Re: [metatuning] Digest Number 1021

Hi Carl,

> http://www.lumma.org/microwave/#2003.05.07
>
> and...
>
> http://www.lumma.org/microwave/#2003.05.02
>

Yes, idealists don't need to be solipsists,
normally aren't at all, it is a distinct view.
For instance Berkely, the kind of prottypical
idealist certainly wasn't a solipsist at all.
Solipsism seems to be a very difficult view
for anyone to hold.

Apart from anything else, if one is a solipsist,
it is hard to understand why one would
want to talk to anyone else about your philsophy
or expect to learn anything particularly fruitful
from your conversations with others.
So if there were any true solipsist philosophers
about I suppose we might never hear from them
as they would have little incentive to
communicate their views to anyone else.
Maybe they might on their way towards
their final conclusion of solipsism.

I can't think of a solipsist philsopher
amongst the ones that we studied when I was undergraduate
- perhaps Descartes came quite close in
his meditations, as he successively denied
everything else but found he couldn't deny
his own existence, so at that moment when all
he was left with that he held certain was
his own existence, I suppose
he had descended to an extreme solipsist
position, but then he ended up
reconstructing everything again.
But I may be misrepresenting him
- read his Meditations
but not really studied it and it
was long ago.

Maybe the boundaries between oneself
and others in ones perception aren't
so sharply cut as they seem to us.

But perhaps others here can say more
about that than I can :-).

Robert

Hi Kraig,

> area, so to speak. another piece based on a
> few pairs (between 3 and 6) starting at one 'junction' all having one tone in
> common
> and going out and later returning

That suggests an idea! - to do a random walk in the pattern
- or even, maybe a walk that follows around some kind of
a route e.g. you could bring out the five fold
symmetries of the patches of tiles by following a
five fold symmetric path so that the pitches and rhythms show those
symmetries too.

Indeed, as a way to do that,
how about using the markings of the tiles with red and blue lines,
for the matching conditions - the interesting thing
there is that the blue lines always trace curves with
five fold symmetry. Then try
following one of the blue lines around the tiling
until it joins back around.

Indeed follow a long a row, and every time you come
to a blue line, digress onto it, folow it all teh
way around back to your starting point, and then
keep going along the row to the next one and so on
so you get these cicrular paths all with five fold
symmetry but some large and some small and as the
piece goes on you get them indefintely large.

BTW in one of my unpublished results,
I extended Penrose's idea to make a non periodic
tiling that could only make tilings with seven fold
symmetry. I explained that proof to him once
and he was interested in it.

The seven fold patterns are well known
but at the time anyway I didn't know of
any other paper that proved the existence
of a non periodic set for them.

You can see one of my patterns at:

http://www.robertinventor.com/robert/7g2o7detail.htm

All the curves there have seven fold symmetry.
It is a set of I think it was 28 tiles
and as you see the colours often change
in the middle of a tile - but the
tiles must be put together so that
the colours are continuous across
tile boundaries.

I did try to publish that result once but
alas my paper was so poorly presented,
I think I didn't even manage to communicate
to the referee that it was intended
as a non periodic set of tiles :-(.
So it is one of my collection of
three or four unpublished papers.
I also generalised the Penrose tiles
to prove non periodicity for
a 4 tile set that is also aperiodic
and can make more patterns. The four tile set
was already known but not known to be
an aperiodic set at the time that I did this
work:

http://www.robertinventor.com/robert/pkpcdetail.htm

But here really there is no particlar reason to tie it
down to aperiodic sets of tiles. There are similar
patterns in any dimension. The Penrose tilings
are just a generalisation of that way of showing
a surface of a stacked pile of cubes as a whole lot
of hexagons sub divided into rhombi.
You can do the same in four dimensions and by
then it is already a non periodic tiling if you
choose the slice angle appropriately, and
there is a non periodic set of tiles found by
Ackermann. Then for 5 you have the Penrose
tilings. Then so it goes on - you can
get these non periodic quasi symmetrical
patterns up to any dimension you like
though only a few examples are known with
associated non periodic sets of tiles, just
4, 5, I'm not sure if 6 might have one
too, and then the ones I did for 7, not
sure if there are any more known, or weren't
when I was doing this research.

