469. FELLINGS OF TRAVELLING MOTION AND THE EMOTIONS IN A MELODY

CHROMATIC=BY LAND OR STANDING

MELODIC= BY SEA OR MOVING

HARMONIC=BY AIR OR FLYING

468. HOW TO SYMBOLIZE CHORD TRASITIONAL CHROMATIC ARPEGGIOS (OSTINATOS) SO AS TO MODULATE THEM IN NEXT CHORD TRANSITIONS

 If 1,1#, 2, 2# ,......7, 1 is the full 12-notes chromatic scale based on a 7-notes diatonic scale, and

a1, a3 , a5 , a7 is the first chord C1 while 

b1, b3, b5, b7 is the 2nd chord C2

The transitional chromatic arpeggio is a choice of notes some from the first line and some of the 2nd line of the

C1: A1, a2,A3 , a4, A5 ,a6,  A7 

C2:  B1, b2,  B3, b4, B5, b6, B7

capitals are inside the chords small outside the chords. 

Such a pattern applies by substituting different chords transitions C1->C2.

467. WHAT IS THE SYSTEMATIC RE-HARMONIZATION OF A SONG BY GYPSY JAZZ? IT IS THE RELATIVIZED HARMONIC REFINMENT.

WHAT IS THE SYSTEMATIC RE-HARMONIZATION OF A SONG BY GYPSY JAZZ? 

IT IS THE RELATIVIZED HARMONIC REFINMENT.

RELATIVIZED HARMONIC REFINMENT= 

1) We substitute a major chord X, with an harmonic pair (Y1,Y2) (harmonic pair means that Y1, Y2 have a distance at the roots an interval of 4th, that is Y1 resolves to Y2, so that usually Y1 is a chord with a 7nth) 

2) and so that either Y1 or Y2  is relative to X  (melodic relation which means the roots or middle note have a distance an interval of 3rd ) including the case Yi=X, and including 2nd relative (same root but the one major the other minor chord) , 

3) And the other chord to the relative can be major or minor.

An example is converting the chord progression 

4M  1M  5M7 1M as a cycle , to the gypsy jazz re-harmonized chord progression as a cycle 

(2m, 5M7), (1M, 4maj7), (7dim7, 3M7) , (3m, 6M7). 

(See also post 466) 

466. SUBSTITUTING THE CLASSICAL HARMONIC MINOR PROGRESION 2m 6m 3M7 6m with the Harmonic 7 cycle (2m 5M7) (1M 4maj7) (7dim7 3M7) (6m 6M7).

 Example  the reel  Beatrix by Sharon Shannon. 

465. THE MAJOR-MINOR INDIFFERENCE RULE IN (12 BARS) BLUES IMPROVISATION

 According to this rule, the melodic improviser so as to improvise may assume either a major or a minor or both  scale over the 3 chords of the blues.

https://www.youtube.com/watch?v=C8EAAVxvB4A&ab_channel=JamesHargreavesGuitar

464. THE CHORDS SCALE INDEPENDENCE RULE IN (12 BARS) BLUES IMPROVISATION.

     According to this rule, at each change of a (major) chord in the blues, the melodic improviser assumes a change of the scale too with root note the root of the (major) chord! Thus he makes 3 transpositions

Actually this rule may go far beyond  the 12 bars blues, to any chord progression!

https://www.youtube.com/watch?v=C8EAAVxvB4A&ab_channel=JamesHargreavesGuitar

463. THE PASSEPARTOUT OF IMPROVISATION AND COMPOSITION . RHYTHMIC PATTERNS HARMONIC TRANSITIONS AND MELODIC SHAPES INVARIANTS.

 Since the most detailed ontology is at the melody, then the 3 invariants (rhythmic, harmonic, motion shape) occur as invariants of the melody too. 

