We must distinguish here as something different the rhythm within a measure (that its mathematics with the parameters order and dimension is studied in the post 10 ) and the melodic rhythmic patterns that extend in many measures and refer to a particular line of melody and not to the song as a whole.
Here we have an analogy of duration of the notes of the melody with the pitch of the note. Sequence of notes of shorter duration corresponds to sequence of notes with higher pitch, while sequences of notes with longer duration corresponds to sequence of notes with falling pitch. Thus e.g. a sequence of notes with durations like 1/2-1/4,1/4-1/8,1/8,1/8,1/8 corresponds to an increasing in pitch sequence as melodic pitch pattern. Obviously complicated rhythmic patterns patterns are not very common . So following the same classification as with the melodic pitch patterns the basic melodic rhythmic patterns are the next
The basic rhythmic dynamic patterns of a melody are
(three basic categories, horizontal , skew and almost vertical)
HORIZONTAL
1) Standing horizontal channel of constant width (Balance)
2) Standing horizontal channel of diminishing width (Contraction, expiration with little sadness)
3) Standing horizontal channel of increasing width (Expansion. initiation with joy)
In 2) and 3) one of the sides of the channel maybe horizontal which is an isocratic pattern
SKEW
4) Ascending waving in channel of constant width (Joy)
5) Descending waving in channel of constant width (Sadness)
6) Ascending sequence (Joy)
7) Descending sequence (Sadness)
8) Ascending with larger steps is even higher joy
9) Descending with larger steps is even larger sadness
10) Accelerating ascending is more joy than decelerating ascending
11) Accelerating descending is more sadness that decelerating descending.
8) Ascending with larger steps is even higher joy
9) Descending with larger steps is even larger sadness
10) Accelerating ascending is more joy than decelerating ascending
11) Accelerating descending is more sadness that decelerating descending.
ALMOST VERTICAL
6) Up spike (extreme joy)
7) Down spike (extreme sadness)
Of course the waving inside the channels may be classified in rhytmic intervals of 2^(-n) to 2^(-n-1) increase of speed, or higher.
Then there are combinations of them. E.g. an up spike maybe combined with reactional descending sequence, which is a pair of emotions extreme joy but then gradual sadness.
In song composition we must be careful to follow the next if we want a song with clear emotions easy to sing by many people and not a song with mixed not-clear emotions.
Rhythmic melodic patterns where the emotion of joy, dominates , are correlated with the harmony of joy that is major chords , while patterns where the emotion of sadness dominates are correlated with minor chords.
Rhythmic melodic patterns where the emotion of joy dominates , are correlated with the pitch dynamics of joy that is pitch melodic dynamic patterns that dominates joy , while patterns where the emotion of sadness dominates are correlated with the pitch dynamics of sadness (see post 18)
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We summarize the basic concerns in the melodic improvisation and composition of a voice or melody (similar to the syntax of phrase with subject verb and object etc).
1) Always use a melody motive, theme or move
2) Transform this melodic move which will be the invariant before transforming it.
3) Close it by returning to the original motive
The ways to transform it are at least the next 5 and combinations of them
1) Translate it in different pitches (within a scale or not, changing possibly the pitch distances )
2) Translate in time (repeat it)
3) Invert it in time or change its rhythm (if at the begging is slower and at the end faster it will be now the reverse etc)
4) Invert it or distort it in pitch (if it is ascending now it will be descending etc)
5) Change it as morphology (from a non-waving ascending it may become waving ascending or iso-cratic)
After the chord progression and simplicial submelody we chose,
THE DEFINITION OF MELODIC BRIDGES THAN LINK TWO SUCCESSIVE CHORDS BETWEEN THEM AND START AND END AT THE NOTES OF THE SIMPLICIAL SUBMELODY.
1) WHICH CHORD-TRANSITIONS (PAIRS OF CHORDS) WILL HAVE A MELODIC BRIDGE! (Usually the chord-trasnitions that are in resolutional relation, or resolutional-like relation)
2) THEN WHICH BRIDGES WILL BE ISOMORPHIC IN PITCH AND RHYTHMIC DYNAMIC SHAPE AND WHICH DIFFERENT, DEFINING THEREFORE A PARTITIONING IN THE BRIDGES.
3) THEN IF IN EACH EQUIVALENCE CLASS OF ISOMORPHIC MELODIC BRIDGES IN THIS PARTITIONING, THE BRIDGES ARE EVENTUALLY ASCENDING OR DESCENDING (This besides the emotional significance, determines also where to play the chord in one of the 3 neighborhoods of the fretboard)
4) FINALLY HOW IN EACH EQUIVALENCE CLASS OF ISOMORPHIC MELODIC BRIDGES IN THE PARTITIONING, THE COMPLICATED PITCH DYNAMIC SHAPE OR WAVING AND RHYTHM WILL BE AS A REPETITION OF SUCH PATTERNS OF PREVIOUS ISOMORPHIC MELODIC BRIDGES, OR VARIATION OF SUCH PATTERNAS S SO NOT TO BE TOO BORING. (This pitch dynamic shape has again a significant emotional meaning)
5) THE JUSTIFICATION OF THE CHORD PROGRESSION USUALLY IS NOT DONE BY THE CHOICE OF THE MELODIC BRIDGES (THAT IS GIVEN THE MELODIC BRIDGES MAYBE A SIMPLER CHORD PROGRESSION MAY COVER THEM HARMONICALLY). BUT AN INTERMEDIATE HARPING OR STRUMMING OF EACH CHORD WILL ENHANCE THE MELODY OF THE BRIDGES SO THAT ONLY THIS CHORD PROGRESSION IS JUSTIFIED!
