407. TUNING OF 4-STRINGS INSTRUMENTS WITH CONSECUTIVE RELATIVE MODES PER 3 CONSECUTIVE STRINGS IN THE PATTERN OF INTERVALS 5TH-6TH-5TH E.G. D2-A2-F3-C4 (AEOLIAN-IONIAN MODES)

 See also post 308 , 90 and 164 (Mexican instrument Jarana tuning)

The pattern of intervaslamong the strings are  5-6m-5 and 5-6M-5  where by 5 we denote interval of 5th (7 semitones) and by 6m interval of 6th minor (8 semitones)  and by 6M interval of 6th major (9 semitones) .

The modes are defined the the 3-notes chords that are shaped as triads across 3-consecutive strings.  The first chord is the open 3-strings chord. 

Pairs of modes , all the 7 , that can be tuning in this way 

AEOLIAN-IONIAN  e.g. D2-A2-F3-C4     (f -major) pattern 5-6m-5 

IONIAN-FRYGIAN  e.g. F2-C3-A3-E4      (f major) pattern 5-6M-5 

DORIAN-LYDIAN  e.g.   G2-D3-Bb3-F4   (f major) pattern 5-6m-5 

FRYGIAN-MIXOLYDIAN e.g. A2-E3-C4-G4  (f major) pattern 5-6M-5 

LYDIAN-AEOLIAN  e.g. Bb1-F2-D3-A3 (f major) pattern 5-6m-5 

MIXOLYDIAN-LOCRIAN e.g.  C2-G2-E3-Bb3  (f major) pattern 5-6M-5 

LOCRIAN-DORIAN e.g.  E2-Bb2-G3-D4  (f major) pattern 5-6m-5 

In total the advantages of this inverse tuning (e.g. D2-A2-F3-C4 )relative to the standard 4-strings tunings (e.g. C3-F3-A3-D4) are the next

1) It has two intervals of 5th among the strings that it sounds better in open and barre chords compared to intervals of 4th. 
2) It has larger range
3) It has the one-fret triad major  chords at higher strings and the one-fret triad minor chords at the lower strings,  thus  favors a bit mor joyfull music of major chords
4) It is more ergonomic in the fingers when playing the A-shape and E-shape chords The D-shape triad chords are almost the same difficulty. (the minor triad D-shape is slightly more difficult).

5) The 4-strings  chords span 2 octaves and have more magical and reach sound.

6) Because the chords are in one or 3 only frets, their arpeggios also and neighboring melodies are in fewer frets thus easier to play as finger picking style. 

Similarly we could utilize the inversions involving intervals of 4th and 3rds (instead of 5ths and 6ths) and have again all 7 pairs of relative modes

IONIAN-AEOLIAN  e.g. C2-F2-A3-D4     (f -major) pattern 4-3M-4 

FRYGIAN-IONIAN e.g. E3-A3-C4-F4     (f major) pattern 4-3m-4 

LYDIAN-DORIAN  e.g.   F2-Bb2-D3-G3   (f major) pattern 4-3M-4  

MIXOLYDIAN-FRYGIAN e.g. G2-C3-E3-A3  (f major) pattern 4-3M-4     

AEOLIAN-LYDIAN  e.g. A2-D3-F3-Bb3 (f major) pattern 4-3m-4   

LOCRIAN-MIXOLYDIAN e.g.  Bb2-E3-G3-C4  (f major) pattern 4-3m-4 

DORIAN-LOCRIAN e.g.  D3-G3-Bb3-E4  (f major) pattern 4-3m-4   

406. HOW DJANGO REINHARDT REINVENTED HIS PLAYING OF THE GUITAR MAINLY WITH TRIADS DUE TO HIS FINGER ONLY HANDICAP.

405. THE BIG DIFFERENCE BETWEEN TRANSPOSITIONS AND MODULATIONS. ADOPTIONS AND RE-HARMONIZATION OF BLUES AND OTHER SONGS BY MODULATIONS

