THE 3 CLASSES AND 7 INDEPENDENT PATTERNS OF MELODIC THEMES FROM THE COUPLING OF POSITIVE AND NEGATIVE EMOTIONS.
WE MAY COMPARE THE NEXT PERCEPTIONS AND TECHNIQUES WITH THE 3 BASIC SOUNDS IN SOLOING 1) THE CHROMATIC (MAINLY INTERVALS OF 2NDS) 2) THE MELODIC (MAINLY INTERVALS OF 3RDS) 3) THE HARMONIC (MAINLY INTERVALS OF 4THS/5THS/8THS )
b) The waving ascending (or descending) melodic theme
c)The abrupt jump (spike) interval ascending (or descending) by an interval larger than an octave without intermediate steps.
2) The The stationary waving melodic patterns are divided to 3 cases
a) The stable amplitude stationary waving pattern
b) The diminishing (contracting) amplitude stationary waving pattern
b) The expanding amplitude stationary waving pattern
Therefore the above 3 classes (and 6 cases of types which when including their inverses become 11 ) make base of melodic themes for a melody or a melodic seed for a melody of a song.
Their nature in melodies is similar to the type of chords in chord progressions (major , minor, diminished, augmented,, seventh etc)
We may compose after these patterns melodies utilizing rules for the rhythm, scales, underlying harmony and musical morphology e.g. as in posts 229,221, 214, 203
If we put the restriction that these patterns of melodic theme and their variations are consisting from intervals that are 2nds in less that 1/3 (=33%) of the cases, then we get an "Irish" but also "south american", melodic/harmonic sound in the melody.
See also post 282
WE MAY COMPARE THE NEXT PERCEPTIONS AND TECHNIQUES WITH THE 3 BASIC SOUNDS IN SOLOING 1) THE CHROMATIC (MAINLY INTERVALS OF 2NDS) 2) THE MELODIC (MAINLY INTERVALS OF 3RDS) 3) THE HARMONIC (MAINLY INTERVALS OF 4THS/5THS/8THS )
All the 3-classes of dynamic coupling of positive and negative emotions have been applied also in the psychology of social behaviour, and even in the psychology of behaviour of couples in the marriage
(see "The mathematics of marriage" by Gottman, Murray, Swanson, Tyson, and Swanson, MIT press 2002. See also for the Voltera's equations "Models in Ecology" by J. Maynard Smith, Cambridge University press )
All of the above 3 classes of non-linear coupling have been solved and their solutions have been classified.
The 3 classes of melodic patterns from the coupling of positive and negative emotions are
1) The ascending (or descending ) melodic pattern (3 patterns)
2) The stationary waving melodic pattern. (3 patterns)
3) The isocratic note melodic pattern (1 pattern)
The 1st class the ascending (or descending ) melodic pattern are subdivided by three patterns
a) The straight stepwise ascending (or descending) melodic theme
c)The abrupt jump (spike) interval ascending (or descending) by an interval larger than an octave without intermediate steps.
2) The The stationary waving melodic patterns are divided to 3 cases
a) The stable amplitude stationary waving pattern
b) The diminishing (contracting) amplitude stationary waving pattern
b) The expanding amplitude stationary waving pattern
Obviously these patterns (and "Dolphin words" as defined e.g. in post 114 ) are variational independent, in the sense that no translation or inversion can produce one from another. On the other hand pitch translations within the scale or pitch inversion within the scale will not change the type and order-topological shape of the melodic theme pattern ( a straight ascension will remain such or a stationary waving will remain such etc)
On the other hand if we pass from one such pattern of the above 6 cases to another such pattern we have called this transition as mutation of the melodic theme.
Therefore the above 3 classes (and 6 cases of types which when including their inverses become 11 ) make base of melodic themes for a melody or a melodic seed for a melody of a song.
Their nature in melodies is similar to the type of chords in chord progressions (major , minor, diminished, augmented,, seventh etc)
We may compose after these patterns melodies utilizing rules for the rhythm, scales, underlying harmony and musical morphology e.g. as in posts 229,221, 214, 203
THE MELODIC IMPROVISATION AS A SEQUENCE OF "ROTATIONS". EACH "ROTATION" HAS THE NEXT 3-LEVEL RHYTHMIC OR MORPHOLOGICAL STRUCTURE
THE 4 PARTS A1 A2 A3 BI STRUCTURE
This structure is rhythmic morphological and comes as a pattern from the 15-syllable poetry.
