The Golden Route To Chaos

Hi folks I've not been here for a bit but my last post was about
obtaining a sub-harmonic series with 2 coupled relaxation oscillators.
http://facta.junis.ni.ac.yu/facta/macar/macar200401/macar200401-06.pdf
The above paper explains that this is just one route to chaos by means
of a diagram called a "Farey tree". I know when you see this you will
immediately think of musical intervals.
I've not yet investigated the musical possibilities but I think there
might be some gold in them there hills.

Enjoy

John S

jsnelsonone wrote:
> Hi folks I've not been here for a bit but my last post was about > obtaining a sub-harmonic series with 2 coupled relaxation oscillators.
> http://facta.junis.ni.ac.yu/facta/macar/macar200401/macar200401-06.pdf
> The above paper explains that this is just one route to chaos by means > of a diagram called a "Farey tree". I know when you see this you will > immediately think of musical intervals.

The Farey tree is well known in these parts. It's also called the Stern-Brocot tree and, by Erv Wilson, The Scale Tree. It can represent frequency ratios, and has practical application in finding the gear ratios for Hammond organs. It also represents MOS scales by the ratio of their generators in a representative ET.

> I've not yet investigated the musical possibilities but I think there > might be some gold in them there hills.

Looks interesting, I'll see if I can understand it. The "golden route" is also an idea used in tuning theory. Not usually the golden ratio in particular, but zig-zag paths come up every now and then. If this is news to you, have a look at the Wilson Archives:

http://www.anaphoria.com/wilson.html

Graham

Erv also lately has been looking into all of this is relation to the co prime grid and pattern there in which has been most of the papers he has had me put up.
Novaro is also significant on this level too.
Each added layer one adds to the Farey tree ( which was not done by Farey) one has that many more zigzag patterns that converge on gold/noble numbers.
There is an infinite number of them
Also in relationship of Ster-Brocot, no papers of brocot have been found so far that actually shows him using this series. If one knows of such document , please inform for our records

>
>Message: 4 > Date: Sat, 13 Aug 2005 12:17:16 +0100
> From: Graham Breed <gbreed@gmail.com>
>Subject: Re: The Golden Route To Chaos
>
>jsnelsonone wrote:
> >
>>Hi folks I've not been here for a bit but my last post was about >>obtaining a sub-harmonic series with 2 coupled relaxation oscillators.
>>http://facta.junis.ni.ac.yu/facta/macar/macar200401/macar200401-06.pdf
>>The above paper explains that this is just one route to chaos by means >>of a diagram called a "Farey tree". I know when you see this you will >>immediately think of musical intervals.
>> >>
>
>The Farey tree is well known in these parts. It's also called the >Stern-Brocot tree and, by Erv Wilson, The Scale Tree. It can represent >frequency ratios, and has practical application in finding the gear >ratios for Hammond organs. It also represents MOS scales by the ratio >of their generators in a representative ET.
>
> >
>> I've not yet investigated the musical possibilities but I think there >>might be some gold in them there hills.
>> >>
>
>Looks interesting, I'll see if I can understand it. The "golden route" >is also an idea used in tuning theory. Not usually the golden ratio in >particular, but zig-zag paths come up every now and then. If this is >news to you, have a look at the Wilson Archives:
>
>http://www.anaphoria.com/wilson.html
>
>
> Graham
>
>
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--
Kraig Grady
North American Embassy of Anaphoria Island <http://anaphoria.com/>
The Wandering Medicine Show
KXLU <http://www.kxlu.com/main.html> 88.9 FM Wed 8-9 pm Los Angeles

Thanks for the link Graham, is this where Partch got his Tonality
Diamonds?

TTFN

John S

--- In tuning@yahoogroups.com, Kraig Grady <kraiggrady@a...> wrote:

> Also in relationship of Ster-Brocot,

That's Stern-Brocot.

> no papers of brocot have been
> found so far that actually shows him using this series. If one
knows of
> such document , please inform for our records

Have you read:

Brocot, A. "Calcul des rouages par approximation, nouvelle méthode."
Revue Chonométrique 3, 186-194, 1861.

?

Since you didn't ask about Stern, you may already be familiar with:

Stern, M. A. "Über eine zahlentheoretische Funktion." J. reine angew.
Math. 55, 193-220, 1858.

Hi John,

--- In tuning@yahoogroups.com, "jsnelsonone" <jsnelsonone@y...> wrote:

> Thanks for the link Graham, is this where Partch got
> his Tonality Diamonds?

No ... i'm convinced from my research that Partch's
Tonality Diamond came from Max Meyer, in his book
_The Musician's Arithmetic_, cited several times by
Partch in _Genesis of a Music_.

I've written about this here several times before ...
now i've finally made a graphic of the Meyer diagram
and put it in the Files section of the
Yahoo tuning_files group:

log on to Yahoo, and click on "diamond-meyer.gif" here:

/tuning/files/monz/

I have a webpage about Tonality Diamond in the Encyclopedia:

http://tonalsoft.com/enc/t/tonality-diamond.aspx

-monz
http://tonalsoft.com
Tonescape microtonal music software

i've written about it so much that i already had a
graphic. see this post:

/tuning/topicId_57427.html#57446

-monz

--- In tuning@yahoogroups.com, "monz" <monz@t...> wrote:

> Hi John,
>
>
> --- In tuning@yahoogroups.com, "jsnelsonone" <jsnelsonone@y...>
wrote:
>
> > Thanks for the link Graham, is this where Partch got
> > his Tonality Diamonds?
>
>
> No ... i'm convinced from my research that Partch's
> Tonality Diamond came from Max Meyer, in his book
> _The Musician's Arithmetic_, cited several times by
> Partch in _Genesis of a Music_.
>
> I've written about this here several times before ...
> now i've finally made a graphic of the Meyer diagram
> and put it in the Files section of the
> Yahoo tuning_files group:
>
> log on to Yahoo, and click on "diamond-meyer.gif" here:
>
> /tuning/files/monz/
>
>
>
> I have a webpage about Tonality Diamond in the Encyclopedia:
>
> http://tonalsoft.com/enc/t/tonality-diamond.aspx
>
>
>
> -monz
> http://tonalsoft.com
> Tonescape microtonal music software