Re: Pajara tuning examples/34et

for those who don't follow the math
the point of the below is that 34 does have quite a few intervals that makes different tones close to other notes in the scale.
What you could consider a 'scalar' consonant.
one can find out more about these under the section in the Wilson Archives labeled
Scales of Mt. Meru. http://anaphoria.com/wilson.html

Erv found one recurrent sequence close to34 ET. It is number 25 in figure 12 of his Scales of Mt.Meru. found on page 2
http://anaphoria.com/meruthree.PDF
on he original he did a small pencil mark where he wrote 34 ET which did not reproduce. The generator is about 2 scents off but does form a 34 tone scale
Hn+Hn-9 + Hn-5.
it is close to 5 units of 34

i found some others in my own http://anaphoria.com/MERUcream.PDF
one i found is off just over a half cent off .the numbers behind the minus signs should be subscript
Hn=4Hn-5 + Hn-4. converging on a generator in cents 671.137

another
Hn=4Hn-4+ Hn-3= 740.477 cents

More
Hn=4Hn-5+ 4Hn-4= 810.444 cents

Hn=2Hn-3+ 2Hn-2= 987.807 cents

Hn=16Hn-5+ Hn-3= 1024.302 cents

Hn=16Hn-5 + 4Hn-4= 1093.431cents

--
Kraig Grady
North American Embassy of Anaphoria Island <http://anaphoria.com/index.html>
The Wandering Medicine Show
KXLU <http://www.kxlu.com/main/index.asp> 88.9 FM Wed 8-9 pm Los Angeles

--- In tuning@yahoogroups.com, Kraig Grady <kraiggrady@...> wrote:
> for those who don't follow the math
> the point of the below is that 34 does have quite a few intervals
>that
> makes different tones close to other notes in the scale.

Tunings whose number of tones are multiples of 17 (assuming a fair
balance, ie all tones falling within relatively narrow equally-
spaced regions) are very cohesive as far as Tartini tones. This is
what I was trying to explain to George Secor about a month ago, when
I said that I'm expanding 17 by means of difference tones rather
than literally going to 34 or 68 etc. tones per octave.

> What you could consider a 'scalar' consonant.
> one can find out more about these under the section in the Wilson
> Archives labeled
> Scales of Mt. Meru. http://anaphoria.com/wilson.html

Wow, this is very interesting! Have to study it...

What I suspect to be the source of the cohesion for x17 tunings is
so simple and bizarre that

> i found some others in my own http://anaphoria.com/MERUcream.PDF

and this.

Thanks, man!

-Cameron Bobro