Rereading mandelbaum

I'm rereading the Mandelbaum thesis. I'd like anyone else's thoughts on this - I think it's a very good introduction to microtones in a way, and good for the time...

just getting to grips with the Brun calculations. Has anyone performed them for more partials than 2/1 3/2 5/4???

Mark

First an apology that i have not finished putting this book up yet, it is still in progress and will happen.

As for expanding Brun calculations beyond 5 limit , both Erv and myself and i imagine others have done so. Brun himself i notice mentions 7 limit intervals, although is do not read this language to see quite where this lead him.

The examples in the archive merely showing how the method can be applied to more than two intervals, figuring this would be enough to let others explore by themselves. It is so process oriented, that it undermines what is going on if one just supplies 'answers'. one cannot grasp what is going on till one has the process of running it

I quite like working with them as one can use it for steps in an ET system, mixed noble and gold ratios and even rhythms.

One can also take a more 'artistic approach and go down to a certain point and changes the order or even introduce new ratios according to what one wants. It leaves quite a bit of room for individual creativity.

It also results in a few scales missed by MOS and constant structures that do work quite well

tuning@yahoogroups.com wrote:

>Message: 1 > Date: Sun, 6 Nov 2005 14:00:04 +0000
> From: Mark Gould <mark@equiton.waitrose.com>
>Subject: Rereading mandelbaum
>
>I'm rereading the Mandelbaum thesis. I'd like anyone else's thoughts on >this - I think it's a very good introduction to microtones in a way, >and good for the time...
>
>just getting to grips with the Brun calculations. Has anyone performed >them for more partials than 2/1 3/2 5/4???
>
>Mark
>
>
>
>
> >
>
>
> >

--
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

On Monday 07 November 2005 12:57 pm, Kraig Grady wrote:
> First an apology that i have not finished putting this book up yet, it
> is still in progress and will happen.
>
> As for expanding Brun calculations beyond 5 limit , both Erv and myself
> and i imagine others have done so. Brun himself i notice mentions 7
> limit intervals, although is do not read this language to see quite
> where this lead him.
>
> The examples in the archive merely showing how the method can be
> applied to more than two intervals, figuring this would be enough to let
> others explore by themselves. It is so process oriented, that it
> undermines what is going on if one just supplies 'answers'. one cannot
> grasp what is going on till one has the process of running it
>
> I quite like working with them as one can use it for steps in an ET
> system, mixed noble and gold ratios and even rhythms.
>
> One can also take a more 'artistic approach and go down to a certain
> point and changes the order or even introduce new ratios according to
> what one wants. It leaves quite a bit of room for individual creativity.
>
> It also results in a few scales missed by MOS and constant structures
> that do work quite well

This sounds interesting....where can I get the lowdown on 'Brun calculations'?

-Aaron.

--- In tuning@yahoogroups.com, Mark Gould <mark@e...> wrote:
>
> I'm rereading the Mandelbaum thesis. I'd like anyone else's thoughts
on
> this - I think it's a very good introduction to microtones in a way,
> and good for the time...

One flaw in this book is that, after spelling out the problems with
strict JI, Mandelbaum later presents 53-equal in a glowing light,
without mentioning that the very same problems which "afflict" JI
(relative to common-practice triadic diatonic norms) also "afflict" 53-
equal.

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

> It also results in a few scales missed by MOS and constant
structures
> that do work quite well

Can you list some of these? As you know the work on tuning-math has
been closely geared around constant structures (since that's what
periodicity blocks normally are) and what some people call MOS. The
pentachordal decatonic for example isn't MOS by anyone's definition.
But it's still a constant structure. So please fill us in!

--- In tuning@yahoogroups.com, Aaron Krister Johnson <aaron@a...> wrote:

> This sounds interesting....where can I get the lowdown on 'Brun
calculations'?
>
> -Aaron.

Brun made a neat attempt in this area:

http://mathworld.wolfram.com/IntegerRelation.html

Brun's algorithm is like the Euclidean one

http://mathworld.wolfram.com/EuclideanAlgorithm.html

for two terms but applies to more than two terms; Brun's method is to
rotate regularly between the terms as you iterate.

