String-length ratios of small integers produce the most consonant musical intervals.

Evidence

Whatever the length and pitch of the string initially, a pitch exactly an octave higher is reached by reducing the length of the string by half: L → L/2; f → 2f. Similarly, if you make the string 2/3 of its original length, the pitch rises exactly a perfect fifth, a fraction 3/2, above the original pitch. Or, if you make the length three-quarters as long as it was originally, the pitch rises a perfect fourth, or a fraction 4/3, above what it was. If you believe in the primacy and even mystical qualities of small numbers, the numbers 1 and 2 and 3 must be among them. Their ratios, 2/1, 3/2, and even 4/3 = 2×2/3 are precisely the most consonant musical intervals. — Eric J. Heller, Why You Hear What You Hear- An…, 2359

Categorization

• XREF: Connects to the reader’s underlying why-question about auditory perception — the physical basis of consonance feeding into perception of pleasantness.
• CANDY: The core fact that halving a string length raises pitch exactly an octave is an accessible elevator-conversation tidbit.