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?**

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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>
### TL;DR

The curriculum for one modern course (ca. 2012) is based on:

1. Fux, *The Study of Counterpoint*
2. Morris, *Figured Harmony at the Keyboard*
3. Kearney, *Figured Bass for Beginners*

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I took a course in figured bass as part of a university music degree program. It was considered an upper-level course and the prerequisite was a standard two-year music theory course, which included introductory figured bass concepts.

The foundational material in most modern music theory curricula comes from **Fux's "The Study of Counterpoint"** and his "species" of counterpoint. Fux lays out several "species", starting from the very simple (a melody comprising whole notes — the "cantus firmus" — against which the student writes a whole-note counterpoint) to the more complex, involving the use of suspensions.

Modern textbooks adapt Fux as preparation for the modern, triad-based major/minor system, but the original Fux is based in the pre-Rameau modal system and modeled on Palestrina. His book holds up very well as a learning model, and provides an outstanding starting point toward learning figured bass.

The counterpoint course itself used two books:

1. R.O. Morris, *Figured Harmony at the Keyboard: Part 1* (Oxford University Press, 1933).
2. Helen Keaney, *Figured Bass for Beginners* (E.C. Schirmer Music Company, 1981).

The Morris book is a collection of graded exercises, with chapter-by-chapter explanations of the technique being introduced.

Kearney is a collection of standard realizations of common figured bass techniques and situations. The idea is to memorize the exercises to create a readily available "toolbox".

Used together, these books allow for the development of a very solid foundation.