The Goldberg Variations (the link is to the Wikipedia article, which has much worthwhile detail) show one example of the way Bach took a simple form and added additional structure to it to create something much larger and more complex. The only requirement of a theme and variations is that the variations should have a clear relationship to the theme, and usually there's an obvious progression from one variation to the next in terms of rhythmic activity and complexity. Here is a link to a YouTube video of a variation set by Bernardo Pasquini, on a theme known as La Folia, performed by organist George Becker, MD.
In Bach's set, though, the variations take a much wider variety of forms, which helps sustain interest for the immense length of the work. The variations can be subdivided into groups of three; each group consists of a dance movement or genre piece, an arabesque, and a canon. Among the genre movements are a French Ouverture and a Fughetta; the final variation is a Quodlibet.
The canons begin at the unison, and proceed by steps up to a ninth (an octave and a second). By convention, all of the canonic voices should use similar articulations and ornamentation, though players don't always observe this rule.
One of the problems with Bach, which is also one of his great advantages, is that he does not write in as much detail as one might expect to find in a modern score. Articulations, tempo marks, and dynamics are much less frequent, and, at least in some cases, have different meanings than they would have in a work by a modern composer. Ornaments (e.g. trills) may have changed their meanings somewhat. This is a problem because different people interpret Bach in different ways, and each of us tends to be attached to our own way of doing things. One teacher told me never to play Bach for an audition, because no matter how you choose to play it, you will most likely offend someone on the committee. But the lack of detail is also an advantage, because as a performer you don't have the option simply to play what is written; it demands interpretation. You have to express yourself when playing Bach, because you have no other choice. You can (and, in my view, should) use relevant historical sources available to you to guide your choices, but that does not change the fact that you are making choices.
Historical performance has tended to be a moving target, with each new generation of scholarship challenging the conventional (but perhaps less well founded) practice of its day. Unfortunately, those of us who are not experts get left behind; we may use older editions, may not be familiar with all of the relevant sources, and may have missed out on developments such as the rediscovery of Bach's preferred tuning system. This makes it intimidating to write about Bach's music; the odds are high that you are showing off your ignorance. An important project to know about is the Open Goldberg Variations, which includes a fine recording by Kimiko Ishizaka, and an open edition of the score; you will need to scroll down the page after clicking the link, in order to find the link to download it from IMSLP.
Another worthwhile source, also on IMSLP, is the first edition proof with Bach's corrections. This is the edition published in 1741 by Balthasar Schmid. It's quite readable, and there are some notable differences between it and, say, the Bach Gesellschaft edition.
I make no representations about following historical practice in my home recording. I've certainly done some reading and listening on the subject, and will continue to do so, but for the last word in historically informed practice, select another recording.
This blog is mainly about personal experience. While there will certainly be links to historical/musicological information at times, the best sources for that are historians and musicologists.
A quick check of various websites found 81 recordings of the Goldbergs
on piano, 23 on harpsichord,and one on clavichord. As of this writing,
the "Goldberg Variations Discography" article in the English
Wikipedia mentions 101 recordings on piano (including one on jazz
piano), 53 on harpsichord (including one on harpsichord and
clavichords), and 6 on organ. There are probably many more. The two
lists don't entirely coincide; I included some non-commercial recordings in my
count, and missed a lot of the ones Wikipedia includes. Many of these recordings are wonderful. Some are more historically informed than others. A few are cringe-worthy. All of the
performers can say they have recorded the Goldberg Variations.
