111. INDEPENDENT AND PARALLEL COMPOSITION OF MELODY AND CHORD-PROGRESSION. RULES OF COMPATIBILITY AND FITTING.

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In this post we describe how to combine two different methods of composition
1) The one that starts from the melody first utilizing the Dolphin Language of order-topological melodic shapes (as in post 101) as historically the  melody composition was easier , it come historically first  , and is  closer to the human voice pitch changes,
  and the one
2)  that starts from the chord-progression , as in Jazz improvisation described in posts like 49, 83 which historically came later, after discovering music with  harmonic structure. Still harmony determination at first in composition very often may be a simpler specification than melody shapes.


One of the first rules of compatibility of course of a melodic phrase M during a time interval that a single chord  C is sounding is as we described in post 27.

RULE 1

If the notes as notes of the melodic theme (a piece of the melody that we have not yet found its underlying chord yet) in total do not sound less time  (preferably >2/3 of the total time) compared to the total duration of the notes of the melodic theme that do not belong to the chord then we accept this chord as underlying chord. We may have also a slightly different and less strict rule:  If we divide all notes of this piece of melody to equal smaller duration  notes, and make a statistical histogram of the re-occurrence of their  pitch , then the triad of notes of maximum duration compared to the duration of any other  triad should correspond to the 3 notes of the underlying  chord. Obviously there is no requirement in the second version of the rule that the notes of this triad in total sound more than the total duration of all other notes that do not belong to the chord. Only that they sound more than any other triad.  A third variation of the previous rules involves also not only the time duration but the loudness of he notes in the obvious way. The previous rules , in particular the first one,  of course may determine more than one chord as underlying chord or no chord at all!. And we may chose with criteria of better quality chord progressions relative to the alternatives. Or if one particular chord progression and chord transition is more common in the particular style of music. We may also put a requirement of lest possible  number of underlying chords, which means that if for the previous melodic theme and previous chord, is so that its notes as notes of the melodic theme both current and previous  in total do not sound less (preferably >2/3 of the total time) compared to the total duration of the notes of the two melodic themes that do not belong to the previous chord then we extend the duration of the previous chord to the current melodic theme.

RULE 2 

There mainly two correlations of a piece of a melody with a chord a) The local condition. This is the next: If we divide all notes of this piece of melody to equal smaller duration  notes, and make a statistical histogram of the re-occurrence of their  pitch , then the top 3 peaks of the histogram should correspond to the 3 notes of the chord. b) The global condition. This is the next: The local condition is overruled according to a quantitative weight of significance, if the previous chord defines with maximum transition probabilities (among a great sample of popular chord progressions)  a different chord (e.g. G7 resolves to C rather than Am or Em)

110. The 7-notes 2-octaves and 10-notes 3-octaves arpeggio-scale of a chord, as sufficient space for rich melodic order-topological shapes composition.

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When spending time with an improvised melody that harmonically fits a chord the best idea is to have the chord in 4-notes form e.g. like a with 7nth or with 6th, and in the current octave or in the next. Then start the melody at a note of the chord and end it again at a note of a chord in this or the next octave. Since the chord has 4-notes and the scale  7 notes the passing or transient notes are only 3, less than the 4 of the chord, therefore, any such melodic theme fits harmonically to this chord.

Here is an example :

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

109. 2ND HARMONIC ORDER MELODIC THEMES BRIDGING TWO SUCCESSIVE CHORDS AND THE ROLE OF THE HARMONIC AND CHROMATIC SIMPLISTIC SUB-MELODIES

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Melodic themes that span from one chord to the next have more complicated harmony as the underlying harmony is two successive chords compared to a melodic theme that sounds during a single chord. That is why they are called 2nd harmonic order

Methods of creating melodic themes during a single chord sounding have been already described at least in post 141. We had described there that one of the simplest methods is the next:

When spending time with the melody with an underlying chord the best idea is to have the chord in 4-notes form e.g. like a with 7nth or with 6th, and in the current octave or in the next. Then start the melody at a note of the chord and end it again at a note of a chord in this or the next octave. For example, we may compose the melody from 3-notes micro-themes, the first and last inside the chords and the middle possible outside the chords. Since the chord has 4-notes and the scale  7 notes the passing or transient notes are only 3, less than the 4 of the chord, therefore, any such melodic theme fits harmonically to this chord.

