in mathematical terms, the doubling, tripling, quadrupling, etc., of numbers as they go up or the halving, thirding or quartering, etc., of numbers as they go down. This last is not generally realized, that harmonics also go down. But here is an example of a harmonic: A pitch vibrating at, let us say, 200 vibrations a second will have a harmonic at 400, 600, 800, 1000, 1200, 1400, etc., vibrations a second. It can also have a harmonic of 100, 66 2/3, 50, 40, 33 1/3, 28 4/7, etc. While these upper or lower harmonics are of far less intensity they are still there. They might not be apparent to the ear at first listen but almost any pitchhas upper and lower harmonics. —Science of Survival Glossary (app 11.7.90)