 See also post  222 where the 7 modes are identified as 7 harmonic triads of chords    and post   356, 402  and     205 , 215, 216     for compositions and improvisations based on harmonic triads of chords

404. Improvisation on the fado guitar, tuned by overtones.

 I have a fado guitar (scale length 44 cm, thus a type of mandola-guitar) with 6 courses of strings. I eliminated the double strings to be single thus it has 6 strings tuned by overtones tuning to  

G2-D3-G3-B3-D4-G4.   (and in degrees of a diatonic scale 1-5-1-3-5-1).

Therefore it is an open tuning to G major scale. I have put white marks on the notes of the G-major default scale across the fingerboard and for every string.

 Because the fretbaord is at most 44 cm the improvisation is easy, and because the fado guitar has very bif sound box the sound is both sweet and strong. 

  The chords of the scale appear as vertical simple patterns across the 6 strings. This is very convenient and simple as we have all the scale and chords of the scale across the fretboard in the right sequence of their roots in the scale. One octave is of course the full 12-frets of the fretboard.

 

When improvising with melodically (sequence of single notes) or harmonically (sequence of 3rds or 3-note chords) we follow the next geometrically and harmonically convenient patterns

 

1) We go up and down a single string with oscillations around notes for a purely melodic improvisation, which is dictated purely from our emotional center  over the melody note by note. We utilize repetition of a pitch-order and rhythmic pattern that would bethe first melodic theme.

2) We do the same but with double consecutive strings which make a major or minor interval of 3rds  , pressing the fingers always upon the white marks, 

3) We do the same but with 3 consecutive strings which make a 3-notes major , minor or diminished chord , by  pressing the fingers always upon the white marks that define  also the shape of the chord on these 3 consecutive strings,

4) We play 3-notes chords triads, on 3 consecutive strings where the dominating relation among the consecutive chords is being relative chords (minor-major with 2 common notes. It is odd or even order of chords

5) We do the same but with harmonic relations of the chords

6) We bridge two consecutive chords with notes upon the white marks making leaks and leads

7) We pair 2 or 3  chords that are consecutive in the order of their roots in the scale (chromatic relation of the chords) and bridge them with the melodic leads that interlink them. There is at least one bridge for each of the 6 strings that link the 2 chords, as each chords spans with a simple a patterns among the 6 strings due to the tuning.

8) We interpolate very often the open strings root chord

9) When we move in a melody up and down we try  moving horizontally (chromatic melodies ) and vertically (harmonic melodies) with a proportion 1/3=33%, 2/3=66% respectively

10) We use blue notes of the scale in the melodic improvisation , e.g. 7b, 5# , 2#, 5b , 1# etc.

11) We utilize the diminished 3-notes chord , among 3 consecutive strings (the pattern is visible at the 7 degree of the scale) and resolve to1 semitone or 1 tone up or down nearest scale chord.

12) We utilize drone melodies where one note that of the open string interpolated among any two notes of the rest of the melody, in any string with the same order and rhythm pattern and because of the tuning this a modulation of the melody on the 1,3,5 modes (Ionian, Phrygian, Myxolydian) of the diatonic scale.

13) We may at the same time as in 12) to play isocratically the root open chord or only the 6th 5th strings that are 5th 1-5 while practicing the 12) 

14) We start at the triad of minor chords of the scale 2m, 3m , 6m and we gardually with bridging melodic themes we shift to the triad of majors 1M, 4M 5M.

15) We play a chord of the scale (usually the 1M, 4M 5M) which is across the 6 strings and simplest pattern, but only partially each time 3 consecutive strings and the 3 other  higher or lower on the same chord but asit changes octave and timbre of the strings are heard as...different chords or at least radically different voicings of the chords.

16) We play the andaluzian cadenza (6m, 5M 4M 3M)  with melodic themes bridging the chords, (6 strings 6 bridges) we reverse to andaluzian ascenza etc. 

