Whether two vibration frequencies are commensurate with small integer ratios shapes their musical meaning

Evidence

What can result from this? One important question is whether the two frequencies are commensurate. By that we mean, is some integer multiple of one of the frequencies exactly equal to an integer multiple of another? This question will be more meaningful, in music and in practice, if the integers are small. In other words, we are not usually interested in whether 2057 f1 = 1317 f2, but we are interested if 2f1 = f2 or 3f1 = 2f2. — Eric J. Heller, Why You Hear What You Hear- An…, 309

Categorization

• DEFINE: Defines commensurate frequencies and stresses that small-integer ratios are the musically meaningful case.
• XREF: This prefigures consonance and the role of simple integer ratios in harmony — connects to Pythagorean tuning and the physics of musical intervals.