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Top > Cadences
 
 When European composers were doing their earliest experiments with harmony they discovered that chords whose roots differed by an interval of a perfect fifth sounded most related to each other. There is a reason for this that is grounded in physics and in the way the human ear perceives musical pitches.
 When pitches differ by an octave plus a perfect fifth, the lower of the two pitches as a side effect of sounding also produces an overtone, a pitch that vibrates three times as fast as the lower pitch. This overtone exactly matches the higher pitch of the pair. This overtone and the higher pitch can be made to sound like perfect replicas of one another. The ear finds this coincidence of overtone and pitch to be highly pleasurable.
 When a composer arranges a chord, he can decide to place any of the pitches any number of octaves higher or lower in the chord. If he reduces the high pitch by an octave, then the low pitch and the high pitch vary by a perfect fifth. In this case, both pitches produce overtones whose frequencies are integer multiples of their pitch. In this case, the higher note produces an overtone (a quietly sounding alternate tone) that is an octave above its main pitch. This coincides with the overtone produced by the lower pitch that vibrates 3 times faster than its main pitch. Since these overtones are very audible and exactly coincide the ear is also pleased by this arrangement of notes.
 When two chords of the same type have a root that differ by an interval of a perfect fifth are played in sequence, every pitch in one of the chords will share very pronounced overtones with a matchng tone in the succesor chord.
 One of the earliest harmonic games tried in Western harmony started out with the composer playing an initial major triad chord. He would next play a major triad whose root was a perfect fifth below the root of the first chord. They would then come back to the original chord and follow it by the major triad whose root is a perfect fifth above the original chord root. Finally they would come back to the original chord.
 If you laid out the chord roots on a line, you could place the initial chord in the middle, place the root a fifth below on the right, and place the root a fifth above on the left. If you placed your finger on the chord roots as their chord played, you would touch the middle root, touch the one on the right, come back to the middle, touch the one on the left, and then come back to the middle.
 The motion your finger traces out is an oscillation that starts on the middle chord, moves right, moves to the center. moves left and then comes back to the center.
 The name given to this oscillation of chords is I-IV-I-V-I. It is incredibly pleasant to listen to. Click here to play one arrangement of it.
 The three different chords in the progression produce three separate feelings in the listener. The I chord establishes an initial sound for the listener a reference that she or he will use to understand what comes after.
 The IV chord as it sounds produces overtone sounds which match up with the octave overtones of the I chord. In some sense a quiet reorchestrated echo of the I chord sounds when the IV chord plays.
 When the I chord plays it produces overtones which match up with octave overtones of the V chord. When the I chord plays, the listener hears a rearranged version of the V chord as an after-echo. When the progression moves from I to V, the I chord produces a pre-image of the following V chord, which gives the ear a prediction of the next chord that will be visited.
 
Editor: David Luebbert; Updated: 2/8/01; 4906 hits.




Last update: Friday, November 10, 2000 at 12:50 PM.