new wilson archive/meta meantone

this is the direct link as so far as it has not been cross indexed in
the Wilson Archive page yet!~

http://www.anaphoria.com/meantone-mavila.PDF

being recurrent series,
one can reseed such series according to one art,
as well as sellecting just what sample of the series serves one purpose.

this is why it is possible to have many vewrsions of each.

-- -Kraig Grady
North American Embassy of Anaphoria Island
http://www.anaphoria.com
The Wandering Medicine Show
KXLU 88.9 FM WED 8-9PM PST

> http://www.anaphoria.com/meantone-mavila.PDF

Gene, can you make any sense of this?

-Carl

--- In tuning@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
> > http://www.anaphoria.com/meantone-mavila.PDF
>
> Gene, can you make any sense of this?

I'll need some time, but glancing at the first page it discusses a
linear recurrence, and erroneously states the ratios converge. They do
not, as x^4-x-2, the characterisitic polynomial, is not a PV number or
even a Salem number, having more than one root with absolute value
greater than one. Hence, it oscillates.

*Why* he is looking at this I don't know, but it could be something
related to our heavy metal discussions (Golden, Osmium, etc.)

>

Carl/Gene-

It is quite simple. It is a recurrent sequence that causes the elements of triads to beat equally. Sure it oscillates and converges just as much as your ol' fibonacci series into phi. He includes the formula for finding this convergence. It is in that area before it converges though that these scales have the most musical interest, at least to Erv and myself. And we don't alway agree on such things either. look at page 4 and you will see that 268 dropped in octaves fits between 54 and 80. 54 -67- 80, each divided by 13, hence equal beating. One can also go just to
where it converges and construct your scale there and this same property of triads will also occur. One really interesting thing of this series though is how Wilson has been able to "seed" this formula in such a way that you have a just major scale and then proceed toward a converging point. One can thus start with a just tuning and proceed to an "meantone". The other seeds have there own qualities. As with Meta slendro- the resultant music produces beating which when not equal, reinforces these beats by having beats tuned to these beats. This is exactly what i
have been doing for the last 8 years with meta mavila and meta Slendro. Meta mavila is on both the hammer dulcimer and organ pieces on "from the interiors of Anaphoria CD. meta slendro although used on the wedding song on "from the island of Anaphoria" is best illustrated on my upcoming CD "the stolen Stars: an Anaphorian Dance Drama, which will be available in a little over a month. If you have a tuning based on beating the result is that all your intervals have basically the same degree of consonance/disonance hence allowing a freedom of melodic counterpont
unattainable otherwise. The stolen stars illustrates (although the piece is NOT about "tuning") 3 different compositions are superimposed in counterpoint is a very Ivesian like fashion(in the sense of having groups in counterpoint).

>
> From: "Gene Ward Smith" <gwsmith@svpal.org>
>
> --- In tuning@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
> > > http://www.anaphoria.com/meantone-mavila.PDF
> >
> > Gene, can you make any sense of this?
>
> I'll need some time, but glancing at the first page it discusses a
> linear recurrence, and erroneously states the ratios converge. They do
> not, as x^4-x-2, the characterisitic polynomial, is not a PV number or
> even a Salem number, having more than one root with absolute value
> greater than one. Hence, it oscillates.
>
> *Why* he is looking at this I don't know, but it could be something
> related to our heavy metal discussions (Golden, Osmium, etc.)
>
>

-- -Kraig Grady
North American Embassy of Anaphoria Island
http://www.anaphoria.com
The Wandering Medicine Show
KXLU 88.9 FM WED 8-9PM PST

KG,

--- In tuning@yahoogroups.com, Kraig Grady <kraiggrady@a...> wrote:
> ...the wedding song on "from the island of Anaphoria" is best
> illustrated on my upcoming CD "the stolen Stars: an Anaphorian
> Dance Drama, which will be available in a little over a month.

Oh, goody! I've just about worn out "from the...", just listened to it again the other night. Always puts me in another place.

Please let us know when the new CD is available!

Cheers,
Jon

--- In tuning@yahoogroups.com, Kraig Grady <kraiggrady@a...> wrote:
> >
>
> Carl/Gene-
>
> It is quite simple. It is a recurrent sequence that causes the
elements of triads to beat equally. Sure it oscillates and converges
just as much as your ol' fibonacci series into phi. He includes the
formula for finding this convergence.

It doesn't converge, but it might not need to. I still am not clear
what it is a recurrence for, but with the clues you provide below I'll
try to sort it out.

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
> > > http://www.anaphoria.com/meantone-mavila.PDF
> I'll need some time, but glancing at the first page it discusses a
> linear recurrence, and erroneously states the ratios converge. They
do
> not, as x^4-x-2, the characterisitic polynomial, is not a PV number
or
> even a Salem number, having more than one root with absolute value
> greater than one. Hence, it oscillates.

1.353209964 is a root of the polynomial. And, lo and behold, ratios
of consecutive numbers in the recurrence series do indeed converge to
this value. Generate a couple hundred terms of the series out on a
spreadsheet and watch the ratios converging. Not sure where the
confusion is.

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

> 1.353209964 is a root of the polynomial. And, lo and behold, ratios
> of consecutive numbers in the recurrence series do indeed converge to
> this value. Generate a couple hundred terms of the series out on a
> spreadsheet and watch the ratios converging. Not sure where the
> confusion is.

Sorry about that; I was thinking of converging to Ar^n, where r is the
root above, which is what things like the Fibonacci sequence do. It
doesn't do that, but the ratios of successtive terms do converge, a
weaker condition.