Here is an example :

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

Now, this technique can be extended when passing from one chord to a next. Instead of having the one chord on two octaves and moving from the one octave to the next, we have two chords and we start from a note of the first chord so as to end with a note of the 2nd chord, and controlling of course that the passing or transient notes that do not belong to either chord, are less or sound  less time than the notes of the chords..

As we analyzed in post 104, the Harmonic simplicial sub-melody is a kind of extreme maximum distances among successive chords, while the chromatic simplicial sub-melody is a kind of minimum distance among two successive chords. As we mentioned the harmonic simplicial submelody has at most one note per chord, while the chromatic simplicial submelody has at most 2 notes per chord. 

Now methods of creating melodic themes even inside single chord as in post 103, can be based on the harmonic and chromatic sub-melodies. 

For example we may create from the melodic seeds  order-topological pattern or shape of a melodic themes, a realization of them . For a chord this creates two themes one that starts from the left (first) note of the chromatic simplicial submelody and ends to the harmonic simplical submelody note, and a second which starts from the harmonic simplicial submelody note and ends to the right (second) note of the chromatic simplicial submelody. These themes concatenated with a chromatic link of the right and left notes of the chromatic simplicial submelody of two successive chords and  may create a full and dense melody for the given chord progression.

If the duration of the chord is rather limited, then obviously we create one only of the two such melodic themes.

Because of the property of maxima of the harmonic submelody, the melodic theme is somehow long enough and between harmonic intervals. While because of the property of minimum distances of the notes of the chromatic simlpicial submelody, such a melody also links in the shortest and most chromatic way two succesive chords. This creates an oscillation or wave between harmonicity and chromaticity in the melody which is a beautiful form of balance.

Since the interval distance of the notes of the harmonic Simplicial submelody for two successive chords is in general quite variable, the initial melodic seed order-topological shape of the initial melodic theme may or may not be preserved. But even if its preserved we have an homeomorphism variation of the melodic theme from chord o chord instead of a standard mode-translation. In this way the contraction-expansions (dilations or hoemorphisms) of the seed melodic themes is created naturally as in conformance with the existing harmony of the initial chord progression.

Obviously this method creates also a constraint of how long or how short the chords should sound, therefore it suggests also a rhythm standard to the chord duration neither too long neither too short so that the melody is neither too slow neither too fast. In other words the rhythmic duration of the chords (poetical measure as it has been called earlier) should be determined only after the creation of the melody.
 Therefore in the suggested above method the order of determinations is the next
1) The chord progression
2) The harmonic simplicial submelody
3) The chromatic simplicial submelody
4) The full melody after the melodic seeds and the 1),2),3)
5) The duration  of each one beat and how many beats per chord. 

MELODY-HARMONY INTERACTIVE COMPOSITION (BY INTERVALS OF 5THS AND 8THS).

The technique of melody composition which is described in this post 109, and which is supposed to require a chord progression in advance, can be applied also for melody composition without a chord progression given in advance, but in recursive way starting from the melody . This means that we start with the first realization of the order-topological theme, and so as to compose the next we compose simultaneously an underlying harmony , in other words a  next chord, and also a next melodic theme and so on. This interactive method for reasons of simplicity may compose as correlated harmony a power chord always in various positions, but the harmonic and chromatic simplicial sub-melody need again calculation. The power-chord play only the role of placing the melodic theme, inside the scale, and requiring that the melody passes from harmonic intervals of 8th or 5th. The actual chords that finally would accompany the melody may be different!.
We may of course predetermine a scale but this is nit always necessary.

Since determining a scale determines also a set of chords but not an ordered sequence of the (chord-progression), we may also conceive such a more lose condition in the composition of the melody : Instead of a predetermined chord progression a predetermined set of chords with no pre-decided order. Then as we want to go to the next melodic theme, w just choose a next chord from the predefined set of chords, and apply the method of the post 109.

