Twelve equal steps
One tuning plays in every key.
Play both triads below. Hold their thirds together and a slow beat appears.
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. Temperament walks the same chord shape through seven steps and into other keys.
Play the pure-ratio triad, the equal-steps triad, then hold their thirds together. Listen for the chords to keep the same identity while the two upper tones produce a slow beat. Equal steps shift the pure fifth and third slightly so twelve identical steps close at the octave. That compromise lets one fixed tuning carry the same chord shape into every key.