We are inclined to think that there must be something in common to all games, say, and that this common property is the justification for applying the general term "game" to the various games; whereas games form a family the members of which have family likenesses. Some of them have the same nose, others of which have family likenesses. Some of them have the same nose, others the same eyebrows and others again the same way of walking; and these likenesses overlap. The idea of a general concept being a common property of its particular instances connects up with other primitive, too simple, ideas of the structure of language. It is comparable to the idea that properties are ingredients of the things which have the properties; e.g. that beauty is an ingredient of all beautiful things as alcohol is of beer and wine, and that we therefore could have pure beauty, unadulterated by anything that is beauty.That last phrase is particularly relevant to the point I wish to make: It is as silly to describe a prelude or fugue in terms of ingredients as it is to think that way about "pure beauty." Presumably Wittgenstein already knew that Immanuel Kant had come to a similar conclusion about beauty, but he might not have been aware of John Dewey's more recent attempts to analyze aesthetic reactions.
Bach affords us an interesting opportunity to play on Wittgenstein's use of the noun "family." Consulting the catalog included in the book that Wolfgang Sandberger compiled for the Teldec Bach 2000 collection, I realized that the second volume of The Well-Tempered Clavier was completed in 1742, when Bach was in his late fifties with less than ten years before his death. Put another way, by this time just about all of the keyboard works that we associate with him had been completed, most of them for quite some time. He had not yet visited the court of Frederick the Great, who would offer a theme that inspired his Musical Offering; but the "Goldberg Variations" were also completed in 1742. Even his organ preludes and fugues had become a thing of the past, not to mention the two-part and three-part inventions and the English and French suites. Most recent were the first three sections of his Clavierübung project (the final being the "Goldberg Variations"); and I would argue that this project shares with The Well-Tempered Clavier a retrospective reflection on a life of making music in a wide variety of settings. From this point of view, I would invoke a metaphor I recently applied to Sergei Prokofiev's final symphony serving as a "family album of photographs" of past accomplishments, the "family" being not Bach's many sons who had also begun to distinguish themselves as musicians but his past compositions. The "family likenesses" of the preludes (or the fugues) have more to do with their being products of Bach's practices than with their having distinguishing "properties."
There is thus a way in which particularly the second volume of The Well-Tempered Clavier may be heard as the only autobiographical account Bach would be capable of telling. We know from anecdotes that he probably had no good memory for the birthdays of his many children; and, for all we know, he may not even have kept track of just how many children he had. However, his "musical progeny" were always with him; and in The Well-Tempered Clavier he could look back on them all not just "without blushing" but with a deep sense of pride in accomplishment. This is not the sort of narrative autobiography that Richard Strauss would later attempt in Ein Heldenleben; but it is a reflective examination of one's past, which, after all, is the fundamental nature of autobiography. To appreciate it, we just have to be aware of those past achievements on which Bach was reflecting, which is why we are at an advantage in having so many different ways to listen to performances of so much of Bach's music.