of chords

Of course the less total number of different chords that we may use is better and it sounds more familiar if such chords belong to an harmonic personality (diatonic or harmonic minor or double harmonic minor etc).We may use either minor or major chords. 

TRIPLE ALTERNATION OF CHORD-TRANSITIONS

More generally   and we paralel chords  X1->X2->X3->...->Xn  that are in  one of the relations chromatic, melodic harmonic , with chords X1->X2->X3->...->Xn so that the relation of Xi with Yi is always constantly in one of the 3 basic relations  relative chords (melodic relation of chords) or a 4th apart (harmonic relation of chords) .

When playing the scale as progression X1->Y1->X2->Y2->... it is equivalent with having a triple alternation of chord relation and  transitions of the chromatic-melodic   , chromatic-harmonic,  melodic-harmonic,  chromatic-chromatic, melodic-melodic or harmonic-harmonic relations and a third which is variable. 

Such constant alternating patterns of chord relations somehow determine also that the melodic themes (either within a single chord or within a chord transition), are structured and translated or inverted or expanded with similarly alternating intervals of 2nd, 3rd or 4th/5th. 

ETC.



In order to create the melody over such a  cycle of chords we may proceed as follows.

1)We compose 2 or 3  simplicial sub-melodies one for each part of the song ,  with one note per chord, over the cycle of chords preferably at a chromatic sequence ascending and descending . 

2) We create moves or waves for each note of the simplicial sub-melody by sequencing during the chord with two types of notes a fast (usually outside the chord) and a slow of double duration on the notes of the chord again ascending or descending with smaller waves

3) We arrange a continuous sound instrument to play the simplicial sub-melody only and a discrete sound (guitar mandolin etc) to play the full waves melody.



Other determinations of these songs or improvisations;


0) THE HARMONY.

Although the cycle of chords is fixed, the order and duration that these chords are played may vary, from song to song, or even inside the same song ("random" permutation of the chords of the cycle).
E.g. 1M->4M->5M->1M    (Cretan matinodies, kondilies) 
or only 1M (3rd note) ->1M->5M(5th note)->1M (3rd note)
or only 1M (3rd note) ->1M->1M->1M (3rd note)



1) The rhythm:
The duration of the beat is determined by clock-standards. Then each chord of the cycle is determined how many beats has duration. Furthermore, the rhythm is specified as in post 10. Usually, the powers of 2 are utilized. So a triad of chords will have a repetition of a chord in duration. E.g. a cyclic pattern A B C A, of 4 groups of beats so that each chord has equal duration will also determine a variational repetition pattern of the variating melodic themes, usually 3 variations and the last time a resolution.  The melody itself can be classified to the simplicial say in 4 chord-durations, or the normal in 8 chord half durations, or embellishing in 16  chord quarter durations, or fast embellishing  32 , eighths chord durations etc.
Initially, it seems that the rhythm of the main melody was patterned over 15-syllables poetry, with 4+4 beats at the first line of 8 syllables and 4+3 beats at the 2nd line of 7 syllables.
The term mantinodies is quite similar and meanings and methods with the term rhapsody of the ancient poetry of homer (Iliada, Odyssia etc)
E.g. for Cretan mantinodies (condilies)

as rhythm from 15-syllables poetry
10010100
1001010
(a combination of anapestik  100 with trochaic 10 )






2)  The pitch order pattern of the roots of the chords of the chord-cycle.
In general, there are 4 classes:
1)The ascending (happy)
2) The descending (unhappy)
3) The upper cyclic (happily sad),
4) The lower cyclic (sadly happy).

This is a general pitch order pattern which of course has emotional significance: Increasing pitch order in the roots =joy, decreasing pitch order in the roots=sadness.

e.g. as order of notes in adiatonic scale (Cretan mantinodia, condilia)
3 3 3 4 3 5 5 5 4  2 3 4 5 5 3


3) The pitch order pattern of the induced by the melody harpism (permutation) of the notes of each chord.  

Although the part of the melody accompanied by a single chord may have notes outside the chord, it will have also notes of the chord that it is expected that they have a longer duration. Thus this part of the melody induces a permutation or harpist of the notes of the chord.

4) The variational repetition pattern of the melodic themes as part of the melody accompanied by a single chord.



