Mathematicians have finally proved that Bach was a great composer

[Judi Lynn]

Converting hundreds of compositions by Johann Sebastian Bach into mathematical networks reveals that they store lots of information and convey it very effectively

By Karmela Padavic-Callaghan
2 February 2024

Johann Sebastian Bach is considered one of the great composers of Western classical music. Now, researchers are trying to figure out why – by analysing his music with information theory.

Suman Kulkarni at the University of Pennsylvania and her colleagues wanted to understand how the ability to recall or anticipate a piece of music relates to its structure. They chose to analyse Bach’s opus because he produced an enormous number of pieces with many different structures, including religious hymns called chorales and fast-paced, virtuosic toccatas.

First, the researchers translated each composition into an information network by representing each note as a node and each transition between notes as an edge, connecting them. Using this network, they compared the quantity of information in each composition. Toccatas, which were meant to entertain and surprise, contained more information than chorales, which were composed for more meditative settings like churches.

Kulkarni and her colleagues also used information networks to compare Bach’s music with listeners’ perception of it. They started with an existing computer model based on experiments in which participants reacted to a sequence of images on a screen. The researchers then measured how surprising an element of the sequence was. They adapted information networks based on this model to the music, with the links between each node representing how probable a listener thought it would be for two connected notes to play successively – or how surprised they would be if that happened. Because humans do not learn information perfectly, networks showing people’s presumed note changes for a composition rarely line up exactly with the network based directly on that composition. Researchers can then quantify that mismatch.

More:
https://www.newscientist.com/article/2415469-mathematicians-have-finally-proved-that-bach-was-a-great-composer/

[Shermann]

1. So improbable or surprising notes mean not-so-great music? Better not run this algorithm on jazz. nt

[erronis]

2. And this wouldn't work well on original literature vs. algorithmic romance novels...

[SarahD]

3. Just in time!

I was listening to Toccata and Fugue in D Minor and wondering, "Is this really good, or do I just think it's good?" It's good. The numbers prove it.

[JoseBalow]

4. That's one way to win an argument!

[Biophilic]

5. There may be some people with too much time on their hands.

He was a great composer because his music reaches out, touches people, and they respond. Not everything needs a scientific reason. Chill.

[Jim__]

6. Regis Iussu Cantio Et Reliqua Canonica Arte Resoluta

In his book, Gödel Escher Bach: An Eternal Golden Braid, Douglas Hofstader used Bach's music as an example of logical constructions. Here is a short excerpt from the beginning of the book:

...

Of course there is no way of knowing whether it was King Frederick or Baron van
Swieten who magnified the story into larger-than-life proportions. But it shows how
powerful Bach's legend had become by that time. To give an idea of how extraordinary a
six-part fugue is, in the entire Well-Tempered Clavier by Bach, containing forty-eight
Preludes and Fugues, only two have as many as five parts, and nowhere is there a six-part
fugue! One could probably liken the task of improvising a six-part fugue to the playing of
sixty simultaneous blindfold games of chess, and winning them all. To improvise an
eight-part fugue is really beyond human capability.

In the copy which Bach sent to King Frederick, on the page preceding the first sheet of
music, was the following inscription:

Regis Iussu Cantio Et Reliqua Canonica Arte Resoluta

("At the King's Command, the Song and the Remainder Resolved with Canonic Art." )
Here Bach is punning on the word "canonic", since it means not only "with canons" but
also "in the best possible way". The initials of this inscription are

R I C E R C A R

-an Italian word, meaning "to seek". And certainly there is a great deal to seek in the
Musical Offering. It consists of one three-part fugue, one six-part fugue, ten canons, and a
trio sonata. Musical scholars have concluded that the three-part fugue must be, in
essence, identical with the one which Bach improvised for King Frederick. The six-part
fugue is one of Bach's most complex creations, and its theme is, of course, the Royal
Theme. That theme, shown in Figure 3, is a very complex one, rhythmically irregular and
highly chromatic (that is, filled with tones which do not belong to the key it is in). To
write a decent fugue of even two voices based on it would not be easy for the average
musician!

Both of the fugues are inscribed "Ricercar", rather than "Fuga". This is another
meaning of the word; "ricercar" was, in fact, the original name for the musical form now
known as "fugue". By Bach's time, the word "fugue" (or fuga, in Latin and Italian) had
become standard, but the term "ricercar" had survived, and now designated an erudite
kind of fugue, perhaps too austerely intellectual for the common ear. A similar usage
survives in English today: the word "recherche" means, literally, "sought out", but carries
the same kind of implication, namely of esoteric or highbrow cleverness.
The trio sonata forms a delightful relief from the austerity of the fugues and canons,
because it is very melodious and sweet, almost dance-able. Nevertheless, it too is based
largely on the King's theme, chromatic and austere as it is. It is rather miraculous that
Bach could use such a theme to make so pleasing an interlude.

The ten canons in the Musical Offering are among the most sophisticated canons Bach
ever wrote. However, curiously enough, Bach himself never wrote them out in full. This
was deliberate. They were posed as puzzles to King Frederick. It was a familiar musical
game of the day to give a single theme, together with some more or less tricky hints, and
to let the canon based on that theme be "discovered" by someone else. In order to know
how this is possible, you must understand a few facts about canons.

...

An example:

[Judi Lynn]

8. Thank you for posting the music with the book excerpt. It was tremendous discovering that instrument, as well!

Had never seen one like that, and noticed the sound was completely different as well. Amazing.

It was excellent reading and listening, such a helpful high point for the week, with something to think about, and listen to again.

Following the link you shared there was an interesting item available following the YouTube link, which was interesting to me, and I'd like to add it to this post, as it discusses Bach's writing, as well:

Thank you, so much, for taking the time to add your terrific post.

[Jim__]

9. You're welcome. And thank you for the second video. I had not seen that. Fascinating!

[pansypoo53219]

7. my fav.