Quasi crystals of 4, 5 and 6 fold symmetry have
all been found in real material quasi crystals
by materials researchers. The surfaces
are two dimensional slices at carefully
selected angles through higher dimensional
hypercube lattices.

> I think Ervs idea was to use the harmonic series represented by the centered
pentad
> (plus the inversion of these) that way you actually can end up with full
> harmonic and
> subharmonic hexads in the most unusual places!

Rightio. I think when I programmed the tonescapes in FTS that
was rather long ago and I hadn't quite apprecieated the significance
of the diagram, looking at it now again (figure 18) then I can see that
e.g. the rhombs are all otonal or utonal tetrads, and the projections
of the three dimensional cube faces of the five dimensional
hypercube tiling (the groupings of three rhombi that look like
a projection of a cube) are hexaads.

I suppose then an interesting thing to do might be to
go along a row of the tiling and then use the
chords for the rhomb tetrads and for the hexads too
that you encounter along the row.

My tonescapes only use one size of ratio for
each rhomb, so as you go along the row
then you go up in pitch by the same amount
as you go down for the same size rhomb
sloping in the other direction.
But I coudl do it so you have two ratios
instead like that, one going up then one
going down. Just need to alternate because
along each row the Ls alternate in direction,
and so also do the Ss (this is a well known
propery of the tilings).

Depending on the row,just taking one example,
I see Erv Wilson's pattern goes,
S (1/11) L (1/9) L (5/1) S(3/1)

which come to think of it would have the same long
term effect on the pitch as using 11/3 for the S ratio and
5/9 for the L one, which would lead to pitch drift.

However, if one had instead

S (1/11) L (1/6) L (7/1) S (10/1) where I'm delibarately
using 6 instead of 3 and 10 instead of 5 to eliminate
the pitch drift, and the two Ss and Ls there are
sloped in opposite directions (e.g. as they
are when the row crosses a decagon), then the pitch along that row
would again be steady over long periods in the
tiling.

Leads to an interesting question, could one choose
pitches for all five directions of the Penrose tiling
in Erv Wilson's diagram in such a way as
to keep the pitch steady in any direction
over large areas of the tiling.

Then can work out that one of the other rows would be:

S (1/7) L (1/6) L (?) S (10/1)
so getting FTS to look for a companion ratio
for 10/7 as the S it makes 77/32 for
an example with small pitch drift.

So that would be
11 6 7 10 77/16
as the lattice vectors.

Then if you work out the L and S ratio pairs
(i.e. ratio of the two L numbers and the two L numbers)
the rows in the five directions are:
S 11/6 L 11/16
S 10/7 L 77/48
S 77/160 L 11/7
S 7/6 L 10/11
and
S 7/16 L 10/6

FTS confirms that all those rows minimise pitch
drift over long range in the pattern.

That is just experimentally, but I can also
see why it would work. It relates to the
way of viewing the tiling as a Weiringer
roof as it is so called, where the roof is
a two dimensional surface that undulates
according to the tiles. Here if we think of
pitch as a third dimension, we have constrained
the amount of wander along all the rows in
two non parallel directions in the tiling,
and that will constrain it in the other directions
as well.

So, this shows that it would be possible to do it.
But 77 is high in the harmonic series, so I wonder if there
is any group of lower numbered harmonic
series terms that can give a large
patch of the tiling steady in pitch.

This all could be relevant if one wants to
wander around larger areas of the pattern
without octave shifts.

> This is indeed an interesting addition to Dave Canwright's Fibonacci rhythm
> and my own Horogram Rhythms.

Rightio. Yes I used Dave Canright's idea of placing the L next
to the most deeply emphasized beat in some of the other
tunes - it is an option in FTS. I also extended
it to three beats - well that's all explained
on that web page. How do your Horogram rhythms work?
Did you come up with them independently?

In my case it wasn't independently - I got the idea
of a Fibonacci rhythm by reading Dave Canright's paper
about Fibonacci gamelan patterns. But did extend
his work to make new rhythms.

Robert