2 lines in a 15-syllables poetry are divided to 4 parts A1 A2 A3 B1, each of the Ai having 4 syllables and the B1 3 syllables. Similarly here in the melody the A1 A2 A3 , B1 are of 2 measures. Each of the A1 A2 A3 B1 contain at least one melodic theme. If we put the restriction that both the melodic theme and its variations are consisting from intervals that are 2nds in less that 1/3 (=33%) of the cases, then we get an "Irish" but also "south american", melodic/harmonic sound in the melody. The melodic theme of A1 is translated or inverted to that of the A2 and that of the A2 to that of A2. Finally the melodic theme of A3 is mutated to that of B1. The simplicial sub-melody has one note in each measure therefore two notes in each of the A1 A2 A3 B. These two notes signify a MELODIC MOVEMENT (VECTOR) which is the basis of an emotion. If we superimpose the melody at the first two levels, the detailed improvisational notes of the melodic theme (1st level) and the melodic move or vector of the simplicial submelody (2nd level) we get a new musical entity and concept that we may call WAVING MELODIC VECTOR. The wavings are as in the above 7 melodic themes patterns. Another classification of them is that they are of 3 classes a) Chromatic (of length an interval of 2nd) b) Melodic (of length an interval of 3rd) c) Harmonic (of length an interval of 5th). The choice in the improvisation of one of these 3 classes is similar to the choice in a chord progression if the chord-transition will me chromatic , melodic or harmonic.
Very often the wavings are of diminishing amplitude as we reach the melodic center-end note of it. This is very convenient to have in mind when we improvise because we think that we will move from a persisting note a (melodic center) to a persisting note b (melodic center ) in a scale but with improvisational waving way that we may change each time at willAll the melodic movements of the A1 A2 A3 B make a DOLPHIN WORD (as defined also in post 101, 114 ). Each part A (thus melodic move too) has an underlying chord. The chords of two parts like A1 A2 may be the same or different chords. The melodic move can be also a melodic triad (alternating major minor vector interval of 3rd as in post 208) . The Dolphin word of the "rotation" may be a closed polygon (e.g, triangle) of waving melodic vectors , so that the length of the melodic vector indicates also the length-interval of the waving melodic vector, which may also be the distance as musical interval of the middle notes of the underlying chords, of the melodic move. Each side of the polygon has its own waving melodic theme pattern as the above 7 .
This melodic polygon allows for simple and very concise, simple and visually beautiful methods of writing the improvisation with not less information than the necessary but no more than a minimum too, so that each time we see the written paper and play the melody a different melody will emerge (mainly at the first layer/level of it) while still it will be "the same" song.
Very often the wavings are of diminishing amplitude as we reach the melodic center-end note of it. This is very convenient to have in mind when we improvise because we think that we will move from a persisting note a (melodic center) to a persisting note b (melodic center ) in a scale but with improvisational waving way that we may change each time at willAll the melodic movements of the A1 A2 A3 B make a DOLPHIN WORD (as defined also in post 101, 114 ). Each part A (thus melodic move too) has an underlying chord. The chords of two parts like A1 A2 may be the same or different chords. The melodic move can be also a melodic triad (alternating major minor vector interval of 3rd as in post 208) . The Dolphin word of the "rotation" may be a closed polygon (e.g, triangle) of waving melodic vectors , so that the length of the melodic vector indicates also the length-interval of the waving melodic vector, which may also be the distance as musical interval of the middle notes of the underlying chords, of the melodic move. Each side of the polygon has its own waving melodic theme pattern as the above 7 .
This melodic polygon allows for simple and very concise, simple and visually beautiful methods of writing the improvisation with not less information than the necessary but no more than a minimum too, so that each time we see the written paper and play the melody a different melody will emerge (mainly at the first layer/level of it) while still it will be "the same" song.
When playing again such an improvisation the simplicial sub melody is repeated (thus the "rotation" A1 A2 A3 B or Dolphin word of it), but the other notes inside the measures that are embellishments may change. All together the "rotations" or Dolphin words make the total melodic phrases of the song. Therefore we have here at least a 3-level structures of the melody a) notes b) melodic moves c) "rotations" or Dolphin words,and in time it is 1, 2^3=8 (2 measures) and 2^5=32 (A1A2A3B parts).
If we put the restriction that these patterns of melodic theme and their variations are consisting from intervals that are 2nds in less that 1/3 (=33%) of the cases, then we get an "Irish" but also "south american", melodic/harmonic sound in the melody.
See also post 282
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
Or
AS THE COMBINATION SIMPLICIAL MELODIC MOVES (ORIENTED INTERVALS SEE POST 282) CREATE PATTERNS THAT ARE CALLED "DOLPHIN WORDS" , WE MAYS AS WELL CLASSIFY THE "SIMPLICIAL DOLPHIN WORDS" . The simplest such patterns are of course the 3: 1) THE CYCLE 2) THE ASCENDING SEQUENCE 3) THE DESCENDING SEQUENCE.