Monday, October 21, 2019

279. A CLASSICAL GROUP OF MELODIC THEME VARIATIONS FOR BEAUTIFUL DIATONIC TONAL MUSIC TRANSLATIONS EXPANSIONS,INVERSIONS MUTATIONS

 A  CLASSICAL GROUP OF MELODIC THEME VARIATIONS FOR BEAUTIFUL DIATONIC TONAL MUSIC. TRANSLATIONS , EXPANSIONS, INVERSIONS, MUTATIONS


THE KEY-WORD HERE IN THE 4TH GENERATION DIGITAL MUSIC FOR THE MUSICAL-THEORETIC IDEAS OF THIS   POST (AS FAR AS MORDEN SOFTWARE FOR MUSIC MAKING IS ) IS MELODY-SEQUENCERS 

THE TERM  SEQUENCER MEANS HERE A LOOP OR RHYTHMIC CYCLE OF   A  MELODIC THEME THAT IS VARIATED INTERACTIVELY BY THE USER  IN A MELODIC SEQUENCER.

THERE ARE MANY GOOD SOFTWARE PROGRAMS FOR THIS COMPOSITION AND IMPROVISATION LIKE FUGUE MACHINE, YAMAHA MOBILE SEQUENCER, THUMPJAM ETC

By studying e.g. the art of Vivaldi melodic themes variations (but other folk music too, e.g. Celtic and Irish music), we can directly get the idea of a nice finite group of melodic themes transformations. We use of course the term finite group in the standard mathematical algebraic meaning of a set of transformations closed to composition and inversion. The transformations  are most often  tonal translations (in other words shifting the melody inside the diatonic scale and preserving the nature of intervals as 2nds, 3rds, 4ths, 5ths etc). From the mathematical algebraic point of view such a finite group has a finite set of generators and a  finite set of defining relations for the presentation of the group (https://en.wikipedia.org/wiki/Presentation_of_a_group).

And the group of such transformations are of course 
1) Tonal translations by 3rds (melodic translation) , 5ths or 4ths (harmonic translation) , when we ae inside the accompanying of a single chord (but also in different chords related melodically or harmonically to the first) And by 2nds (chromatically) which requires usually changing the underlying chord too. This tranasformation includes the  Harmonic Complementation (Blue Shaffling). If the instrument is harmonica tuned as a Zamponia panflute (double row of odd-even notes of a diatonic scale, called also cyclic tuning, or melody king tuning) we have an additional variational transformation that we may call complementation (Blue shuffle) . E.g. if the melodic theme has notes 1,1 , 2, 3,3 a complementation of it would be to inverse even with odd numbers e.g. 2,2,3,4,4 etc

2) Tonal inversion . It is an inversion of the pitch order of the notes of the melodic theme which results in melodic theme again inside the initial diatonic scale. Besides the pitch-inversion there is of course also the time-inversion of the melodic theme, which is a different concept.

3) Tonal expansions-contractions: It is when we keep an initial part of the melodic theme fixed while expand or contract the rest of it , but always resulting again inside the initial diatonic scale. E.g. the initial melodic theme over chord A maybe within ione octave and when we translate it to fit the next chord B we also expand it to span 2 octaves. 

 The statistical frequency of such tonal translations is at least 2/3 of the times by intervals of 3rds and 5ths/4ths (melodic and harmonic tonal translations) and at most 1/3 of the time by intervals of 2nds (chromatic tonal translations). A more tolerating quantification would be to require that the statistical frequency of such tonal translations is at least 50% of the times by intervals of 3rds and 5ths/4ths (melodic and harmonic tonal translations) and at most 50% of the time by intervals of 2nds (chromatic tonal translations).

In the formation of such group of variations of melodic themes and in creating such nice melodies and music we utilize of course the closure properties of the diatonic scale in shifts by intervals of 3rds, and 5ths or 4ths. (Which is also a good opportunity for the reader to refresh and re-discover. E.g. For every note of the diatonic scale there is an interval of 3rd and of 5th or 4th such that up or down of the note and away by that interval it is again a note of the diatonic scale). So that such variations create cycle of melodic themes that repeat.