17) Similarly we improvise over the triad of main chords 1M 4M 5M ) as in the 12 bars blues with links (6 strings 6 links or bridges)  for each   chord transition. 

403. THE SEVEN SYMMETRY TYPES OF RHYTHMS WITH TWO TYPES OF BEATS

 Every such 2-types of beats rhythm can e represented geometrically when writingit as frieze pattern

Now there exactly 7 different symmetry groups of frieze patterns, thus also 7 symmetry groups of such rhythms

See also https://en.wikipedia.org/wiki/Frieze_group

402. REVIEW OF SIMPLE RULES TO COMPOSE A NICE MELODY WITH A CHORD PROGRESSION.

We summarize here some simple rules to compose a nice melody after a chord progression.

 

1) The rule to fit the melody to an underlying chord is that at least 50% of the time the notes of the melody  that sound during the underlying chord must be notes belonging to the chord.

2) The chord progression must be so that each melodic theme, has as underlying chords 1, or 2 or 3, and this is the same time duration though out the song Thus the chord progressions may be partitioned in to pairs or triads of chords which are called melodic phrase chords. Each such pair or triad of chords is the local "scale" on which the melody is running. Usually it is a good quality relation of chords e.g. harmonic, melodic or harmonic chromatic. The number 3 for the melodic theme cords is a critcal value as it defines also a mode (see post 222) and a diatonic scale, so that translations of the theme may be considered modulations (see post 405 )  in other words changes of the mode. After all , all 12-bars blues utlize for their melodic themes 3 chords which is neither poor harmony neither too complicated harmony .

3) It is good that each chord has duration of time unit or half or double this time unit throughout the song. In other words the time duration of the chords is a simple and not complicated numeric  pattern.

4) The span-range of the melody with its highest note and lowest note is a good simple chart for the emotions that go parallel to the height of the notes of the melody.

5) It is good to create the melodic themes first from its centers , one per chord, so that the centers make the simplicial submelody, and then enhance it to the full melodic theme.

6) The main 4 variations here from melody theme to melody theme are of course the translation-modulation over the chord, or pair or triad of chords with which it is accompanied, the pitch or time inversions, and the mutations, The expansions contractions are much more rare. As the transaltion is the more often variation, this  applies also to the melodic phrase chords. Therefore the relation of the melodic phrase chords amomg themselvs is important too and preferably they are also good quality like harmonic. 

7) Topological concepts of the dynamics of the variations of the melodic themes and the melodic themes themselves (Dolphin words) like cycle, up move, down  move etc are useful for creating corresponding psychological feelings. 

8) Morphology of the parts of the melody like "couple"=first verse , "refrain"=resolving chorus are also useful in integrating the final melody of the song. 

After the above rules the creation of melodies after their harmony or chord progression is as easy as writing a text. We may call this method "Bach's method" . The reason it becomes easy is because we proceed from the simplicity to the complexity,and here the simplicity both in harmony and melody is the a) melodic phrase b) melodic phrase chords. 

 The above rules lead to the next 6 steps in composing a nice melody

1) CHOSE THE TYPE OF CHROMATIC-TONALITY HARMONY 

2) COMPOSE THE CHORD PROGRESSION AFTER THE CHOSEN CHROMATIC TONALITY

3) PARTITION THE CHORD PROGRESSION TO SINGLETS, PAIRS, TRIPLETS ETC OF CHORDS THAT  WOULD SUPPORT BRIDGING MELODIC THEMES

4) COMPOSE THE SIMPLICIAL SUBMELODY (A DEFAULT IS THE MIDLLE NOTES OF THE CHORDS) . For each partition segment of chords, the last note of the simplicial melody ofthe last chord is the main note of the simplicial submelody for this segment. 

