The equal temperament system of tuning is based upon the principle that each semitone is exactly the same distance harmonically from the two semitones bordering it. Professional piano tuners have adopted this system as the modern standard for instrument tuning.
The well temperament method of tuning is centered on the idea that adjusting the size of certain intervals within the scale produce more consonant, tuned sounds than those created by equal temperament. Proponents of the well-tempered system claim that this method of tuning produces more musical sounds than equal temperament. An example justifying the use of well-tempered tuning would be the perceived tuning discrepancies between a major third interval and its inverse, the minor sixth. If the major third is adjusted in accordance with equal temperament, the minor sixth will be out of tune in relation to the musical key.
One of the most popular works propagating the validity of the well-tempered system is J.S. Bach's "Well-Tempered Clavier," composed in 1722. Incorporating each of the 24 musical keys, the "Well-Tempered Clavier" demonstrated the formidable power of the new tuning system. Unlike prior methodologies, well-temperament enabled J.S. Bach to create harmonically rich works without having to compensate for tuning discrepancies.
Those in favor of equal temperament have watched their preferred tuning system gain popularity around the world. The consistent, quantifiable distance between semitones has allowed for a global standard in tuning. Many argue that this consistency allows for mathematically true -- and thus correct -- music performance.