Who invented equal temperament

Chinese prince and musicologist Zhu Zaiyu in 1596 and French philosopher and mathematician Marin Mersenne in 1636, among others, wrote of such a system. The idea of equal temperament had its most effective advocates among German musicians and theorists, beginning with Andreas Werckmeister in the early 18th century.

1. Who invented 12 tone equal temperament?
2. Did Bach invent well temperament?
3. What temperament did Bach use?
4. Is equal temperament out of tune?

Who invented 12 tone equal temperament?

Simon Stevin was the first to develop 12-TET based on the twelfth root of two, which he described in Van De Spiegheling der singconst (ca. 1605), published posthumously nearly three centuries later in 1884.

Did Bach invent well temperament?

Bach's motivation for composing the WTC was to demonstrate the feasability of composing in well temperament and to demostrate the varying key colors in well tempered tuning as one progresses around the circle of fifths.
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Well v.s. Equal Temperament.

What temperament did Bach use?

In more recent times, Johann Sebastian Bach has been seen, on the one hand, as a pioneer of Equal Temperament [8] and, on the other, as a proponent of unequal Well Temperaments. In this latter regard, suggested temperaments have included those of Werckmeister [9] and Kirnberger [10].
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Is equal temperament out of tune?

One of those tunings was already known to the ancients: equal temperament. Here the poison is distributed equally through the system: The distance between each interval is mathematically the same, so each interval is equally in, and slightly out of, tune.