2017 Aug 6: Preludes in C

August 06, 2017 10:30

Prelude in C J.S. Bach (1685-1750) [ PIANO]
Prelude in C F. Chopin (1810-1849)


Bear with me for a bit of mathematical music theory. In music, two notes at the same time are called an ’interval’, and two intervals in particular are profoundly fundamental to human music worldwide. If you’ll recall your "do-re-mi’s", our two biggie intervals are the ’octave’ – from ’do’ through re, mi, fa... back to ’do’, and the other is the ’fifth’ (if ’do’ = 1, then ’re’, ’mi’, ’fa’, and ’so’ = 5 ... from ’do’ to ’so’ is a ’fifth’).

Remarkably, Pythagoras (5th century BCE — or the school he founded) figured out that these two foundational musical intervals have a basis in mathematics/physics. Using modern terminology, we know that a musical pitch is the result of regular vibrations of air. In the case of the 'octave', the ratio of vibrations per second is 1:2, in the case of the 'fifth': 2:3.

Fast forward to, say, the early Renaissance – when keyboard instruments were becoming increasingly important. I have to simplify a little, but the gist is that it’s not possible on an acoustic (not computer-based) keyboard instrument, regardless of tuning system, to have all its octaves and fifths in tune at the same time. This anomaly was demonstrated by Pythagoras in the 5th century BCE. (Other instruments like strings and woodwinds can tune on the fly.)

What we in the West have done is start with a keyboard tuning system (more or less Renaissance era) in which a few keys are in very good tune — e.g. the ’just’ tuning system in which keys with few sharps and flats are in good tune. But over time, of course, composers wanted to be more adventurous, and so the keyboard tuning system was revised to the ’mean’ tuning system in which more (but not all) keys were usably in tune.

By the time of Bach in the early 18th century, the notion of being able to play in ALL 12 KEYS on a keyboard was in the wind. The idea was ’well-tempering’ (’tempering’ is how you fudge the Pythagorian anomaly) — ’well tempering’ indicating a tuning system in which all the keys are usable, but some keys like C major might be more in tune than Gb major. (We now use a system called ’equal-tempering’ — all 12 keys are equally out of tune, but we’re used to it.)

"Well tempering" was cutting-edge musical technogy in Bach’s day, and he decided to do something with it. So he wrote the "Wohltemperiertes Klavier" – a Prelude & Fugue in each of the 12 possible major and minor keys — 24 preludes and fugues in all. And he had such a good time doing it he wrote a second set, so we have two volumes.

He named these collections "Wohltemperiertes Klavier": "wohl" = "well", "temperiertes" = tempered, and "Klavier" = "keyboard". But you won’t find it published under the English name "Well Tempered Keyboard" – instead "Well Tempered Klavier" is standard (I see, only translate HALF of it from German into English).

But Bach’s "Well Tempered Keyboard" was much more than a demonstration of the 12 posssible major and minor keys: ever the pedagoge, Bach composed it to be an encyclopedic demonstration of the available musical styles and forms: English, French, North German, South German, Italy, Poland (all through his own compositional stylistic lens, of course).

The first prelude in the first volume of the Well Tempered Keyboard is especially famous – using a simple arpegiated motif (a chord played one note at a time instead of all at once) he migrates through jazz chords that won’t be invented until centuries later.

Bach’s "Well Tempered Keyboard" had an enormous influence on subsequent composers: Mozart, Beethoven, Brahms, etc. all studied it, and even Stravinsky would play from it to ’warm up’ for a composition session. Other composers were inspired to write their own sets of preludes (but not fugues so much) in all the keys. Including Chopin, whose first prelude in his own set of 24 preludes is also in C major, and based on an arpeggiated motif — clearly an hommage.


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