The above group of variations of the melodic theme can be both in the context of tonal music but also in the context of chromatic tonal music as in the post 263

As we mentioned in post 263  the order of the chromatic notes 5#, 4#, 1# , 2#, 6# would give the next order of altering majors to minors or vice versa

3 minor ->3 major or 4 major->4 minor (for 5#) 
2 minor-> 2 major (for 4#)
6 minor -> 6 major (for 1#)
1 major-> 1 minor (for 2#)
5 major-> 5 minor (for 6#)

Boldly speaking, the topological shape of the melodic themes are of three  kinds:
A) Oscillations (arpegios of a chord or vector-chord)
B) Up or down Continuous Moves 
C) Discontinuous  jump (Spike) by an interval of 5th/4th or larger.

THE DIATONIC-GUITAR OR HARMONICA-GUITAR  AS IN POST 90 HAS A DIRECT ADVANTAGE OF APPLYING THE CLASSICAL GROUP OF VARIATIONS OF MELODIC THEMES AS DESCRIBED IN THIS POST  (TONAL TRANSLATIONS BY 3RDS AND 5THS OR 4THS IN AT LEAST 2/3 OF THE CASES AND CHROMATICALL IN AT MOST 1/3 OF THE CASES). THE MELODIC THEME SUCH TONAL  TRANSLATION BY 3RDS OR 5THS/4THS IS SIMPLY SHIFTING THE MELODIC THEME FROM ONE STRING ON THE SAME FRET  VERTICALLY TO  THE ADJACENT STRING ( A 3RD) OR NEXT TO ADJACENT STRING (5TH OR 4TH). (SEE POST 90).

See also about chromatic inversion  (pitch inversion)

https://www.youtube.com/watch?v=0oI2iFrzA0o

Thursday, September 19, 2019

278. THE Eb MAJOR OR C MINOR 4-DOUBLE STRINGS GUITAR


This variation of the guitar is with double strings. Nevertheless none of the double strings are of the same frequency or pitch but one or two octaves difference. The reason that it is  so is that the slight deviation from the original tuning during playing (especially when tis t many hours playing) is not creating an irritating  dissonance. The one o two octaves difference guarantee  that such deviations are  middle and do not created acute dissonance. In addition the innovation of two -octaves difference in the 2 lower pitch courses creates a very sweet sound.

Further innovation is  that the tuning is not like the 4 higher double strings,  say of a 12-string guitar, but as the harmonic guitar in post 90. In other words alternation of minor and major thirds, exactly as in  diatonic scale , that create chord triads. This tuning is an open tuning.

In detail the tuning is 

C2C4-Eb2Eb4-G2G3-Bb2Bb3. 

Thus it is an open Cm7 

So  this guitar has lower note the C2 as the Cello and some Arabian Uds.


The choice of the scale Eb major (or C minor) as privileged scale is so as to fit well with the lower registry of the Boehm clarinet in Bb, which nevertheless at the lower registry sounds in Eb.

Because the guitar is tuned one major 3rd lower with the same strings of a standard guitar, the pressing of the strings in the frets is softer, that a standard 12-string guitar. Furthermore  the impedance of the vibrations is lower as in the saz which is usually longer, but of low string tension. 

As the Eb diatonic scale has only one flat difference from the Bb diatonic scale, this guitar is accompanies  preferably Jazz music that utilizes , trumpet or cornet in Bb, Saxophones in Bb and clarinets in Bb. But such instruments are also used in folk music of various cultures (e.g. Greek folk music) therefore is suitable for such music too.

This tuning is optimal in the sense that it has the maximum number per frets (maximum density) of triad-chords (3-strings chords, major , minor , diminished augmented ) .

The lower 3-strings give naturally sequence of  triad-chords of the Aeolian mode (Cm) of the  Eb and the higher 3-strings naturally sequence of triad chords of the Ionian (major) mode.



In the next pictures is seen, the body of a  12-string guitar which has been converted to a 4-double strings 8-string guitar, with the above tuning.

