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Re: [F_minor] random observation / Hofstadter on mathematicalpatterns in Chopin

Most everybody here is familiar with Douglas Hofstadter's
mathematically-oriented ideas about the music of J.S. Bach in "Godel,
Escher, Bach," but this thread makes me want very enthusiastically to
recommend a less-well-known Hofstadter essay, remarkably illustrated, about
the profoundly interesting mathematical patterns -- both musical and, in
the printed scores, visual -- of Chopin. The essay (originally Hofstadter's
Scientific American column for April 1982) can be found in the book
"Metamagical Themas," and is entitled 

Pattern, Poetry and Power in the Music of Frederic Chopin

(please put accents acutes above both e's in Frederic, I have permanently
despaired of using diacriticals in e-mail and e-text because half the time
they get all screwed up)

It's slightly odd that this particular List strays so rarely into
mathematical analyses and critiques of our favorite music, because we all
know the naughty little secret -- that the most talented and impassioned
classical musicians are so heavily also talented and impassioned
mathematicians, physicists, chemists (Hi Eric!) and astronomers. 

William Herschel (geboren Friedrich Wilhelm Herschel) became immortal by
discovering the planet Uranus, but his day job was as a highly successful
and respected symphony conductor and composer in England. In high school,
the most talented kids in the orchestra are also routinely the stars of the
Math and Science Club. Northern Ontario's isolated Deep River / Chalk River
government nuclear research community ...

Among the numerous community accomplishments is the creation of the Deep
River Symphony Orchestra, formed in 1951, making Deep River one of the
smallest towns (pop. 4200 as of 2006) to have a Symphony Orchestra.

I would modestly like to bring up the subject of upgrading F_minor to a
List capable of accepting not just ASCII text, but other kinds of files as
well, **** particularly music **** and images. 

I know that evil cooties can lurk in these files, but most other lists,
which celebrate both the sublime and the ridiculous, have learned over the
last few years to risk an occasional malware incident in exchange for using
the Internet to its fullest and most glorious tech capacities. It's a
little embarrassing to be flooded with so much love for wonderful music
while at the same time being forced to be mute, deaf and blind, our
messages strictly limited to the alphanumeric keyboard.

Perhaps F_minor could bifurcate into a traditional Perfectly Safe ASCII
half for the cautious and timid, and an experimental full-featured
file-capable compartment for us wild and crazy thrill-seekers out there.

I mention this because of a spectacular illustration of the score of
Chopin's Etude in C major from Opus 10, generated by a computer program
called SMUT by Donald Byrd of Indiana University that accompanies
Hofstadter's essay. I can't find an on-line image of it, so you may have to
find the (remarkable) book, but it differs from a playing score by
emphasizing the startling visual symmetry (which reflects the startling
musical symmetry) of the Etude.

The first few pages of the essay are sampled as a Google book at


or you can get there with a Google search for "Metamagical Themas" and
going to Page 173.

Donald Byrd himself has a very interesting music-math-computer rich
website, and particularly interesting and fun is

The limits of conventional Western notation are fascinating and sometimes
revealing. Have you ever wondered what the highest, lowest, shortest, or
longest note ever written is? Or what the densest chord, or the shortest or
longest piece is? I have; in fact, I've been working for years on a list of
Extremes of Conventional Music Notation. Drawing on that list and a
collection of rule-breaking notation in my dissertation, here is a small
Gallery of Interesting Music Notation.



There's a lot about Bach's scores and notations in it.


> [Original Message]
> From: Brad Lehman <bpl@umich.edu>
> To: <f_minor@email.rutgers.edu>
> Date: 7/4/2008 10:40:07 AM
> Subject: Re: [F_minor] random observation
> Etha Williams wrote:
> > In my free time I enjoy writing little compositions, and my latest
> > is a fugue using the c - d flat - g - a flat motif from GG's string
> > as subject and the B-A-C-H theme from Art of Fugue as countersubject.
> > 
> > Anyway, while doing this, I noticed something kind of cool -- the motif
> > GG's string quartet is a musical palindrome: pitch-wise, the retrograde
> > flat - g - d flat - c) is the same as the inversion at the sixth!
> > 
> > Well, I thought it was cool...
> Singing hymns in church last week I noticed a big B-A-C-H in the alto 
> line of MELITA.  (Same hymn that's used at a climactic point in 
> Britten's opera for children, "Noye's Fludde"....)
> That four-note Gould subject, C-Db-G-Ab, was also used a few years later 
> all the way through the Star Trek episode "The Corbomite Maneuver", in 
> Fred Steiner's soundtrack.  (You know, the one where there's that 
> spinning cube giving off radiation, and then they do half an hour of 
> bluffing and posturing about whose ship is going to destroy whose, and 
> then they go visit the bridge of the other one...and find young Clint 
> Howard having a drink of tranya?)  Don't know if Steiner got that 
> melodic idea from Gould or not.
> I'm tempted to do a little "separated at birth?" assemblage sometime, 
> putting together classical themes with other pieces that used them 
> later.  Some ideas for it:
> - This Gould/Steiner thing with the Corbomite fugue subject
> - Chabrier's "Espana", Waldteufel's "Espana" waltz using it, Perry 
> Como's "Hot diggity", and Satie's "Espanana"
> - Rachmaninoff's second symphony (2nd mvt theme), Leroy Anderson's 
> "Horse and Buggy" quoting it, and the Eric Carmen song "Never gonna fall 
> in love again"
> - Bach's A minor fugue subject from WTC 2 and Handel's "And with his 
> stripes" from "Messiah"
> - Rossini's "William Tell" overture and the way it turns up in 
> Shostakovich's symphony #15
> Brad Lehman

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