For years I have been looking for the most comprehensive and convenient concept for improvisation and composition from the simplest to the most complex ie starting from rhythm then harmony then melody. I had found it parts but not in total. Listening to a young street musician explaining how she improvises a steel percussion instrument called hand pan that plays also melodies, she flashed my intuition. ....the most comprehensive concept is something very well known in mathematics and geometry ......

https://www.youtube.com/watch?v=PEuwaKR0cbY&t=50s&ab_channel=AmyNaylor-HandpanConnect

It is Felix Klein's Erlangen program idea that every 

geometric structure is defined by the group of 

transformations that leaves it invariant.

Here that every musical structure is defined and created 

by the rhythmic harmonics and melodic invariants of their 

variations......

This girl said about  the repetition of the invariants in 

improvisation: "repetition is your friend".

I called the description of this in the context of music the 

PASSEPARTOUT of musical improvisation and 

composition.

You keep one of the 3, rhythmic pattern harmony 

(chords transitions)  melodic shape fixed and change 

the other two and thus you create the music, 

 provided the emotion approves it.

You keep the rhythmic pattern constant and change 

the melodic shape or the harmony (chords transitions) 

You keep the harmony (chords transitions)  constant and 

change the rhythmic pattern or the melodic shape

Keep the melodic shape constant and change the rhythmic 

pattern  or harmony (chords transitions).

462. VECTORS, WAVES AND SPIKES IN DIATONIC CHROMATIC OSTINATOS

 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)

461. ABOUT THE RHYTHM OF MELODIES

 https://www.youtube.com/watch?v=WTj-b6oD-Ks&ab_channel=HackMusicTheory

https://www.youtube.com/watch?v=TbDUsEmbsPw&ab_channel=HackMusicTheory

460. WHEN COMPOSING THE CHORD PROGRESSION AFTER COMPOSING THE MELODY IT IS ALWAYS IMPORTANT TO IDENTIFY AT FIRST THE SCALES OF THE MELODY.

459. THREE MODULATED CHORD PROGRESSIONS OF ANY MELODY

https://www.youtube.com/watch?v=kr8XbNHk5QA&ab_channel=SoundGuitarLessonsWithJared

SIMPLICIAL SUBMELODY =1 5 1 4 1 

The 3 chord progressions

1M 5M7 1M 4M 1M

6m   3m  6m  2m  6m

4M  1M  4M   7dim  4M

Actually at least 5^3=125 alternative chord progressions for the melody

We can infer that for any harmonic pair of successive notes of the simplicial submelody n1, n2

The corresponding chords are either a) in harmonic relation  majors b) in harmonic relation minors

c) In melodic relation from minor to major d) In melodic relation from major to minor

Therefore emotionally the harmonic transition of 2 successive (consecutive)  chords of 2 successive (consecutive) notes of the simplicial submelody are one of the 4

1) happy to happy (harmonic transition)

2) sad to sad  (harmonic transition) 

3) sad to happy (melodic transition)

4) happy to sad  (melodic transition).

458. PLAYING ANY DIATONIC SCALE MORE CONVENIETLY (MAXIMAL SYMMETRY) FROM ITS MYXOLYDIAN MODE ON 3 STRINGS AND 6 FRETS

 

457 . HARMONY PASSEPARTOUT : IMPROVIZATIONAL RANDOM WALK OF HARMONIC PAIRS OF CHORDS . THE CHORDICASTER (INSPIRED FROM THE MUSIC OF I. ALBENIZ)

 

1) Each harmonic pair (Xi,Yi) is usually alternated many times. This may be with an arpeggio type or more general chromatic arpeggio too (ostinatos). 

Thus the melody are cycles with 2 melodic scales defined by each of the chords, with starting and ending persistent note on one of the notes of the chords

If the alternation of the chords of the harmonic pair is fast , the the melodic cycle is of diameter an interval of 4th or 5th. Otherwise it even can be longer than an octave.