A more natural solution would be to utilize the bodies of 4-double strings tenor guitars (used mainly in jazz as arc-top tenor guitars) and tune it as above








Monday, September 9, 2019

276. ALTERNATING HAPPINESS AND SADNESS IN SLOW MELODIC IMPROVISATION BY ALTERNATING MAJOR MINOR INTERVALS OF 3RD. THE ANCIENT 2-VOICES HARMONY:CELTIC MINOR AND MAJOR 6-NOTES SCALES

See alo post 208

MELODIC TRIADS: SOLO COMPOSITION AND IMPROVISATIONS BASED ON ALTERNATING (MELODIC TRIADS AS  VECTOR) INTERVALS OF MAJOR(HAPPY) /MINOR(SAD) 3RD:RECIPES OF HAPPINESS AND SADNESS

THE 2-VOICES HARMONY:

HERE IS EXAMPLE OF SUCH  IMPROVISATION

https://www.youtube.com/watch?v=Hxym5yTmdC8&t=1420s

When improvising is a solo in an almost random way in a diatonic or more general scale but who tries to listen also to the inner emotions, a good path is to walk by intervals of 3rd and alternate  major (4 semitones happiness ) and minor (3 semitones, sadness ) exactly as it happens in a diatonic scale, as this also creates an underlying  major or minor chord. If on the other hand it is two consecutive intervals of minor 3rd it would create an underlying diminished chord and if consecutive major intervals of 3rd an augmented chords (that occur in the harmonic and double harmonic minor) , both more  rare compared to major and minor chords. 

In a diatonic scale only in one place two consecutive intervals of 3rd are minor.

This type of walking intervals or vector-intervals (=intervals with all intermediate notes in a diatonic scale, see also post 183 1nd 159) In other words intervals closed together with all the intermediate notes of a diatonic scale that it belongs to it we have called previous post as vector-chord improvisation as contrasted to arpeggio improvisations.

Therefore instead of the concept of scale (and as here we do not assume a chord progression or scale of chords) we have the concept of TRIAD  as vector interval of 3rd MINOR (SAD) OR MAJOR (HAPPY) By composing triads we get various types of scales known or unknown but with recognizable hidden harmony.
OF COURSE WE MAY VERY WELL WALK BY TRIADS IN A DIATONIC SCALE GIVING SEQUENCES OF MAJOR (HAPPINESS) AND MINORS (SADNESS) 3RDS IN THE PROPORTION AND COMBINATION WE WANT.
KNOWING THIS IN MAJOR-MINOR 3RDS WE ALWAYS KNOW WHERE TO FIND HAPPINESS AND MORE HAPPINESS AND SADNESS AND MORE SADNESS.


Thus these "recipes" of happiness (+) and sadness(-) would look like thsi

+++--+----++----+-+- etc

BECAUSE THE COMPLEXITY OF THIS 2-VOICES HARMONY IS LOW, IT IS SMORE CLEAR THAT ITS SIMPLICITY IS A LEVERAGE ONLY TO THE INNER FLOW OF NEW SEQUENCES OF EMOTIONS. SO IT IS MORE THAN  50% INNER FLOW AND LESS THAN 50% EXTERNAL FLOW OF MUSICAL SOUNDS.


THE HAPPY ENHARMONIC CELTIC MAJOR  6-NOTES SCALE

In a diatonic scale there are 3 intervals of major 3rd 1-3, 4-6 , 5-7 (e.g. in C major C-E, F-A , G-B) and 4 minor 2-4, 3-5, 6-1, 7-2. If we want a  scale with more happy intervals of 3rd (major) than sad (minor) then should start with the 3 major 3rds 1-3, 4-6 , 5-7, and create the 6-notes enharmonic generation scale 

1-3-4-5-6-7-1 (e.g. in C major C-E-F-G-A-B-C) with interval structure

4-1-2-2-2-1  

WE may call it the happy enharmonic CELTIC MAJOR 6-notes scale

Also in Japanese folk music are used a few enharmonic gendre 5-notes scales with more intervals of major 3rd than minor 3rd.

There is  of course the Celtic Minor scale which can be derived by the 3 minor 3rd intervals of the diatonic scale 2-4, 3-5, 6-1 or in C major

C-D-E-F-G-A-C with interval structure 2-2-1-2-2-3 (see also post  204 )



Inharmony a chord is a triad, and triads of chords define usually in  a minimal way the harmony of a scale. Similarly here in melodic composition, the basic composition element is a melodic triad as above, and and triads of melodic triads define somehow an scale of an octave.

