Small-integer frequency ratios yield short periodic traces while irrational ratios never repeat

Evidence

If the frequencies of the two vibrations are commensurate—for example, 3f1 = 2f2, or more generally mf1 = nf2 for small integers m and n—the path y(t) traced out by the fork will be periodic, with a period. This is made clear in the following. If the two frequencies are commensurate but only with large integers involved, such as m = 16 and n = 17, the trace will still be periodic, but with a longer period. Last, the two frequencies could have a ratio that is an irrational number such as the —in that case, the trace never exactly repeats any pattern. — Eric J. Heller, Why You Hear What You Hear- An…, 310

Categorization

• DEFINE: Explains how commensurability of frequencies determines periodicity of the combined vibration path.