How does meantone temperament make major thirds sound pure?

In meantone temperament, major thirds are made pure by intentionally flattening the fifths within the scale.12

By narrowing each fifth by a quarter of a comma, the system distributes the necessary tuning adjustments across the keyboard cycle. When a series of four of these slightly flattened fifths is tuned (such as C–G, G–d, d–a, and a–e′) and the excess octaves are removed, the resulting major third (C–e′) aligns with the simple 5:4 ratio required for a pure, natural interval.21

This approach creates a notably pleasing sonority for triads and provides a more consistent melodic scale than just intonation by substituting a single, uniform mean whole tone for the varying whole tones found in other systems. However, this purity comes at the cost of creating highly dissonant intervals, known as the "wolf," when the music requires notes outside the system's limited range.12