If you have a JI chord you want to find an ET to approximate (or
equivalently, want to find the cardinality of fairly even JI scales
which include many instances of this chord, etc.), you can run an
integer relation algorithm (on the logs of the ratios in the chord) to
spit out a series of appropriate ETs much faster than you could do a
brute-force search (though the latter is fast enough on today's
computers). Brun's algorithm will result in a series of ETs which may
not be "optimal" in the way the Ferguson-Forcade results would be, but
can still be musically interesting or suggestive.

Would it be possible for someone to put up an example with say four
ratios. So far as I could work out, you process the top two lines as
Mandelbaum describes then sort the four rows into descending order of
the left hand column. It's iterative, and therefore programmable. At
work I have matlab and now spend my lunches programming the odd
tuning thing or two.

alternatively someone could email an example to me. You don't need to
do more than explain a couple of iterations.

As for saying that the thesis is a good introduction, i meant it in
the sense that it covers a number of things, rather than subscribing
to Joel's point of view.

Mark

>
> As for expanding Brun calculations beyond 5 limit , both Erv and
myself
> and i imagine others have done so. Brun himself i notice mentions 7
> limit intervals, although is do not read this language to see quite
> where this lead him.
>

in the wilson archives are 3 papers pertaining to brun' s algorithm
the original can be found. http://anaphoria.com/viggo0.PDF
as for Paul request, yes i was mistaken it them producing non constant structures.
but some of these quite stretch the idea to the max, i haven't check them all, as i need my coffee first
but does have some that i have not seen anywhere else see
http://anaphoria.com/viggo3.PDF
thanks for the link to the other .

while viggo brun method can be applied to reiterating in a set sequence, one can change the rules between three or more ratios at any time with equally good results which is why i consider it artistically viable. one can decide one has a certain limit up to a certain size and shift where you want.
or if need be one could alternate say the a-b and a-c formula or systemize it how one wishes
--
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

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

> but does have some that i have not seen anywhere else see
> http://anaphoria.com/viggo3.PDF

I recall quite a discussion on this on tuning-math. Mark should read
this article too, as it shows the Brun calculations quite explicitly.
Anyway I think all of these look like periodicity blocks; perhaps Gene
has more to say on the issue at this point.

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

> I recall quite a discussion on this on tuning-math. Mark should read
> this article too, as it shows the Brun calculations quite explicitly.
> Anyway I think all of these look like periodicity blocks; perhaps Gene
> has more to say on the issue at this point.

The first page isn't Fokker blocks, but multiset decompositions of the
octave as recently discussed on tuning-math. What comes after may be
Fokker blocks.

--- In tuning@yahoogroups.com, "wallyesterpaulrus"
<wallyesterpaulrus@y...> wrote:
>
> --- In tuning@yahoogroups.com, Kraig Grady <kraiggrady@a...> wrote:
>
> > but does have some that i have not seen anywhere else see
> > http://anaphoria.com/viggo3.PDF
>
> I recall quite a discussion on this on tuning-math. Mark should read
> this article too, as it shows the Brun calculations quite explicitly.
> Anyway I think all of these look like periodicity blocks; perhaps Gene
> has more to say on the issue at this point.

Starting from (10/9)^2 (9/8) (6/5)^2, giving pentatonic scales, this
gives successively scales (including Fokker blocks) of sizes 5, 7, 10,
15, 22, 34, 53, 84, 118, 171, 258, 376, 494, 612, 730, 1289, 1901, 2513,
4296, 6197 ...

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
>
> --- In tuning@yahoogroups.com, "wallyesterpaulrus"
> <wallyesterpaulrus@y...> wrote:
>
> > I recall quite a discussion on this on tuning-math. Mark should
read
> > this article too, as it shows the Brun calculations quite
explicitly.
> > Anyway I think all of these look like periodicity blocks; perhaps
Gene
> > has more to say on the issue at this point.
>
> The first page isn't Fokker blocks, but multiset decompositions of the
> octave as recently discussed on tuning-math. What comes after may be
> Fokker blocks.

I was referring to the older discussion on "unimodular matrices" (maybe
search for that text) and three-term recurrence relations or whatever
you call them. You pointed out that the 3-by-3 matrices Wilson shows
here are unimodular matrices, and . . .