How did equal temperament make modulation between keys easier?

Equal temperament facilitates modulation between keys by dividing the octave into 12 semitones of equal size, ensuring that the intervals between notes remain consistent regardless of the key signature.1

In earlier systems like just intonation or meantone temperament, intervals were calculated based on acoustically pure ratios. As a result, these systems accumulated intonational errors when moving to distantly related keys, causing instruments with fixed intonation to sound out of tune in those tonalities. Because each raised key in meantone tuning was restricted to a single function—such as sounding only as E♭ rather than D♯—musicians were often limited in their ability to modulate.12

By distributing minor intonational defects equally across all 12 tones, equal temperament allows keyboard instruments to play in any major or minor key without requiring retuning. This system also relies on enharmonic equivalence, where notes like F♯ and G♭ sound the same, providing the flexibility necessary for fluid modulation throughout the entire chromatic scale.1