Re: [tuning] Digest Number 6184-Brouncker

Cameron: Thanks for finding this and bringing it to our attention. I've managed to track down the reference in the Cambridge History of Music (p 211) via Google Advanced.

--John

--- In tuning@yahoogroups.com, "John H. Chalmers" <JHCHALMERS@...> wrote:
>
> Cameron: Thanks for finding this and bringing it to our attention. >I've
> managed to track down the reference in the Cambridge History of >Music (p
> 211) via Google Advanced.
>
> --John
>

Although, given the general untrammeled grooviness of the 17th century, it wasn't surprising to find this, what does surprise me is that I haven't come across any 19th-century tuning speculation along these lines. As far as I know, the 19th century was a golden age of finding the golden section in everything.

Personally, I use the golden section and the fibonacci sequence in tuning, rhythm, and timbre continually, and I find from experince that it is important to be very strict about what you're calling a golden section, or phi.

And humorously, I have found as much bogus thinking among phi debunkers as phi worshipers. The sophistry on either side tends to be pretty funny, and ultimately betrays some pretty silly preconceptions: neither the Pyramids, nor the Mona Lisa, nor Mozart Sonatas are natural, divine, extraterrestrial, or even particulary beautiful to a whole lot of people, so it doesn't matter in the slightest if you prove or disprove their golden proportions. Meanwhile the tangible fascinating aspects of phi get lost in the waffle. Googling this, I find that Keith Devlin has made the same observations, more politely of course.

By the way, the beautiful phi tuning of antiquity can be found in your awesome "Divisions of the Tetrachord".

-Cameron Bobro

--- In tuning@yahoogroups.com, "Cameron Bobro" <misterbobro@...> wrote:

> ...the general untrammeled grooviness of the 17th century,...
Hi Cameron,
see for that
/tuning/topicId_34816.html#34825
http://www.gap-system.org/~history/Biographies/Brouncker.html
http://home.vicnet.net.au/~colmusic/opticks3.htm
there especially
"Illustration 13 :
DESCARTES' MUSICAL CIRCLE & BROUNCKER'S ENGLISH VERSION."
http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6WG9-4NS2GPC-2&_user=2717328&_rdoc=1&_fmt=&_orig=search&_sort=d&view=c&_acct=C000056831&_version=1&_urlVersion=0&_userid=2717328&md5=6cc6ad7161746a29dd61f7a618ebdc16
or as PDF file:
http://www.sciencedirect.com/science?_ob=MImg&_imagekey=B6WG9-4NS2GPC-2-1&_cdi=6817&_user=2717328&_orig=search&_coverDate=02%2F29%2F2008&_sk=999649998&view=c&wchp=dGLbVlz-zSkzV&md5=52ea534852cf87238f69b44dfa2b8e44&ie=/sdarticle.pdf

bye
A.S.

--- In tuning@yahoogroups.com, "Andreas Sparschuh" <a_sparschuh@...> wrote:
>
> --- In tuning@yahoogroups.com, "Cameron Bobro" <misterbobro@> wrote:
>
> > ...the general untrammeled grooviness of the 17th century,...
> Hi Cameron,
> see for that
> /tuning/topicId_34816.html#34825

thanks for the links-

Brouncker's 17 equal divisions of 1+Phi actually sounds very nice. With 98 cent steps the octave is a comma flat, but it sounds good anyway- this probably wouldn't be apparent to people who equate Western circle-of-fifths crap with "music", though. :-)

> http://www.gap-system.org/~history/Biographies/Brouncker.html
> http://home.vicnet.net.au/~colmusic/opticks3.htm
> there especially
> "Illustration 13 :
> DESCARTES' MUSICAL CIRCLE & BROUNCKER'S ENGLISH VERSION."
> http://www.sciencedirect.com>>/science?_ob=ArticleURL&>_udi=B6WG9-4NS2GPC-2&_user=2717328&_rdoc=1&>_fmt=&_orig=search&_sort=d&view=c&_acct=C000056831&_version=1&_urlVersion=0&_userid=2717328&md5=6cc6ad7161746a29dd61f7a618ebdc16
> or as PDF file:
> http://www.sciencedirect.com/science?_ob=MImg&_imagekey=B6WG9-4NS2GPC-2-1&_cdi=6817&_user=2717328&_orig=search&_coverDate=02%2F29%2F2008&_sk=999649998&view=c&wchp=dGLbVlz-zSkzV&md5=52ea534852cf87238f69b44dfa2b8e44&ie=/sdarticle.pdf
>
> bye
> A.S.
>

I don't have a subscription there, but I've seen Brouncker's translation of Descartes, and the wheel.