The usual  triads  are the next 3 in semitones

1-2
2-1
2-2
  giving in total  semitones 3 or 4 or an interval of  3rd




Of course we add wavings by intervals of 2nd and we go up or down according to the alternation of sad and happy changes of the emotions. The major/minor 3rds alternation also corresponds to alternation of sad and happy emotions. We may of course alternate to the solo also triad chords. If we are on string instruments tuned by 5ths, then we can also accompany this solo with the interval of 5th of the two immediately lower strings as a kind of power-5 chord. The melodic themes created in one or two consecutive such (vector) intervals of 3rd can be varied of course with translations, inversions, rotations (including expansions)  and mutations.
Normally two triads are for the first poetic line (8 beats) and two more for the 2nd poetic line (7 syllables).

If we do not walk the intermediate notes of the vector interval of 3rd and we just jump-play it, alternating major minor such intervals of 3rd we are simply in t what we have called in post 94 the melodic corridor, which e.g. how the siku pan-fludes and pan--flutes with double rows of pipes are designed in the folk music of andes.

In composing  melodic themes based on melodic triads we should use also the concept and technique  of  variational  independent base of melodic shapes or melodic seed (see post 106). I other words the melodic themes shapes that are mutually variational independent, in other words neither translation neither , inversion, neither rotation can derive any one of them from the others , and in addition all other melodic themes oft he song can be derived with variations from them.

We should not confuse the melodic triads, which is a concept similar to that of  a scale of notes with the shapes of melodies in a melodic triad (as e.g. in post 100-106).


AGAIN THE BEST INSTRUMENT TO PLAY SUCH IMPROVISATIONS IS THE CELTIC HARP! THE NEXT BEST IS PAN-FLUTES (SAMPONIA) AND SINGLE TUBE WINDS

Friday, September 6, 2019

275. A METHOD OF LEARNING INSTRUMENT PLAYING, IMPROVISATION AND SONG ADOPTIONS-RECOMPOSITIONS BY WHISTLING OR SINGING PARALLEL TO A RECORDED SONG ,


   A METHOD OF LEARNING   INSTRUMENT PLAYING,  IMPROVISATION  AND SONG ADOPTIONS-RECOMPOSITIONS  BY WHISTLING OR SINGING PARALLEL TO A RECORDED SONG , 

HERE IS EXAMPLE OF SUCH A MUSIC

https://www.youtube.com/watch?v=Hxym5yTmdC8&t=1420s

(see also post 128)

Now one could imagine a process in learning an instruments at the same time leaning improvisation For example let us take any one of the instruments below

0) A percussion instrument
1) A Guitar or ukulele
2) A Celtic Harp
3) A Bowed string instrument like Greek Lyra (or fiddle)
4) A diatonic Pan-Flute or a chord or bass harmonica
5) A single tube wind with the fingering system 6+1. E.g.  Irish whistle, flute , or reed instrument like clarinet saxophone , duduk, chalumeau  etc

 The central idea is of course that the versatility of playing a musical instruments is based on the ability to internalize and perceive mentally and emotionally the musical sound  and improvise (mimic, assimilate, innovate) rather than the ability of concentrating separately to technical skill of geometric patterns of playing for the particular instrument And one of the simplest ways to perceive musically harmonically , melodically and chromatically,  all the universe of the 12-notes is the chromatic tonality (as in post 263) (see post 258 that improvisation is at least at 2/3rds an internal feelings and intellect meditation process rather independent from the musical instrument played! The 2/3ds are of course the mental perception of the musical sound and the feelings-emotional  perception of the musical sound, and not the geometric instruments pattern of the musical playing! And one of the simplest ways to perceive musically all the universe of the 12-notes is the chromatic tonality (as in post 263) ).

Here in the next video, the guitar teacher explains why it is simpler for the human nervous system to concentrate on the mental and emotional perception of the musical sound rather than on  the geometric patterns of playing the particular instrument.

https://www.youtube.com/watch?v=iacQvKMSx6A


So a daily or weekly process and practice could be nowadays as follows:

1) Chose in youtube a nice and happy song that you would like to listen and play. Better be happy rather than sad , as such a learning should raise our bodily frequency and should be laso a learning of how to be happy within the good joy (not the bad joy). E.g. it might be an early jazz song like those that the  carling family are playing and enjoying. If we do not want to start with a known song in youtube, he may start by playing and recording in Audacity a rhythm by a percussion instrument, and then use this as a base.

