Bikes

Here�s some that haven�t been mentioned:

24tet-acts like two wheels of 12tet representing 3 and 5-limit intervals,connected by the 11 and 13s.(the 7 is pretty much to poor to be used as a such in any way)

34tet-The 17tet subsets act as wheels of fifths and 13s,connected by 5,7 and 11s.

In fact any non-prime number ET can be thought of as a multiwheel bike in some sort of way.

-=-=-=-=-=-=-
MATS �LJARE
http://www.angelfire.com/mo/oljare
_________________________________________________________________________
Get Your Private, Free E-mail from MSN Hotmail at http://www.hotmail.com.

--- In tuning@y..., "Mats Öljare" <oljare@h...> wrote:
> Here´s some that haven´t been mentioned:
>
> 24tet-acts like two wheels of 12tet representing 3 and 5-limit
> intervals,connected by the 11 and 13s.(the 7 is pretty much to poor
to be
> used as a such in any way)

Yes -- I missed out on any bikes that "skip" any odd factors.

> 34tet-The 17tet subsets act as wheels of fifths and 13s,connected
by 5,7 and
> 11s.

I sort of mentioned that today -- I don't agree that 34-tET gets you
7s -- for that you have to double again and go to 68-tET.

> In fact any non-prime number ET can be thought of as a multiwheel
bike in
> some sort of way.

Well I was also restricting my attention to ETs where the smaller
subset ET provided the best approximation to some consonant interval
available in the larger ET -- otherwise the analogy kind of falls
apart.

--- In tuning@y..., "Mats Öljare" <oljare@h...> wrote:

/tuning/topicId_21613.html#21613

> 24tet-acts like two wheels of 12tet representing 3 and
> 5-limit intervals,connected by the 11 and 13s.(the 7 is
> pretty much to poor to be used as a such in any way)

While Möllendorff didn't actually say anything about rational
implications of 24-tET, those who saw my Microfest presentation
will recognize that he did indeed think of it in the way
Mats describes. He referred to 24-tET tuning as "bichromatic".

There's a good possibility that Webern (and therefore probably
Schoenberg also) thought of it like this too.

(BTW, for anyone who's interested: I still have several copies
of my translation of Möllendorff's book, with parallel German
and English text. $10 US plus postage - email me privately.)

-monz
http://www.monz.org
"All roads lead to n^0"

--- In tuning@y..., "monz" <joemonz@y...> wrote:\

/tuning/topicId_21613.html#21692

>
> (BTW, for anyone who's interested: I still have several copies
> of my translation of Möllendorff's book, with parallel German
> and English text. $10 US plus postage - email me privately.)
>

Monz... I'm sorry to be critical, but I wouldn't call that
a "translation" per se. You've converted from German word for word
and, yes, people can mostly figure it out, but there's really more to
a "translation" than that, I believe. Sorry...

_______ _____ ____
Joseph Pehrson

--- In tuning@y..., jpehrson@r... wrote:

/tuning/topicId_21613.html#21705

> --- In tuning@y..., "monz" <joemonz@y...> wrote:\
>
> /tuning/topicId_21613.html#21692
>
> >
> > (BTW, for anyone who's interested: I still have several copies
> > of my translation of Möllendorff's book, with parallel German
> > and English text. $10 US plus postage - email me privately.)
> >
>
> Monz... I'm sorry to be critical, but I wouldn't call that
> a "translation" per se. You've converted from German word for word
> and, yes, people can mostly figure it out, but there's really more to
> a "translation" than that, I believe. Sorry...

True, Joe. Thanks for the criticism - I should have stated it
myself in my original post. I admit right on the title page
that I'd appreciate any help from German speakers in making
it a better translation.

But the book itself is hard to find, and for those who don't
speak German at all, at least it opens a new door for them into
this fascinating historical area of microtonality.

So, there are all the caveats out in the open. I'd still like
to unload the leftover copies I have... anyone interested?

-monz
http://www.monz.org
"All roads lead to n^0"