The boundaries of the range of the available instruments upper and lower (usually 2 or 3 octaves) serve as reflectors, where the melodic themes may have inversion variations either  in pitch or time.

108. The 4 elementary variation of melodic theme. TRANSLATION, INVERSION, EXPANSION , MUTATION . Total and partial variations. Concatenation of melodic themes.

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The 3 elementary types of variations play to the melodic themes similar role that 3 basic chord-transition relations play for the chords.

107. The 3 basic shapes of melodic themes: EXPANSION, CONTRACTION and CYCLES. The 9 basic 2-sub-moves melodic shapes, and the 21 basic 3-sub-moves melodic shapes. Beatty of melodies based on statistical profile of them. The basic Dolphin-language words

(This post has not been written completely yet)

This post should be read together with post 101.

In the statistics, we may study the shapes of melodic themes bu the polarity of them (similar to the polarity of chords as Power-chords=neutral major chords=positive minor or more exotic chords=negative).


The 3 polarities +, - 0 of a melodic theme, and the 3 basic shapes of them: Expansion, Contraction and Cycles. Ascending, Descending Stationary. 

The 3 polarities + , -, 0 , are the correspondent to the melodic themes that the chord types major, minor and power chord are for harmonic triads.

The 3  basic shapes of them: Expansion, Contraction and Cycles, are the correspondent to the melodic themes that the chord extension  types like with 4th, with 6th with 7nth  are for harmonic triads.

The 9 , 2-moves shapes are the 

a) With + or - polarity

1) Straight 1 move

2) Overacting expansion

3) Counter reaction contracting

b) With 0 polarity

4) Isocratic (flat vector) 

5) Upper cycle

6) Lower cycle

The  12 , 3-moves shapes are 

Expansion

1) Strong expansion

2) Mid expansion

Contraction

3)Strong contraction

4) Mid contraction

5) Counter strong expansion up or down

Balance

6) Upper or down wave.

In total 21 shapes of 2 or 3 moves.

If we do not count as different the + or - polarities then we have only 11 shapes

106. THE VARIATION INDEPENDENT MELODIC SEED AND HARMONIC SEED IN COMPOSING A SONG

(This post has not been written completely yet)

In composing  melodic themes based on melodic triads (see post 208) we should use also the concept and technique  of  variational  independent base of melodic shapes or melodic seed. 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 of the song can be derived with variations from them.

As the melodic seed is usually a melodic theme of the chord-local scale (of the chord-yard melody) and the 3-notes chord in general is denote by 1-3-5, it can be described as number sequence from 1 to 7. E.g. 1-7-1 or 1-5-3-6) etc with the appropriate time duration of course.

See also post 311 about the Melidic maths  of Max Martin

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. 

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

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=1 step

E= 2 steps

I= 3 steps

O=4 steps

OU=5 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

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

105. HOW TO CREATE NICE OCTAVE SPLITS AND OSCILLATIONS (or of 7nth,6th, 4th intervals) IN A MELODY

A simple and common way to create such an oscillations is to take for example a simple chord harping-waving that contains also with the previous rules less than 50% of the time also notes outside the chord , and then half of this simple theme translate it one octave higher, and so oscillate between the two octaves. Normally the initial non-translated melody would have intervals of 2nd, 3rd, and 5th. The interval of 3rd will become 6th , the interval of 5th, a 4th and an interval of 2nd , will become 7nth. In this way also the sttaitical profile of such melodies will have more frequently high intervals  of 5th, 6th, 7nth and 8th compared to intervals of 2nds (see post 93 ) .g. the folk Irish melody Kerry Polka below

We remind the reader that this should be read in the context of general method of creating melodies like in posts 92 and 103

•  HOW TO CREATE MELODIES FROM A CHORD PROGRESSION 1/2:

•  HOW TO CREATE MELODIES FROM A CHORD PROGRESSION 2/2: