By playing every other note in the scale we obtain 7 triads - three major, three minor and one diminished. Playing the notes in a triad simultaneously we get chords. This is called the harmonization of the major scale - we have obtained a family of chords that derive from a certain scale and thus work together.
This is the chord formula for every major scale: I major, II minor, III minor, IV major, V major, VI minor and VII diminished. In the context of four note chords we will be altering a little bit this chord formula.
Superimposing the major triad over the corresponding major chord will produce the most consonant sound possible. By playing triads from the same family - for example, instead of D major over the D major chord we could play F# min or B min - we can still achieve a consonant sound without being too obvious. The three triad families are (I, III, VI) - (II, IV) and (V, VII).
I encourage you to play with these triads and use any of them over any chord. What sounds consonant to me might not sound to you. Nevertheless, being able to hear them and being familiar with them will help you take informed decisions while improvising.
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