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This full score for Bach's St. Matthew Passion helpfully has the figured bass written below the continuo part. I found this particularly illuminating, as it helped me to see the harmonic movement which is "blurred" somewhat by the chromatic alterations in the contrapuntal lines. (A first read through, using a piano reduction in a vocal score was pretty unedifying!)

However, this autograph (?) manuscript doesn't have the figured bass. And I couldn't find figured bass on any Bach original scores I found online. So, I just wondered if Bach did put figured bass in any of his scores? Or in the continuo parts? Or would the continuo player have used the full score, written the figured bass in themselves, or just listened to what was going on in the other parts?!

The main reason I'm interested, is because I presume the figured bass in the score I link to above has been added by the editor, and due to the chromatic alterations in the instrumental parts could have been interpreted in a number of slightly different ways. Would baroque compositions have had a "definitive" figured continuo part?

BTW, I already looked at this post and its answers.

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To Bach, the bass was central and often the first voice that he wrote. As an avid keyboard player and composer he was probably too meticulous to not realize voices for orchestral scores. A first search for "Generalbass" in the official Bach repository results in no mention of figured bass: http://www.bach-digital.de/

However, for chorales that he produced en masse, as part of his job as a cantor, figured bass was a way to play the same hymns over and over again, with room for variation:

Bach, while in Leipzig, had made a collection of chorale melodies with figured basses. It comprises all the melodies in ordinary use there, in number about two hundred and forty. In the year 1764 the manuscript was in the possession of the music seller, Bernhard Christoph Breitkopf, of Leipzig,who offered copies of it for sale at ten thalers each. “This important collection is lost.” A few fragments of it,however, seems to have been saved. Pupils of Bach who took down copies of his organ chorales appended to themthe two-part figured settings from Bach's chorale book,when they could get access to them. Thus, when they played the organ chorale as a prelude, they could afterwards use the melody, as harmonised by their revered master, for accompanying the congregation singing. In this way the figured setting of the melodies "Christ lag in Todesbanden", "Herr Christ der ein'ge Gottessohn", and "Jesu meine Freude".

"Bachs, J. S. Vollständiges Choralbuch mit in Noten aufgesetzten Generalbasse an 240 in Leipzig gewöhnlichen Melodien. 10 thl." Breitkopf catalogue from New Year, 1764, p. 29.

Philipp Spitta, 1899, "Johann Sebastian Bach, his work and influence on the music of Germany, 1685-1750"

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From this http://scholarship.claremont.edu/cgi/viewcontent.cgi?article=1083&context=ppr it seems like JS did include some figuring but not everywhere. Of course, the solo stuff, things like the Italian Concerto or the Goldbergs wouldn't need figuring.

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Remember that composers were also performers, and for the most part weren't thinking about how performers 250 years later would read their manuscripts. They wrote music for them to play, and many times didn't need detailed figures, especially if they didn't have the piece slated for publication. Handel's Messiah is another very popular piece where there are no figures in the continuo part.

Bach wrote other pieces, like the Gamba Sonatas, with an obligato part. He wrote his Violin Sonata in e minor with careful figures. It just depends on the needs of the piece and the audience of the manuscript or publication.

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