Pythagoras’ simple-ratio tuning system proved ultimately unsatisfactory.

Evidence

With such elegant relationships between simple whole numbers and pleasing intervals singing from the monochord, why not try to build a musical system by continuing with the simple ratios? Pythagoras did try, and the results are anything but completely satisfactory. — Eric J. Heller, Why You Hear What You Hear- An…, 2359

Categorization

• QUESTION: What exactly proves unsatisfactory about the Pythagorean system — how and where do the simple ratios break down?