Meantone and well temperaments trade unlimited modulation for purer intervals and distinct key colors

Before 12-tet became standard, keyboards were tuned with meantone and well temperaments — compromises between just intonation (pure but key-locked) and equal temperament (uniform but everywhere slightly impure). Meantone tunings flatten most fifths by a fraction of the syntonic comma (e.g., quarter-comma meantone flattens each fifth by 1/4 comma) to make the major thirds in central keys nearly pure, at the cost of one badly out-of-tune wolf fifth and unusable remote keys. Well temperaments (Kirnberger, Vallotti, etc.) distribute the tempering unevenly but keep every key playable; the sum of all fifth deviations in any octave-based temperament must equal the Pythagorean comma. A defining consequence is key color: because the interval sizes differ from key to key, each key has its own character. This is what Bach explored in the Well-Tempered Clavier — distinct key colors, not (as often misstated) equal-temperament modulation.

Examples

Quarter-comma meantone flattens each fifth by 1/4 comma so that four stacked fifths yield a pure 5:4 major third; a wolf fifth absorbs the leftover. Scarlatti K380 in quarter-comma meantone sounds subtly different in central keys and jarring in remote ones. Bach performed the WTC to show each key had its own color.

Assessment

Explain what problem meantone temperament solves relative to Pythagorean tuning, and what it sacrifices. Why does a well temperament give each key a distinct color while 12-tet does not? Correct the common claim that the Well-Tempered Clavier demonstrates equal temperament.