Getting Bachs number

April 13, 2009 5:38 PM

Interested to know more about the 'numbers' in JS Bach's music. Sometime ago I heard a radio programme about how some of Bachs music had patterns in which could be viewed as significant outside of what the music sounded like.

I'm interested to know what this area of study/interest might be called and where can I (not a musician or a mathematician) read more about it ?

I realise that this all sounds a bit nutty but apparently this is an established field of interest/study ... !

(That radio programme was produced, I'm reasonably sure, by Deutsche Welle english language service. It was part of a series to mark 250 years since JSB died and it was really good so anyone who knew where that was online would get extra points !)

posted by southof40 to media & arts (10 comments total)

You'll definitely want to listen to the gorgeous album, Morimur.

As the Amazon link explains, a German professor discovered (the degree to which the discovery was valid is debated, of course) that there are lots of "secret" musical messages and motifs in the d minor partita for solo violin. Most notably, she found that the last movement, the famous Ciaccona, fits together with many chorales that Bach harmonized through his lifetime. On the CD, the chorales are sung at the same time as the Ciaccona is played. Whether or not the "discovery" is bunk, the performance is stunning. (Total highlight of my young life: meeting Cristoph Poppen when he and the Hilliard Ensemble came to my town to perform the entire Morimur program - the day before I performed the very same piece myself in a competition.)

I'm guessing you've already seen this, about the B A C H motif, but if you haven't, it's fun to find examples of the motif in Bach's music and listen to it.
posted by Cygnet at 5:49 PM on April 13

Basically, you've latched on a particular facet of musicology, the academic discipline regarding the study of music. Music and mathematics have gone together for quite some time, even back to the ancient Greeks.

You'd probably be interested in reading Gödel, Escher, Bach: an Eternal Golden Braid by Douglas Hofstadter. It's considered by many to be part of the canon of hacker/geek culture to boot.
posted by valkyryn at 5:55 PM on April 13 [1 favorite]

I am not a person who can answer this question. one of my friends is -- he is a composer who wrote a play that is structured around and about the patterns in Bach. the play turned out something like a send-up of the Da Vinci Code, but it could also be considered an answer to this question.

his name is Alex Eddington, and this is the play in question.

(I have also passed the question along to him.)
posted by spindle at 5:56 PM on April 13

If you enjoy reading about this sort of thing but need a good story to hook you in, there is a chunk of The Gold Bug Variations that addresses this issue. I like books like I like bacon and this is one of my favorite books.
posted by jessamyn at 7:38 PM on April 13

This is quite well known (and it isn't just Bach by any stretch of the imagination, another very significant example can be found in the works of Alban Berg particularly the Lyric Suite.) This is indeed a branch of musicology and I'm sure there are many papers on it, but, yeah, the Hofstadter is probably where you want to start if you don't have solid music theory.

As I say it's not just Bach. I should say that none of this is remotely my field as I'm a composer not a theorist/musicologist, but I do recall reading years ago that there are such things all over the Matthew Passion, the only thing that I remember is that in one recitative dealing with Judas' betrayal the bass line has thirty notes in it. Of course this is just the tip of the iceberg, but Gödel, Escher, Bach should get you started.
posted by ob at 8:29 PM on April 13

This may be a stretch, but could a fugue be considered as a time series that roughly follows the relation:

f_sub_1(t) = k * f_sub_2(t-c),

where f_sub_1 and f_sub_2 are voices, k equals a constant and c equals the time between voices?

A "round" such as "Row, Row, Row Your Boat" would have k equalling 1.

There are probably some musicology/mathematics theses out there along these lines.
posted by Napoleonic Terrier at 11:05 PM on April 13

this is what the Alex mentioned earlier had to say:

I made up the term "cryptomusicology" but hey, maybe it's real.

Bach's number is 14, because B-A-C-H translates to 2-1-3-8 in a really simple code. This number (and 7) turns up in a lot of music in a lot of ways: number or notes in a phrase, rhythmic motives, etc. etc.

Like many composers, the number 3 represents the Holy Trinity and is EVERYWHERE.

Bach also coded his name into music through pitches. In the old German spellings, B actually means B-flat, and H means B-natural: so the Bach motive (which is quite easy to hear when you're used to it), is Bb-A-C-B or transpositions, inversions etc. of that.

And there's much more I'm sure. Bach was a master word-painter - using musical gestures to evoke specific images in the text being sung - and I wouldn't doubt that a lot of these have number significances.

In my play and planned novel, there is an occult significance to all this. But in actuality, he may have just been mucking around. I use lots of numbers in my music simply because it's a way to get started. But then, Bach was a very religious man. The Lutherans inherited the Enlightenment Science view of the world and were quite taken by mathematical things. Luther was interested in the Kaballah and most young Lutherans grew up playing code-games. To them, numbers meant more than numbers.

Incidentally, Bach was apparently an acoustical genius, quite instinctively I think - he knew how good a room would sound, where dead spots would be etc. just by looking at it!

posted by spindle at 8:15 AM on April 14

Napoleonic Terrier, there are a couple of problems with that. Firstly a round is not a fugue. The main differences are that the entries in a round or canon are normally constant, whereas in a fugue they don't have to be and, more importantly, entries in a canon are at pitch whereas in a fugue they are normally transposed. In a fugue, after all the voices enter, there are episodes and the like which imitate the contrapuntal texture without strictly adhering to it. I can absolutely see where you're coming from but the thing about fugues is that in one sense they are much less strict than canons.
posted by ob at 11:00 AM on April 14

Bach's music is one of the mathematical themes that feature in the novel The Eight by Katherine Neville.
posted by _Skull_ at 11:03 AM on April 14

Thanks for all the great answers and apologies for not responding sooner. As a starter I'm going to read "Gödel, Escher, Bach" and see how I go.
posted by southof40 at 3:21 PM on June 24