Well, Bach...

I have posted a lot about Bach, of course, but there is always more to discover. Here is a clip about the canons in Bach's Goldberg Variations:

Why do I say there is always more to discover? Because even now, two hundred and sixty-nine years after his death, we are still stumbling across things he did that hadn't been noticed before. For example, in the clip David Louie points out that the theme to the Goldberg Variations is 32 measures long and this is reflected in the piece generally. Of course we have always known that each of the 30 variations uses the same bass line from the theme. But Louie points out that all the variations are either in triple (3) or duple (2) time. AND if you look at how many variations are in 3 and how many in 2, they turn out to be in a ratio of, yep, 3:2. If it were anyone else, you might just shrug it off to coincidence. Another example: I was at a talk on the Mass in B minor once and the scholar pointed out that there are exactly 2345 measures in the Mass AND that the Dona nobis pacem, the only music that is repeated and that also ends the work, the theme opens with the notes D E F# G, which, if you use fixed doh solfege, are the notes 2345. Again, if it were anyone else but Bach...

In 1974 Bach's own copy of the score of the Goldbergs turned up and lo and behold he jotted down fourteen more canons on the theme. As Wikipedia notes:

When Bach's personal copy of the printed edition of the "Goldberg Variations" (see above) was discovered in 1974, it was found to include an appendix in the form of fourteen canons built on the first eight bass notes from the aria. It is speculated that the number 14 refers to the ordinal values of the letters in the composer's name: B(2) + A(1) + C(3) + H(8) = 14.

I'm sure I have told this story before, but when I took the graduate seminar called "Fugue" I had something of an epiphany with Bach. First of all, the professor prefaced the course by saying that the entire content of the course would be on Bach and only Bach. Despite the fact that many composers wrote fugues and fugue-like pieces before Bach and an enormous number of composers have continued to do so since Bach (a short list: Mozart, Haydn, Beethoven, Mendelssohn, Liszt, Saint-Saëns, Brahms, Bruckner, Bartók, Shostakovich, and so on), none of them were worth taking time away from Bach to cover. By the way, there are not and have never been any other musical forms or genres that have been dominated by one composer so completely as Bach dominates the fugue. All the other guys? Not even worth discussing. But what really made me fall off my chair was when I realized what he had done with the so-called "mirror" fugues (I wrote a post on them here). A pretty good composer can use what is known as invertible or double counterpoint, where one line can be transposed above another without causing any awkward bits. A really good composer can maybe do triple counterpoint which is the same thing with three voices. Bach could write a four-voice fugue that could be completely inverted and it would still work perfectly. As far as I know, no other composer even tried that.

Now in the Goldberg Variations, every third variation is a canon. Ok, cool. But remember, all these canons have to fit over that same 32 measure bass line. Oh, and each of those nine canons is at a different interval. No, you don't have to have the second voice start in the same place, it can be a second above, a third above, a fourth above, a fifth above and so on. Which is exactly what Bach does. For nine different intervals. Over the same bass line. Those of you who know a bit about music theory are now gibbering insanely, aren't you?

Watch the whole clip as it is interesting to see how Nahre Sol, composer, approaches Bach.