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Saturday, July 21, 2018

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

(This post has not being written completely yet)

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)