How do equal-tempered major thirds differ from pure major thirds?

In the context of tuning and temperament, the primary difference between equal-tempered and pure major thirds lies in their acoustic accuracy and harmonic consonance.

A pure major third is based on a simple frequency ratio of 5:4, which is considered acoustically "in tune" or perfectly consonant. In contrast, an equal-tempered major third is constructed by dividing the octave into 12 equal semitones, each measuring 100 cents. Because this divisional system prioritizes the ability to play in all keys, it sacrifices the purity of individual intervals; consequently, an equal-tempered major third is 14 cents sharper than a pure major third.123

While pure major thirds provide a harmonious, beat-free sound, they are fixed to specific keys and cannot accommodate the complex modulations of modern Western music. Equal temperament, by distributing these small intonational defects equally across the chromatic scale, allows for harmonic flexibility at the cost of the perfect consonance found in pure intervals.23