Well, here's an attempt to explain things (a first approximation, anyway -- apologies to those who would ground the explanation in the "written-music" way). Consider the notes that could be sung by a bass voice. They run from the E above low C up to middle C. To be sure, bass singers sometimes sing notes out of that range, but, for example, to sing low C would be something you wouldn't hear that often, outside of the Metropolitan Opera. Now for each of those notes, we have a choice of what higher notes we want to have to harmonize with it. For example, if we are considering the F below middle C, we might choose an A above it, and a C above that, and an F above that, for harmonizing. When we sound all the notes we have a chord. As long as the A, C, and/or F in our example are above the F we started out considering, we can choose quite a number of different A's and/or C's and/or F's to complete the chord. (Though the result may not sound very good if these notes are outside the range of choral voices, or there are two of them that are more than an octave apart with nothing in between.) For example, we could choose the A below middle C and middle C. We can go from F to A by starting on F at the count of 1, and then going up to G on the count of 2 and A on the count of 3. Because we counted to 3 to get up from F to A, that interval is called a third. Similarly, from F to middle C would be a fifth. Because the chord contains only thirds or fifths (or notes a number of octaves higher than such), we say the chord is in root position. We can form a sequence of root position chords. Starting with the E just above low C, we could have E, G and B, or F, A, and C, or G, B, and D, and so on. You can play these chords in succession on the piano with your left hand, using your fifth, third and thumb fingers. However, you discover that they produce a rather bad effect, because of the parallel fifths they make when played one after the other. Much of the work of harmony then centers on creative ways to complete chords, without having any two consecutive ones result in there being parallel fifths, octaves, or unisons (unless the style of the composer involves deliberately using such parallels for special effects). One way to avoid parallel fiths is to "turn off" the lowest note and have one of the higher notes (in our example, the A or the C) of the original chord become its lowest note. In our example, we might take the F below middle C out and put in the F above middle C instead. The lowest note of this new chord would be A. When the lowest note of the new chord is the note that formed a third with the "turned-off" note, that is called a first inversion. If the lowest note is the one that formed a fifth with the turned-off note, that is called a 6-4 chord. (The use of 6-4 chords can produce bad effects; some theorists dislike them almost as much as they dislike parallel fifths.) Enough for today; hope this was helpful.
Topic: Root chords...