2) Derive an mp3 file from the youtube-video, and analyze it with the free software Audacity (or a similar) to verify by its chords that it is a chromatic tonality music song (see post 263 ) 

3) Try singing its melody (improvisationally) or whistle  (improvisationally) its melody. THIS IS PROBABLY THE MOST IMPORTANT STEP IN LEARNING ALL THE INSTRUMENTS SIMULTANEOUSLY.



3.2) COMPOSITE PRACTICE OF IMPROVISATION , REMIX -ADAPTATION OF A SONG AND INSTRUMENT PLAYING.
This ability can be activated as follows: At first listen for some weeks to nice songs preferably Jazz songs and familiarize with their melodies harmonies and techniques. Start with early jazz which is simpler and utilizes the triads of chords 1-4-5 or 1-2-5 etc. The preliminary stage of education of the subconscious determines also the speed of creations of emotions and feelings when improvising. It is important that the speed of actual musical improvisation is not faster than the speed of creation and shaping of the emotions and feelings. In different persons it is different speed.


3.2.1) Besides trying to whistle the melody , it can be tried to whistle a simplicial coutermelody of the melody (see post 289)

Listen them with one only earphone, leaving the other ear open and sing or whistle parallel to the melodies of the song, inspired or stimulated on the occasion of the written and listened song. The whistling improvisation may nevertheless deviate not only from the listened melodies but also from the listened chords and harmony, if the feelings require so. This is an important factor of the improvisation as melodic or harmonic "errors" in whistling a melody most often turn out to be improvements of the melody based on our own memories of nice melodies and inclinations in the feelings. General rules that two parallel melodies fit harmonically together as described in post  128, require only that the number of intervals of 3rd, 4th 5th and 8th are more than 50% compared to intervals of 2nds. In addition alternating with this whistling or singing we may  play on a  desired instrument similar melodies. 
 We may go as far as utilizing this method as a method of creating adoptions or remix of a  song. This requires that the improvised melody will fit only to a percentage x%<50% with the parallel sounding song and the rest 100%-x% the melody , rhythm and chords will not fit and will be the innivated adoption of the song (according to our inner emotional impulses and habits) . Of course the overall  result of the underlying song and its adoptoion will not be audible with good feelings as they will be incompatible , but the intention is to be inspired in real time by the song and create in real time an adoption of it. Finally oly the adioption will be presented not the parallel initialinspiration. 
Depending on the acquired skill on the instrument, the improvisation may be poorer or same rich as the whistling. Furthemore instead of only listening to the song, if opened in a software like  Audacity where its chords can be found and displayed below the waveform, we see also the underlying chords and we learn to associate the whistling or instrument playing ofthe melodies with the underlying chord progression. We keep doing it not only so  as to get pleasure but also to improve improvisation and playing skill on the prefered instruments.
The speed of improvisation must not be faster that the speed of creation of emotions prior or after the musical sound.

The speed of conducting the improvisation may be increased if while we improvise we pretend that there is a mandarin (fruit) flying a few centimeters above the top of our head and we look and listen and conduct the improvisation from that point in air or aether rather than from our hands or mouth.

3.2.2) 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.

4) Start with the  known instrument or easiest instrument that here we  will assume that it is the guitar or ukulele or a wind etc. Play its chords rhythmically and improvise melodically whistling or singing simultaneously as in 3.1).

5)  Make sure that if e.g. you play the Celtic harp (which is a diatonic instrument ) is tuned at the right central diatonic scale of the song Usually Bb, or F , or G , or C etc Play the chord and improvise the melody with the right hand . Alternate chords and melody with the right hand. The melodic improvisation could be very close to the whistling improvisation. Use the left hand for an isocratic  bass line based on simple 2-voices harmony  (usually an interval of 3rd). It could even be the power-5 chord ofthe scale. Or it could be just one note per pentachord or tetrachord at the bass area.

6) If you feel comfortable and satisfied with the result,  record the improvisational playing separately each one upon the previous in Audacity to produce a sound file. Elaborate a bit and on the recording and maybe correct some volume, timing or even pitch imperfections. The idea is to be excellent in creativity , learning and enjoyment rather  in formal perfection. Then  publish it in youtube or facebook in a group of well meaning favourable friends, if you feel so, or simple keep it in your databases.


