In a fugue state of mind…
Leave it to me to get off on a funeral march, but what we have here is one of the two or three finest orchestral fugues EVER written!
This is the second part of the 2nd movement, starting (at 0:40) with the magnificent fugue, marked ‘Adagio assai’ appropriately indicating a ‘very stately’ tempo and feeling…
My favorite version by far of Ludwig Van’s ‘Eroica’ is by Bruno Walter and the Columbia Symphony Orchestra (1959), but I couldn’t find it, so von Karajan is a fair 2nd choice. Plus it starts with the part I wanted to share.
The 3rd symphony was written in 1803, as Beethoven’s hearing was really starting to get bad. I think some of his frustration and despair shows in this great opus. Later in this excerpt you can almost see Ludwig Van shaking his fist at the sky… what a horrible joke for the gods to play on a great composer!… This work is also famous for the dedication to Napoleon which he scratched out in disgust upon his realisation that Bonaparte was turning out to be just another asshole despot…
Enjoy!
Truly gorgeous! I knew we invited you here for a very good reason.Perhaps, if it’s not too dim a question, you could explain in your inimitable way just what it is that distinguishes a fugue. I have a general idea, but I’d like to hear it from you if you deign to pontificate on the subject.
BTW- 3/7 of Jupiter Sheep played live for an audience last night for the first time in a decade and a half. That is part of what I was obliquely referring to in my last post. My hope is that Byronius will do his best to summarize the event- when he recovers.
Comment on December 27, 2009 @ 6:27 pm
Max: Happy to oblige…
I’ve been in a recurring ‘fugue state’ for years!…
Simply put, a ‘fugue‘ is a fancy ‘canon‘ which in turn is a fancy kind of ‘round‘. Remember ‘Row, Row, Row your boat…’? ;0
Basically, a single musical theme is played contrapuntally (in counterpoint) with one or more copies of itself, usually ‘staggered’ in time and/or pitch. The ‘theme’ is usually played simply at first (exposition), and then voices are added, slowly increasing the complexity of the piece. Often, the voices proceed at different tempi… Things can eventually get very complicated indeed! Sometimes a fugue will reverse or invert the theme and change keys (modulate). Choosing the proper theme is crucial… the simpler the theme, the easier it is to ‘fit’ the pieces together. And vice versa!
In the heyday of the Baroque era, it was fashionable for composers to compete with each other to see who could come up with the most elaborate and many-voiced fugue…
The ability to improvise a fugue ‘on the fly’ was a highly prized talent. Early fugues were also sometimes called ‘ricercars’… As things get complex, voices are altered as needed to create the best effect, so they’re not stuck slavishly playing exactly the same thing over and over (as in ‘Row your boat’).
Of course, the great master of this form was J. S. Bach, whose many great fugues are still generally considered the highest expression of the ‘fugal’ art. I argue for Beethoven’s marvelous fugue in ‘Eroica’ as well!
In an extreme example, Frederick II of Prussia (a middling good musician himself) once challenged old Bach to improvise a fugue on a rather chromatic melody the King had written. Bach demurred, but promised to write something using the king’s ‘riff’. Bach then produced ‘A Musical Offering‘ which included an amazing SIX PART fugue on this ‘Royal Theme’, the ‘Ricercar a 6′. The chromatic (read difficult!) nature of the theme makes the piece sound surprisingly modern. In terms of ingenuity and sheer mental virtuousity, it still stuns listeners to this day!
Many interesting arrangements have been done, notably by (atonal composer) Anton von Webern. The way Webern splits the melodic line between two (or more!) instruments adds yet another dimension!
More detailed info with some examples is Wikipedia: Fugue
Hope that helps… and blows your little mind! ;-}
- Sky
Comment on December 28, 2009 @ 12:41 am
BTW: I just saw the re-make of ‘The Day The Earth Stood Still’… while badly flawed in spots it’s not the disaster that most critics claim.
In the context of this post, there’s a nice moment in the film where the ‘alien’ (Keanu Reeves) is at the ‘Professors’ house and stops… listening. Music is playing on the hi-fi. The woman (heroine) notices and says, “It’s Bach”… Keanu listens for a few more seconds and replies “It’s beautiful!”…
The implication of course being that maybe he shouldn’t exterminate the human race after all… Maybe there IS something worth saving of humanity!
(It’s probably a good thing that the professor wasn’t a big fan of the Sex Pistols! ;-})
Comment on December 28, 2009 @ 2:04 am
Aw, what the hell, here’s another version of Bach’s ‘ricercar a 6′… a VERY different take!
It’s a bit easier to hear the fugue structure in this unorthodox but very cool version!
The Modern Jazz Quartet with The Swingle Singers!
And it even swings a bit! ;-}
Comment on December 28, 2009 @ 5:42 am
IF you have the time your should read “Gödel, Escher, Bach: An Eternal Golden Braid” – a Pulitzer Prize-winning book by Douglas Hofstadter. He really gives some excellent descriptions, examples, and analysis of Bach’s fugues, including the aforementioned.
Overview from Wikipedia:
” . . . described by the author as “a metaphorical fugue on minds and machines in the spirit of Lewis Carroll”.
“On its surface, GEB examines logician Kurt Gödel, artist M. C. Escher and composer Johann Sebastian Bach, discussing common themes in their work and lives. At a deeper level, the book is a detailed and subtle exposition of concepts fundamental to mathematics, symmetry, and intelligence.
