The idea is that the selected intervals follow the contour of the melody. When the melody goes up, down or makes a leap, so does the parallel harmony.
Example 1: In the key of C, if the chord in the song is C and the melody goes CDEDC___ you might want to play the third above as your parallel harmony, so you would simultaneously play EFGFE____. That is playing two notes at a time starting with the interval of a major third. If you lower that harmoney EFGFE___ by an octave then you get the sixth below the melody.
Example 2: Still in the key of C, if the chord in the song is Am and the melody goes CDEDC___ you might want to play the third below as your parallel harmony, so you would simultaneously play ABCBA____. That is playing two notes at a time starting with the interval of a minor third. If you lower that ABCBA____by an octave then you get the tenth below the melody.
Example 3: Octave playing always works in every key against any chord. That is playing two notes simultaneously with the interval of an eighth.
So how to choose between #1 and #2 and which inversions to use? The major and minor thirds must match the chords of the song. You could figure it out abstractly or do what I do, just listen and play the appropriate interval. There are only two to choose from. One always sounds better than the other.
As for the thirds octave-lowerd inversions of a sixth and 10th. As a general rule, I prefer those wider inversions, especially when the melody is lowish. When the melody goes high I often play the close thirds too.
Playing parallel harmony requires practice. Scales work well for this. When performing though, I might use just a few notes of this technique at any one point. It can also be nice to let the other musicians play melody while I play the parallel harmony as a single line.
Edited by Jody Kruskal, 23 October 2017 - 07:53 PM.