A simple relationship is reported between vibrational frequencies, bond lengths, and reduced masses for many families of stable, ground state diatomics: the frequency is proportional to the reciprocal of the product of the bond length and the square root of the reduced mass. This is demonstrated with each of the following related families: the alkali metal diatomics, the group 15 diatomics, the group 16 diatomics, the halogen diatomics, the alkali metal hydrides, the alkaline earth oxides, the group 14 oxides and their sulfides, the diatomics of carbon, of silicon and of germanium with group 16 elements, the hydrogen halides, the halides of lithium, of sodium, of potassium, of rubidium and of cesium, the chlorides of the alkali metals and of silver, and the polyatomic hydrides of groups 14 and 15. Although correlation coefficients of 0.99 or greater in each of the 21 families examined demonstrate the validity of the correlation, the deviations found are significantly larger than can be attributed to experimental uncertainties. (C) 2004 American Institute of Physics.