10) The above process 3)- 6) can one play by not starting with a known song in youtube, but by free improvisation directly from our emotional subconscious.
If we do not want to start with a known song in youtube, he may start by playing and recording in Audacity a rhythm by a percussion instrument, and then use this as a base.

See alo post 208

A practice that would implement also instruments is the next

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

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, 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.
5) Then we repeat the whistling simplicial counter-melody with the chosen instrument

6) 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  the with the simplicial counter-melody and consider that we actually we laer a simplicial counter-melody for thsi song rtaher than that we learn  the particular instrument that we play). See also post 271.

MELODIC TRIADS: SOLO COMPOSITION AND IMPROVISATIONS BASED ON ALTERNATING (MELODIC TRIADS AS  VECTOR) INTERVALS OF MAJOR(HAPPY) /MINOR(SAD) 3RD:RECIPES OF HAPPINESS AND SADNESS

When improvising is a solo in an almost random way but which tries to listen also to the inner emotions, a good path is to walk by intervals of 2nd small distances of total length an interval of 3rd and alternate  major (4 semitones happiness ) and minor (3 semitones, sadness ) exactly as it happens in a diatonic scale, as this also creates an underlying  major or minor chord. If on the other hand it is two consecutive intervals of minor 3rd it would create an underlying diminished chord and if consecutive major intervals of 3rd an augmented chords (that occur in the harmonic and double harmonic minor) , both more  rare compared to major and minor chords. 
This does not mean that we create a specific diatonic scale or mode of it but rather pieces of diatonic scales, therefore it is more probable that we are in a bebop scale (union of two diatonic scales).

This type of walking vector-intervals (see also post 183 1nd 159) in other words intervals closed together with all the intermediate notes of diatonic scale that it belongs to it we have called previous post as vector-chord improvisation as contrasted to arpeggio improvisations.

Therefore instead of the concept of scale (and as here we do not assume a chord progression or scale of chords) we have the concept of TRIAD  as vector interval of 3rd MINOR (SAD) OR MAJOR (HAPPY) By composing triads we get various types of scales known or unknown but with recognizable hidden harmony.
OF COURSE WE MAY VERY WELL WALK BY TRIADS A DIATONIC SCALE GIVING SEQUENCES OF MAJOR (HAPPINESS) AND MINORS (SADNESS) 3RDS IN THE PROPORTION AND COMBINATION WE WANT.
KNOWING THIS IN MAJOR-MINOR 3RDS WE ALWAYS KNOW WHERE TO FIND HAPPINESS AND MORE HAPPINESS AND SADNESS AND MORE SADNESS.
Inharmony a chord is a triad, and triads of chords define usually in  a minimal way the harmony of a scale. Similarly here in melodic composition, the basic composition element is a melodic triad as above, and and triads of melodic triads define somehow an scale of an octave.

The usual  triads  are the next 3 in semitones

1-2
2-1
2-2
  giving in total  semitones 3 or 4 or an interval of  3rd




Of course we add wavings by intervals of 2nd and we go up or down according to the alternation of sad and happy changes of the emotions. The major/minor 3rds alternation also corresponds to alternation of sad and happy emotions. We may of course alternate to the solo also triad chords. If we are on string instruments tuned by 5ths, then we can also accompany this solo with the interval of 5th of the two immediately lower strings as a kind of power-5 chord. The melodic themes created in one or two consecutive such (vector) intervals of 3rd can be varied of course with translations, inversions, rotations (including expansions)  and mutations.
Normally two triads are for the first poetic line (8 beats) and two more for the 2nd poetic line (7 syllables).

If we do not walk the intermediate notes of the vector interval of 3rd and we just jump-play it, alternating major minor such intervals of 3rd we are simply in t what we have called in post 94 the melodic corridor, which e.g. how the siku pan-fludes and pan--flutes with double rows of pipes are designed in the folk music of andes.

In composing  melodic themes based on melodic triads we should use also the concept and technique  of  variational  independent base of melodic shapes or melodic seed (see post 106). I other words the melodic themes shapes that are mutually variational independent, in other words neither translation neither , inversion, neither rotation can derive any one of them from the others , and in addition all other melodic themes oft he song can be derived with variations from them.