The 3 elementary melodic themes, as we mentioned earlier (e.g. in posts 66 and 69 ) , are the ascending melodic interval of two notes, the isokratic melodic interval of two equal notes and the descending melodic interval of two notes.
1) the translation (either with intervals of 2nd , (or diatonic density) or intervals of 3rd (or middle harmonic density) or of intervals of 4th or 5th (or high harmonic density))
2) The inversion where the ascending move becomes descending.
3) Rhythm transformation (which may vary)
The 5 basic melodic moves (see e.g. post 69) , being more complicated have more types of transformations, as derived by the writing in a pentagram :
1) Translation
Bach has often used the above 6 transformations in his fugue.
After the chord progression and simplicial submelody we chose,
THE DEFINITION OF MELODIC BRIDGES THAN LINK TWO SUCCESSIVE CHORDS BETWEEN THEM AND START AND END AT THE NOTES OF THE SIMPLICIAL SUBMELODY.
1) WHICH CHORD-TRANSITIONS (PAIRS OF CHORDS) WILL HAVE A MELODIC BRIDGE! (Usually the chord-trasnitions that are in resolutional relation, or resolutional-like relation)
2) THEN WHICH BRIDGES WILL BE ISOMORPHIC IN PITCH AND RHYTHMIC DYNAMIC SHAPE AND WHICH DIFFERENT, DEFINING THEREFORE A PARTITIONING IN THE BRIDGES.
3) THEN IF IN EACH EQUIVALENCE CLASS OF ISOMORPHIC MELODIC BRIDGES IN THIS PARTITIONING, THE BRIDGES ARE EVENTUALLY ASCENDING OR DESCENDING (This besides the emotional significance, determines also where to play the chord in one of the 3 neighborhoods of the fretboard)
4) FINALLY HOW IN EACH EQUIVALENCE CLASS OF ISOMORPHIC MELODIC BRIDGES IN THE PARTITIONING, THE COMPLICATED PITCH DYNAMIC SHAPE OR WAVING AND RHYTHM WILL BE AS A REPETITION OF SUCH PATTERNS OF PREVIOUS ISOMORPHIC MELODIC BRIDGES, OR VARIATION OF SUCH PATTERNAS S SO NOT TO BE TOO BORING. (This pitch dynamic shape has again a significant emotional meaning)
5) THE JUSTIFICATION OF THE CHORD PROGRESSION USUALLY IS NOT DONE BY THE CHOICE OF THE MELODIC BRIDGES (THAT IS GIVEN THE MELODIC BRIDGES MAYBE A SIMPLER CHORD PROGRESSION MAY COVER THEM HARMONICALLY). BUT AN INTERMEDIATE HARPING OR STRUMMING OF EACH CHORD WILL ENHANCE THE MELODY OF THE BRIDGES SO THAT ONLY THIS CHORD PROGRESSION IS JUSTIFIED!
The 3 elementary melodic themes, as we mentioned earlier (e.g. in posts 66 and 69 ) , are the ascending melodic interval of two notes, the isokratic melodic interval of two equal notes and the descending melodic interval of two notes.
The 3 basic transformations of them are
1) the translation (either with intervals of 2nd , (or diatonic density) or intervals of 3rd (or middle harmonic density) or of intervals of 4th or 5th (or high harmonic density))
2) The inversion where the ascending move becomes descending.
3) Rhythm transformation (which may vary)
The 5 basic melodic moves (see e.g. post 69) , being more complicated have more types of transformations, as derived by the writing in a pentagram :
1) Translation
2) Inversion relative to a point
3) Reflection relative to an horizontal line
4) Reflection relative to a vertical line.
5) Rhythm transformation
to the above five we may add the
6) Acceleration (e.g. from the diatonic speed or density to the middle harmonic speed or density) or Deceleration (vice-versa).
7) Extension in 2 or more octaves
7) Extension in 2 or more octaves
Bach has often used the above 6 transformations in his fugue.
More complicated ways to transform a theme are at least the next 5 and combinations of them (see also post 41)
1) Translate it in different pitches (within a scale or not changing possibly the pitch distances )
2) Translate in time (repeat it)
3) Invert it in time or change its rhythm (if at the begging is slower and at the end faster it will be now the reverse etc)
4) Invert it or distort it in pitch (Create 1st 2nd 3rd or 4th voice versions, utilizing the chord progression as rules of transformation of the theme, or if it is ascending now it will be descending etc)
5) Change it as morphology (from a non-waving ascending it may become waving ascending or isocratic). We prefer spikes and scaling as the main morphological types, while the waving and isocratic as intermediate bridges.
Often melodic bridges from a chord to the next, may start with harmonic speed or density covering the first chord A and then decelerate to diatonic speed or density when reaching to the next chord B
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