5) COMPOSE THE MOVE OF THE BRIDGING MELODIC THEMES BY THE TRIAD UP-DOWN-STATIONARY BY FOLLOWING PRINCIPLES OF BALANCE AND THE EMOTIONS OF THE UNDERLYING PARTITIONED SEGMENT OF CHORDS. ONE POLARITY FOR EACH PARTITIONED SEGMENT OF CHORDS. E.g. partition segments ending in minor chord may be down-moves and those ending in major chord an up-move. If we assume the x-axis the time and the y-axis the pitch (the simplicial submelody set as basic pitch zero level) we may symbolize a rhythmic melodic bridge with a flag. Glag symmetric to a vertical axis are melodic bridges with inverse rhythmic pattrn. So such arrangments of the melody are like geometric frieze patterns and their 7 types of symmetry (see link below) . Of course most melodies are asymmetric. Furthermore we may utilize the rule of melodic-cromatic scale alternation of melodic themes as described in post 421. In short we play a melodiv theme within the chord and in the melodic version of the scale (steps by alternating minor-major 3rds) and the chromatic version ofthe scale as bridge to the next chord. 

https://en.wikipedia.org/wiki/Frieze_group

6) COMPOSE THE RHYTHMIC PATTERN OF THE BRIDGING MELODIC THEMES AND THEMSELVES TOO.

Here is an example of a paritioned chord progression with chords from 3 tonalities related harmonically (this is common inthe harmony of brazilian songs) e.g. C-F-G.

I have improvised at first these chords inthe ukulele,soI that i like them and make the necesary corections

The melodic phrase chords are 3 , and I write the chord progression so that each line is a traid of melodic phrase chords. 

For simplicity all chords have the same duration

1st verse minor feeling, the translation of t he melodic theme is upwards. It is inthe tonalitis C and  F (with harmonic minors)

Dm      E7      Am

Gm      A7      Dm

1st chorus resolution to a major triad, which is alower shift ofthe melodic theme

Bb       C7       F

Here the next verse moves to the tonality G

E7       Am        Am

B7       E7          Am

Again a chorus resolution to major triads of the toanlity G

C        B7         G

Am   D7          G

Chromatic shift to the 7nth degree of the toanlity G as a new verse

F#7    Bm     Bm

B7     Em      Em

And a resolution to tonal of G tonality

D7      G        G

Now we add the simplicial submelody notes of the melody , one note per chord

We try it in a convenient instrument . I did so in the ukulelel and also on the digital ukulele (Geoshred) in the tablet.  I try to whistle also  threr simplicial submelody

1st verse minor feeling, the translation of t he melodic theme is upwards. It is inthe tonalitis C and  F (with harmonic minors)

Dm  (f5)     E7  (g#4)     Am (c5)

Gm   (Bb5)   A7  (c#5)    Dm  (f5)

1st chorus resolution to a major triad, which is alower shift ofthe melodic theme

Bb  (d5)     C7   (e5)    F (a4)

Here the next verse moves to the tonality G

E7  (e5)     Am    (a5)    Am  (a4)

B7   (f#5)    E7    (g#5)      Am  (e6)

Again a chorus resolution to major triads of the toanlity G

C   (e5)     B7    (d#5)     G  (b4)

Am  (c5)    D7   (f#5)       G  (g5)

Chromatic shift to the 7nth degree of the toanlity G as a new verse

F#7   (F#5)  Bm   (b4)   Bm  (b4)

B7    (f#5) Em   (b5)     Em  (B5) 

And a resolution to tonal of G tonality

D7  (d5)    G (g4)       G (g4)

Finally we write all these in a midi editor and and we enhance the simplicial submelody to an actually rhythmic melody with transition notes also outside the chords. 

In this way it is as if we write a text first fromthe verbs then the subject  and obkect ofthe verb and then the relations of the phrases. 

401. THE SIGNIFICANCE OF THE ROLE OF THE SPAN-RANGE OF THE MELODY IN A SONG.