Through illustration and analysis, the book discusses how self-reference and formal rules allow systems to acquire meaning despite being made of “meaningless” elements. It also discusses what it means to communicate, how knowledge can be represented and stored, the methods and limitations of symbolic representation, and even the fundamental notion of “meaning” itself.”
Hofstadter has a newer book, “I am a strange loop,” that while not as good as GEB, is also interesting and is more transparent in its connections to neuroscience.
A followup note may be in order: there is also an interesting new paper on “alice in wonderland” and its connections to symbolic algebra. See New Scientist article at
http://www.newscientist.com/article/mg20427391.600-alices-adventures-in-algebra-wonderland-solved.html?full=true
-hopefully you can view it – I have a subscription so I have access.
Comment on December 28, 2009 @ 8:58 am
Cat-eyes: Bingo! Where do you think that I learned about much of this stuff? ;-}… Doug Hofstadter has been one of my intellectual heroes for LONG time! A very dog-eared and much perused copy of “Gödel, Escher, Bach” has been in my library and I have been singing its praises since the early ’80′s… I have several other of his books, including, yes, his recent “I Am A Strange Loop” which I’ve only just started. Another very good one that I’m on my second copy of is “Metamagical Themas” (based on articles from his Scientific American days, which is where he first came to my attention)… I went over that one until it literally fell apart!
Hofstadter’s thinking on artificial intelligence, language, recursive programs and processes, logic and pattern analysis largely inspired me to learn the Lisp programming language (its purer brother Scheme actually) and to learn about symbolic and functional programming which, by the way is how I wrote the programs that produced most of the graphic design work that I’ve displayed here!…
A functional analysis of Escher’s “Square Limit” was the initial inspiration for my ‘Functional Geometry’ programs…
M.C. Escher: Square Limit
KMH: functional analysis of M.C. Escher’s Square Limit
I’m gratified (but not at all surprised) that you would have also gravitated to this brilliant guy’s work!…
Thanks also for the link to the analysis of Lewis Carroll/Charles Dodgson… I’ve long recognised his clever logician’s games in the delightful “Alice in Wonderland” and “Through The Looking Glass” stories!…
Comment on December 28, 2009 @ 10:58 am
Thanks for the fugue def Sky. Now I want to go write one! Give me some time. Might take a decade or two. I promise I’ll have it ready before I get my Astrobio PhD and take off on that Mars mission.
Comment on December 28, 2009 @ 11:46 am
Sky, I thought you would be familiar with Hofstadter – thought perhaps others were not. Metamagical themas – ah yes, I have that one too. My fave is still GEB, a classic.
Comment on December 28, 2009 @ 12:40 pm
A quick further comment on the above Escher image and geometric analysis:
It hopefully won’t take much thought to see the clear parallels between a musical fugue or canon and much of Escher’s art… in particular, Square Limit.
For the curious, here’s the ‘theme’…
That’s IT! The entire image is based on that single simple motif!
It’s doubtful if Escher himself saw it quite that way, but his mathematical sense was intuitive, not rigorous… He even claimed to be awful at math! (hard to believe!)…
- Sky
Comment on December 28, 2009 @ 1:26 pm
Quite curious how you derive this.
Comment on December 28, 2009 @ 1:31 pm
Yeah, me too. Fascinating post btw.
Comment on December 28, 2009 @ 1:52 pm
Okay… you DID ask for it! ;-}
Starting from the original ‘motif’ (Step 1) above, we have:
Step 2:
Step 3:
Step 4:
Giving us the ‘basic fish’:
And putting them together, we finally have:
Do you see it now?…
I should also credit a very bright Brit colleague, Peter Henderson, who really saw this first!
BTW: I made these images to illustrate the process to an artist friend of mine… hope they help!
- Sky
Comment on December 28, 2009 @ 2:06 pm
Crystal clear. Ups my already significant appreciation of Escher to another level.
Comment on December 28, 2009 @ 2:18 pm
Max, and anyone else so inclined, if you’d like more information and examples see this site.
http://www.tessellations.org/
and for the nerdly geekoids see this site
http://mathforum.org/sum95/suzanne/tess.intro.html
it has some sample java applets, etal.
Comment on December 28, 2009 @ 4:07 pm
Peeked at the first link and will explore further later. Now you done it though. I didn’t know a favicon could be animated. Now I won’t be happy until I get that little Mars spinning.
Comment on December 28, 2009 @ 4:32 pm
You’re scary-smart Cat-eyes!
Tessellate, Tessellate… Dance to the music!!
(sorry)
Symmetry, Space groups, glide-reflections, crystallography!
brain…
seizing…
multi-dimensional overload…
must… take… NAP!
Max: Yeah, ‘ani’ files are just like small animated GIFs.
You may wish to consider the ‘distraction’ factor though… Just because you CAN do something, doesn’t always mean that you SHOULD!
Your show… just sayin’…
Comment on December 28, 2009 @ 6:24 pm
You’re scary-smart Cat-eyes!
Tessellate!, Tessellate!… Dance to the music!!
(sorry)
Symmetry, space groups, glide-reflections, crystallography! (OH MY!)
brain…
seizing…
multi-dimensional overload…
must… take… NAP!
Max: Yeah, ‘ani’ files are just like small animated GIFs.
You may wish to consider the ‘distraction’ factor though… Just because you CAN do something, doesn’t always mean that you SHOULD!
Your show… just sayin’…
Comment on December 28, 2009 @ 6:27 pm
Yes, you must take a nap because you are sorely mistaken about my smarts.
Comment on December 28, 2009 @ 7:28 pm