Harmony in western music is based on triads.  Triads are simple 3 note chords built on thirds.(See chapter Circle of Fifths/Transposing section intervals)

The chords above are written in root position, which is the most basic way to write a triad.  In root position, the root, which is the note that names the chord, is the lowest note. The third of the chord is written a third above the root and the fifth of the chord is written a fifth higher than the root which is a third higher than the third of the chord.  So the simplest way to write a triad is a stack af thirds above the root.

First and Second Inversions:  Any other chord that has the same named notes as a root position chord is considered to be the same chord but in a different position.  so all chords that have D natural, F sharp and A natural are considered to be a D major chord.  If the third of the chord is the lowest note than the chord is said to be in first inversion.  If the lowest note is the fifth of the chord it is in second inversion. 

It does not matter how far the higher notes are from the lowest note, or how many of each note there are at different octaves, all that matters is which note is lowest.

Naming Triads: The position that a chord is in does make a difference in how it sounds, but it is a fairly small difference. Listen to a G major chord in different positions.

A much bigger difference in the chords sound comes from the intervals between the root position notes of the chord.  For example if the b in one of the above chords were changed to a B flat, you would still have a G triad but the sound would be much different.  So chords are named according to the intervals between the notes when the chord is in root position.

The chords above are all G chords but they are four different G chords.  The intervals between the notes are different so the chords sound different.

Major and Minor Chords: The most commonly used triads form major and minor chords.  All major and minor chords have an interval of a perfect fifth.  A perfect fifth is 7 half steps from the root.  A perfect fifth contains a major third and a minor third.  If the interval between the root and the third is minor, than the chord is a minor chord.  If the interval between the root and the third is major, (with a minor third between the third and the fifth) than the chord is a major chord.

Naming Triads: The position that a chord is in does make a difference in how it sounds, but it is a fairly small difference. Listen to a G major chord in different positions.

A much bigger difference in the chords sound comes from the intervals between the root position notes of the chord.  For example if the b in one of the above chords were changed to a B flat, you would still have a G triad but the sound would be much different.  So chords are named according to the intervals between the notes when the chord is in root position.

The chords above are all G chords but they are four different G chords.  The intervals between the notes are different so the chords sound different.

Major and Minor Chords: The most commonly used triads form major and minor chords.  All major and minor chords have an interval of a perfect fifth.  A perfect fifth is 7 half steps from the root.  A perfect fifth contains a major third and a minor third.  If the interval between the root and the third is minor, than the chord is a minor chord.  If the interval between the root and the third is major, (with a minor third between the third and the fifth) than the chord is a major chord.