How did equal temperament make enharmonic modulation easier?

Equal temperament facilitated enharmonic modulation by establishing a system where notes that are theoretically distinct—such as F♯ and G♭—are tuned to the exact same pitch.12

In earlier systems like meantone temperament, the keyboard provided only one key for two different notes (e.g., E♭ and D♯), which were not acoustically equivalent. Attempting to use these notes interchangeably resulted in highly dissonant intervals, often referred to as "the wolf". Because these older systems were not uniform, music transposed into distant keys would sound unpleasantly out of tune.31

By dividing the octave into 12 equal semitones, equal temperament ensures that intervals are identical across all keys. This uniformity allows composers to treat enharmonically equivalent notes as identical, making it possible to modulate freely between any keys and complete cycles of key changes that return to the original tonic. Consequently, this flexibility became a standard tool for 19th-century composers, enabling the use of the full chromatic scale with complete freedom.132