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.

400. SIMPLICIAL SUB-CHORD-PROGRESSION BESIDES SIMPLICIAL SUB-MELODY IN IMPROVISATION

 The simplistic invariant in our emotional subconsious is not only creating the simplicial sub-melody by the melody centers, but also the  simplicial sub-chord-progression

E.g. when in diatonic scale we play a chord progression involving 1M , 2m, 3m, 4M 5M 6m , we may

realize that the 3 minors 2m , 3m, 6m, are lower relative chords ofthe 4M, 5M, 1M and so we actually may havea salternative well fitting also chord progression one that has only the 3 majors 1M, 4M, 5M. which can of course be called the simplicial sub-chord-progression.

An example is to try to improvise melodically on the next quite long piece of gypsu jazz

https://www.youtube.com/watch?v=wy9LiSeDQiU&t=412s&ab_channel=LewisLuongRelaxationCafe

It becomes after some time easy, because it is as if improvising over a simple chord progression involving only the 1M, 4M, 5M.