Originally Posted by
CliffR
I guess I didn't put that very well. What I meant to say was: assuming we divide by the 12 semitones so that each is 12th-root-of-two times the frequency of its predecessor, then we get the property that the octave is exactly double the frequency of the root. For the fifth, we get 12-root-of-2 to the power 7 (7 semitones between the fifth and the root). This gives approximately 1.5, meaning that the second octave of the fifth has *approximately* the same frequency as the third octave of the root. Similarly, the frequency of the third is given as 12-root-of-2 to the power 4, which is roughly 1.25. This means that the fourth octave of the third is approximately the same frequency as the fifth octave of the root. These correspondences between higher harmonics of the root and its intervals may account for the fact that these intervals sound consonant. However, these correspondences are only approximate, and depend on how you choose to divide up the octave.
Sonny S. -- Les Paul Player
Today, 04:18 AM in The Players