Twelve equal steps
One tuning plays in every key.
A key is the pitch a piece treats as home, together with the notes it uses around that home. Move the home and every note moves with it.
Equal steps split the octave into twelve equal parts. In 1584 CE the Ming prince Zhu Zaiyu published that division and computed its twelfth-root ratio by hand. Simon Stevin described the twelfth root of two about 1605 CE. Every fifth sits 1.96 cents narrow of pure 3:2. Every major third sits 13.69 cents wide of pure 5:4.
Meantone tuning kept the thirds near its home pure and left its far keys unplayable. Move the same chord six steps up in meantone and it lands on a 427-cent third that sours. That sourness lives in the upper partials, so both travelling chords use a reedy tone.
Equal steps make all twelve keys alike, so one chord shape can travel to any home. Temperament walks that shape through seven steps.
Play the pure triad and the equal-steps triad, then hold their two thirds together for the beat equal steps cost. Now move the chord six steps up in both tunings and hear the meantone move sour.