Sit down at the piano and play the chords C and F in root position, back and forth, like so: (C E G) to (F A C). Pretty clunky! Now invert the C chord; that is, move the bottom note up an octave. Alternate that version of the C chord with the F chord, like so: (E G C) to (F A C). It sounds smoother! You just experienced the magic of voice leading.
To understand how voice leading works, imagine that each note in a chord is being sung by a different person. For three-note chords, you will need three people. Let's call them David Crosby, Steven Stills and Graham Nash. (In the photo, they're sitting Nash, Stills, Crosby.)
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