From: hnews <hdunham@uvic.ca>
Newsgroups: sci.math,rec.music.classical
Subject: Re: The golden section and Beethoven's Fifth
Date: Sun, 15 Feb 1998 21:03:51 -0800

Robin Chapman wrote:
> 
> In article <887043017.864616457@dejanews.com>,
>   torgnyk@mail.hf.uio.no wrote:
> >
> > I've heard that the structure of Beethoven's Fifth Symphony is based on
> > the "golden section". Can anyone explain how, more precisely, this
> > principle is applied in this composition? Torgny Koren
> >
> 
> I don't know about Beethoven 5, but I once heard on an interval talk that
> the first movement of Bartok's "Music for Strings, Percussion and
> Celesta" was structured using Fibonacci numbers (whose ratios approximate
> the golden section). If I remember correctly, the movement is 89 bars

Interesting - I've not heard it called the golden section, but rather
the golden mean.  We learned about it in renaissance/baroque history. 
In that time it was a big deal and was composed into music very much on
purpose.

One example that stuck in me brain is Tallis' 40-voice motet, Spem in
Alium (easy mnemonic: Spam in Aluminum).  At the point of the golden
mean, there is a bar of absolute silence, then all 40 voices come in
TOGETHER, the first time this has happened.  Quite a great moment (and I
got to sing it this past fall!)

That same year as baroque history, I was also doing advanced structure
and form.  My major project was an analysis of Brahms piano sonata, op.
5, the great f minor.  Just on a whim I calculated the golden means of
each movement, and found the 1st movement RECAP BEGINS RIGHT AT THE
GOLDEN MEAN!  Did he do it on purpose or was it a natural sense of
balance?  Who knows...

heather the buzzard