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In tonal harmony, or rather in most genres of popular music, most of which happen to be tonal, people grow up listening to, then writing, then listening again to what you may call "tertial" harmony: chords built of superimposed thirds from a given fundamental or "root".

Now, some books (some Berklee textbooks included), present variations on these structures, but for the most part they suggest you use them as "reductions", implications, or plain ol' voicings that, in a tonal context, will function as the chords they are supposed to imply.

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