(This post has not been written completely yet)
By a counter melody we usually mean (improvisational) melodic lines that an instrument is playing parallel or sequentially to a main human voice melody in a song. It is not the 2nd or 3nd voice of the melody. The counter-melody has usually more notes than the main voice melody, because it is played by an instrument, and therefore there are speed and complexity possibilities that a human voice rarely will chose to conduct.
The basic rules are the next 2
RULE 1 The main human voice melody and the instrumental counter have he same underlying chords.
RULE 2 The main human voice melody and the instrumental counter have the same melodic centers (simplicial sub-melody of the melodic centers)
Now the simplicial sub-melody of the melodic centers is not the same as the harmonic simplicial sub-melody or the Chromatic simplicial-sub-melody as described e.g. in post 104 about them.
The simplicial sub-melody of the melodic centers is defined by the melodic centers of the melody (see also post 65 about the centers ) .
HOW TO FIND THE MELODIC CENTERS OF A MELODY:
The way to do it is the next
1) We partition the melody , to time intervals or connected pieces of it defined by the property that each one of then has a single underlying chord, and the piece of the melody is maximal with this property
2) Then for each such time interval or piece of the melody, we define as its center, the note of the melody with the maximal time duration. There is one such note for each instance of a chord in the chord progression. The sequence of these notes is the simplicial sub-melody if the melodic centers of the initial melody.
