The sixteenth-century bargain
Meantone hides the error in one fifth.
A Pythagorean major third comes from four pure fifths lowered by two octaves. Its ratio is 81:64. A pure major third is 5:4, and the 81:80 gap between them is the syntonic comma. Quarter-comma meantone narrows each common fifth by one quarter of that gap. After four fifths, the four small changes make the third pure. Eleven narrowed fifths leave the remaining interval at 737.64 cents, 35.68 cents above a pure fifth. These are reedy tones, because the howl lives in the upper partials an organ pipe supplies. The wolf exposes the cost of that bargain on fixed-pitch instruments.
Play the pure fifth and meantone wolf separately, then press Hear both fifths. Listen for the 701.96-cent pair to settle and the 737.64-cent wolf to rattle 16.3 times a second.
The pure upper tone is 392.44 Hz, and its second partial lands on the third partial of C4. The wolf reaches 400.61 Hz, so the same two partials miss by 16.3 Hz and buzz. Pietro Aron described a close method in 1523. The 678-cent wolf in the Story room comes from Pythagorean tuning.