2) We may have modulations (mode changes inside the diatonic scale) , but we make have transpositions also (translation of diatonic scale) 

3) But the transpositions are of a local character. In other words chromatic, or melodic or harmonic

of the minimum intervals (2nds not 9th-10ths, 3rds not sixths) . 

4) We may very well apply the "partida trick" when  alternating the chords of the harmonic pair, and use as drone the repetition of  their common note. In this way we may cycle  with diameter a whole octave!

5) Practically the length of such random paths of harmonic pairs must  not be very long, so as to fall in the listening habits of harmony. E.g. up to 3 diatonic scales transpositions that give the full chromatic tonality (all 5 blue notes) as in the folk music of Brazil. But for special compositions they can become long cycles covering 12 root notes etc. 

6) The choice of the "state" being an harmonic pair gives high percentage of harmonic transitions in total for the chord progression, making it more beautiful. If the pairs (Xi,Yi) are not harmonic but melodic or chromatic, the chordicaster is called melodic or chromatic. In Latin music dominate the harmonic chordi-casters. In Scandinavian music exist also melodic chordicasters. And in Mediterranean music but also Irish music exist also chromatic chordi-casters. 

Mathematically as improvisation it can be considered a stochastic Markov process, with states , that are  the harmonic pairs, and transitions that are  chromatic (interval of 2nd) , melodic (interval of 3rd) or harmonic (intervals of 4ths or 5ths) shifts of them. 

From 12 bars blues, to Keith Jarrett's Ostinatos , and Iannis Xenakis random music, etc this idea is the abstract mathematical and algebraic formulation. 

If we utilize the DEA system of chord-shapes in the guitar fretyboard, the process becomes simpler.

This will unlock the playing of chords across all of the guitar fretboard, in a way that when playing with these rules the harmony is always beautiful,  what ever we play, while the melodic improvisations very easy familiar and beautiful too. 

The harmonic pairs (Xi,Yi) are always (E,A) or (A, D) or (D,E).

An chromatic transition Yi-Xi+1  for the pairs  (Xi,Yi), (Xi+1,Yi+1) will be such that 

(Xi,Yi) to (Xi+1,Yi+1) is melodic on Xi-Xi+1

And a melodic transition at Yi-Xi+1  will be for the pairs  (Xi,Yi), (Xi+1,Yi+1)  such that 

(Xi,Yi) to (Xi+1,Yi+1) is chromatic transition  on Xi-Xi+1

THE LOCAL (CHROMATIC) TRANSITION RULES OF THE CHORDI-CASTER. Because chromatic transitions are always easier to visualize and execute. The rules for melodic or chromatic transitions become, a rule of chromatic transition of the pairs (Xi,Yi), (Xi+1,Yi+1) , either on Xi to Xi+1  of  (Xi,Yi)  or chromatic on Yi to Xi+1 of (Xi,Yi) correspondingly  . The harmonic transitions work cyclically on the shapes E-A-D-E' etc. where D-E' is the usual positions. In an harmonic transition we set Yi=Xi+1.  But alternatively  it can be converted also to a chromatic shift rule, which is that in the pairs (Xi,Yi), (Xi+1,Yi+1), there is a chromatic transition of a tonal interval of 2nd from Xi to Yi+1. 

Given a Chordi-caster as above, the soli-caster of Rory  Hoffman (see post 455  ) is easier to create as it is melodic cycles and bridges in harmonic pairs (Xi,Yi) very well familiar from 12 bars blues and simple songs. 

Example the Granada by I. Albeniz for guitar where the harmonic pairs are

https://www.youtube.com/watch?v=x4MIAUmW1tc&ab_channel=tubescore.net

(B7-E) (E-A) (G-C)  (C-Fm) (C#-F#m) (B7-Em) (Em-Am) (B7-E)

456. THE FEELINGS OF A BIRD FLYING INSIDE THE GRAVITATIONAL FIELD AS AN EMOTIONAL MODEL FOR THE MELODIES. WHAT ABOUT MOTION OUTSIDE GRAVITATIONAL FIELD?