We should not confuse the melodic triads, which is a concept similar to that of  a scale of notes with the shapes of melodies in a melodic triad (as e.g. in post 100-106).

 The way that an improvisation not based on a played song can be composed is with various methods:

AS IS THE CASE WITH ORGANIZATION STRUCTURES OF VARIOUS ORDERS OF DEPTH LIKE MUSIC AND ITS ORGANIZATION, THE IMPROVISATION CAN BE AT
 THE LOWEST LEVEL: 1) MELODIC ONLY (start with winds, or harp ar guitar , ukulele, with this order see e.g. post 266, 224)
AT A LOW LEVEL : 2) 2-VOICES OR PAIRS OF SIMULTANEOUS NOTES IMPROVISATION , (mainly harp but also guitar, ukulele, E.g. see posts 260 ,82)
AT A MIDDLE LEVEL: 3) CHORDS AND MELODY IMPROVISATION (Harp, or guitar , ukulele, e.g.see post 9 . Of course the closest to happy early Jazz songs is to use triads of major chords and in particular 1-4-5 of the Bb or F major scale, and then extend them possibly with chromatic tonality . See post 263 ).
AND AT A HIGH LEVEL : 4) MORPHOLOGICAL REPETITIONS PATTERNS OF PARTS OF THE PIECE  IMPROVISATION (on any instrument e.g. see post 203, 201)

I believe the most successful order is to start with the chords, and in particular a triad of major chords and in particular 1-4-5 of the Bb or F major scale, and then extend them possibly with chromatic tonality as in  post 263 with minor, diminished and augmented chords but not more than 1/3 of the total time and only if the whistling improvisation suggests it. The next simple idea in improvisational harmony is an harmonic linear progression of major/minor chords by intervals of  4ths. Then improvise fully by singing or whistling melodies on them and pass this whistling gradually to the rest of the instruments. 

The improvisation of each instrument with the chosen order, starting from the rhythm of the percussion instrument, is recorded (e.g. in Audacity) , and the next instruments are played at first live with a background from the speakers or earphones (like karaoke) from the previously recorded instruments, and then are recorded also with the rest of the recorded instruments. The final result as an .mp3 or .wav file is it is liable and satisfying is published a group friends or simply kept in nono-publishing data bases.

If he is lucky he might find some friends and try a group improvisation where he is playing in sequence some of the instruments he is learning or practising.

We remind here why in learning simultaneously many instruments it is by far better the improvisation method than reading a musical score.

THE ADVANTAGES OF IMPROVISING A MELODY VERSUS PLAYING A MELODY

PLAYING THE MELODY

DISADVANTAGES: 1) No sufficient space to interpolate  your own feelings parallel to the melody
                                   2) Rigid stereotypic repetition  , that the slightest deviation will cause the                                                feeling of an "error" or "bad sound". This will create fear and will "slauter" the "wings" to add your own "signature" to the melody. It will stop  also and suppress the ability to compose your own melodies.

ADVANTAGES: 1) You do not have to involve much of your emotions and creativity , after learning it it seems easier to repeat it each time and if the melody is played correctly it is expected by the audience to to appreciate it.


IMPROVISING THE MELODY:

ADVANTAGES:1) Plenty of free  space to interpolate  your own feelings parallel to the melody
                                   2) No rigid stereotypic repetition , each time played it is somehow different . The randomness of the decorative notes of the improvisation allows for searching the appropriate melodic center that corresponds to the intended emotion or for gradual correcting till the melodic center of the original melody is found  (in the scale stepwise glissando as default movements) This will create an euphoria of abundance of creativity and will multiply the ability to compose your own melodies in later times.

DISADVANTAGES: 1) It requires listening to your own mood (or the mood of the  audience) when improvising the  melody, and there is always the risk that the current version of the improvisation of the melody is not good enough compared maybe to previous improvisations or that the audience will not appreciate it enough as you appreciate it when your are improvising it.



IN OVER ALL IT IS OBVIOUS THAT IMPROVISING A MELODY IS BY FAR MORE ADVANTAGEOUS THAN JUST PLAYING THE MELODY.