Question: I've done some reading and I've discovered that our modern system of music theory (I'm looking at you Roman numeral analysis) is not the same system that most of the great composers used, including the "Big Three": Mozart, Bach, and Beethoven. Apparently, they favored the system of thoroughbass. Bach himself was supposedly against Rameau's theory of harmony, from which our modern system is derived.

I did a little more digging and I managed to find some good texts that I would like to study; however, there are just so many to choose from. It seems that thoroughbass was broken down into two different goals, writing down a realization (taking as much time as necessary to do this), and realizing a figured bass extemporaneously at a keyboard, as if sight reading.

My question is this: **What is the modern approach to teaching/learning thoroughbass?**

---

I wonder if a few particular items are still used in modern curricula:

It seems to me that the C.P.E Bach essay, as well as J.S. Bach's precepts and principles, are well known, but are a little difficult. There's also the Albrechtsberger book and a book that seems to be written by Mozart on the subject, though I don't know if the claim of Mozart's authorship is reliable.

Ultimately, I would like to be able to look at a figured bass and be able to provide a realization, either written down or extemporized, in any key.

Answer: 
There are several texts that are readable. One is available on IMSLP: <https://imslp.org/wiki/Thorough-Bass_Made_Easy_(Pasquali%2C_Nicolo)>

Arnold's two volume set is available from Dover so not too expensive. Not all thorough bass manuals agree with each other. Likewise, much modern stuff (like secondary dominants AKA applied or attendent chords) were not well described until around 1890 (Francis York's and Frank Shepard's books freely available). It probably pays to look at older stuff in conjunction with modern texts.

Bach, Mozart, and Beethoven did have somewhat different educations. Bach studied with his brother and did lots of score study from well known musicians (as did others). Mozart studied with his father (a rather famous teacher at the time) and did lots (apparently) with "Partimenti" (See the site: Monuments of Partimenti) to see how various patterns were learned. Beethoven studied with Neef who was a well-known composer and teacher (and later with Haydn and Albrechtsberger). Albrechtsberger's teachings are available on the net.

All of these though use the hexachord description of scales (combined with some major-minor theory). One overlaps 6-note series with each other C-D-E-F-G-A and F-G-A-B(b)-C-D and G-A-B-C-D-E (which go by the names ut-re-mi-fa-so-la). This gives a method describing all notes from low G (gamma-ut) for several octaves. The name get funny as F can be either "ut" in the "soft" hexachord or fa in the "natural" hexachord (it doesn't occur in the "hard" hexachord.) It's rather complicated. Renaissance counterpoint used notes not describable with this system so more flats (and some sharps) were introduced and composers and performers were supposed to know how to insert unmarked accidentals. Here's a good description of hexachordal theory.

<http://www2.siba.fi/muste1/index.php?id=72&la=en>
For myself and others a list of terms... 

* figured bass: a system to represent chords, synonymous with 'thorough bass'
* basso continuo : executing a figured bass
* partimenti : figured bass exercises to teach students harmony and practice basso continuo performance

[The Art of Partimento](https://rads.stackoverflow.com/amzn/click/com/0195394208): History, Theory, and Practice by Giorgio Sanguinetti 

This isn't a collection of partmenti, but rather a text about the method and its history. Lots of musical illustrations, but not really a book from which to practice.

[The Langloz Manuscript: Fugal Improvisation through Figured Bass by William Renwick (Author)](https://rads.stackoverflow.com/amzn/click/com/0198167296)

This may not have a lot of immediate practical value, but it's very interesting to read about how partimenti and figured bass as the foundation for the master skill of fugue improvization.