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Kapellmeister at Anhalt-Cothen:
In 1717, Bach became Kapellmeister (the chapel master, who directed and/or composed music for a church or chapel) in the court of the music-lover Prince Leopold of Anhalt-Cothen.

During this period, Bach's major works included the Brandenburg Concertos (1721), The Well-Tempered Clavier (first book, 1722). In 1721, the Prince married a woman who did not share the Prince's interest in music, and the Prince's support of Bach lessened. Bach would soon leave.

Bach's Second Marriage:
Bach's wife Maria had died in 1720. In 1721, he married Anna Magdalena Wilcke (the daughter of the town trumpeter); they would have 13 children together (including Johann Christian Bach). Altogether, Bach had 20 children with his two wives, but 10 of his children died in infancy. Four went on to become well-known composers and musicians.

Life in Leipzig:
Bach left Anhalt-Cothen in 1723 for Leipzig. He became Kantor (teacher and director of music) of St. Thomas's in Leipzig. Bach remained in Leipzig for the rest of his life.

During this period, Bach's major works included St. John Passion (1723), St. Matthew Passion (1727), Suite No. 3 in D (1729), Magnificat in D Major (1731), Christmas Oratorio (1734), Italian Concerto (1735), Goldberg Variations (1741-1742, originally called "Aria With Diverse Variations," but later nicknamed after Bach's student Johann Gottlieb Goldberg), The Well-Tempered Clavier (second book, 1742), the Musical Offering (1747), and The Art of the Fugue (unfinished, 1749).

Bach's Death:
By 1740, Bach's eyesight was failing. Two eye operations resulted in Bach's complete blindness; these operations also damaged his health and may have hastened his death. He died of a stroke on July 28, 1750. Bach is buried at St. John's cemetery, Leipzig. Bach's widow Anna lived for another ten years, dying in poverty in 1760. Bach's death in 1750 marked the end of the Baroque period in music.

Look at the following of the above.

Bach's wife Maria had died in 1720. In 1721, he married Anna Magdalena Wilcke (the daughter of the town trumpeter); they would have 13 children together (including Johann Christian Bach). Altogether, Bach had 20 children with his two wives, but 10 of his children died in infancy. Four went on to become well-known composers and musicians.

It is incorrect to say Bach's wife had died in 1720 in the given context. It should be Bach's wife died in 1720.
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In 1721, he married Anna Magdalena Willcke. So it is incorrect to say he would have 13 children. It should be 'he has 13 children'.

I want to know your opinion on two questions I have raised here.
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Andrei, you're full of questions today! ~L~

"Bach's wife Maria had died in 1720" is not incorrect, actually.
I assume the past perfect was used because the title of the paragraph is "Bach's second marriage", and Maria had already died by the time Bach married his second wife. The past perfect may not be absolutely necessary, but it is still acceptable.

"In 1721, he married Anna Magdalena Willcke. So it is incorrect to say he would have 13 children. It should be 'he has 13 children'."
"He has 13 children" is incorrect. He is dead (and so are his children by now), so he no longer has any children.
"Would have" is not the only possibility, but it is as correct as saying "he had 13 children". The use of "would have" gives the idea of future within the past, meaning that the children came after they got married.

Miriam
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Something pedantic:

As it is a proper name, you should spell the town "Köthen" rather than Cothen. If you don't have an Umlaut (ö), then you can also spell it as "Koethen", which would still be more correct than Cothen.