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Sometimes the feeling you want to convey in your music is one of two tonally related, but rhythmically independent melodic ideas. In a case like that you might be weaving two entirely different melodies together - or the same melody at different times (a round).
One way to create this sense of independence is to have both voices play variations of the same melody, but stagger the starting points. This creates an interlaced, tapestry-like effect.
One of the challenges of this “staggered” type of approach is the danger of becoming too hopeful that your entire melody will hold up to harmonic scrutiny when it overlaps itself. You may find that there are some dissonances to be resolved by altering a few notes in one or the other melody line from time to time.
You can use Polyrhythms to do independent voicings on one instrument.
If you have time signature 1: x/y and 2: z/y, you have to repeat the 1st pattern 'y' times and the 2nd pattern 'x' times before both of the rhythms match up again.