Tetrad

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Not to be confused with Tetrachord.
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A tetrad is a chord of four pitch classes. Some examples are Major 7ths, Minor 7ths, Harmonic minor 7ths, Regular 7ths, and dimished and augmented 7th cords. Some microtonal ones include: Harmonic 7ths, (Basically regular 7ths but detuned) and Neutral 7ths.

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There are lots of 7th cords, but they can also be add chords, like Major Add 2, or Major add 6.