Music Banter - View Single Post - Some really cool animated depictions of Classical music

Quality Cucumber · 03-02-2015, 02:48 AM

Nobody said it was going to be easy.

Fugues are generally challenging, and Beethoven's Große Fuge is definitely in the category of "freakshow" fugues. Sharing that distinction are the fugato at the end of Mozart's Jupiter Symphony and the first movement of Bartók's Music for Strings, Percussion, and Celesta.

Wolfgang Amadeus Mozart - Symphony No. 41, mvt. 4

The five-subject (!) fugato starts at 10:32 and is over by 10:58.

And now my favorite fugue:

Béla Bartók - Music For Strings, Percussion, and Celesta, Mvt. 1

No animation, but some nice Spanish speaker did a little graphic analysis for us. Basically what's going on is that the strings are divided into two antiphonal groups (meaning that there are effectively two string orchestras on stage), and a single subject is presented in the key of A before each string group takes the subject in an opposite direction on the circle of fifths. (The perfect fifth is an ancient and archetypal relationship in music.) At the climax, both groups hit the key of E♭, which is a tritone away from the original key of A. (The tritone is an important interval, especially in twentieth century music, because it divides the octave into equal halves. Symmetry is a big part of 20th century harmony and melody, especially in Bartók's music. The tritone also has connotations from early church music, where it was called "diabolus in musica" ["the devil in music"] for being a pain in the ass to sing. The name has garnered romantic speculation ever since.) Anyway, after reaching the tritone, the pitch axis collapses back to its original key, A.

Ernő Lendvai claimed that this movement exhibits Fibonacci numbers, golden sections, ratios, and the golden mean. I had a composition teacher who was an adherent of this analysis. In Charles Dutoit's recording with the Montreal Symphony Orchestra, the performance is such that the proportions of the piece make that magical golden mean. On paper, it's very very close but not quite perfect. The subject itself is built using Fibonacci numbers, and the entrances are similarly determined, so there is that, but the third movement really has more of the Fibonacci/golden ratio stuff than the first movement.

http://mathcs.holycross.edu/~grobert...Bartok-web.pdf

I love this fugue. There's nothing else like it.

03-02-2015, 02:48 AM	#7 (permalink)
Quality Cucumber Music Addict Join Date: Feb 2015 Posts: 60	Nobody said it was going to be easy. Fugues are generally challenging, and Beethoven's Große Fuge is definitely in the category of "freakshow" fugues. Sharing that distinction are the fugato at the end of Mozart's Jupiter Symphony and the first movement of Bartók's Music for Strings, Percussion, and Celesta. Wolfgang Amadeus Mozart - Symphony No. 41, mvt. 4 The five-subject (!) fugato starts at 10:32 and is over by 10:58. And now my favorite fugue: Béla Bartók - Music For Strings, Percussion, and Celesta, Mvt. 1 No animation, but some nice Spanish speaker did a little graphic analysis for us. Basically what's going on is that the strings are divided into two antiphonal groups (meaning that there are effectively two string orchestras on stage), and a single subject is presented in the key of A before each string group takes the subject in an opposite direction on the circle of fifths. (The perfect fifth is an ancient and archetypal relationship in music.) At the climax, both groups hit the key of E♭, which is a tritone away from the original key of A. (The tritone is an important interval, especially in twentieth century music, because it divides the octave into equal halves. Symmetry is a big part of 20th century harmony and melody, especially in Bartók's music. The tritone also has connotations from early church music, where it was called "diabolus in musica" ["the devil in music"] for being a pain in the ass to sing. The name has garnered romantic speculation ever since.) Anyway, after reaching the tritone, the pitch axis collapses back to its original key, A. Ernő Lendvai claimed that this movement exhibits Fibonacci numbers, golden sections, ratios, and the golden mean. I had a composition teacher who was an adherent of this analysis. In Charles Dutoit's recording with the Montreal Symphony Orchestra, the performance is such that the proportions of the piece make that magical golden mean. On paper, it's very very close but not quite perfect. The subject itself is built using Fibonacci numbers, and the entrances are similarly determined, so there is that, but the third movement really has more of the Fibonacci/golden ratio stuff than the first movement. http://mathcs.holycross.edu/~grobert...Bartok-web.pdf I love this fugue. There's nothing else like it. Last edited by Quality Cucumber; 03-02-2015 at 04:19 AM.