Yahoo Tuning Groups Ultimate Backup tuning Visual perceptive illusions

Paul wrote:
these are beautiful images -- clearly indebted to erv wilson (yes?),
but perhaps unknown to him.
Indebted? Surely not directly but indirectly, maybe, I don't know. I was inspired by the Dave
Keenan's image Miracle45Keyboard.gif to use hexagonal shape rather than circle, the first time,
in the representation of the gammier ib1215, which differs, as you probably know, very few from
Studloco scale. I saw it would be easy to rotate and skew the hexagones so intervals would be
linearly projected as required by a pure mathematical approach.

Precedently, I was yet inspired by Dave to adapt one of the representations I used since more
than 20 years in my Turbo Pascal software Gammiers, the symmetrical one, which was very
similar, in that case, to the matrix he generates with the 7/72 generator, since that gammier is
decatonic. I had simply to superpose few intervals having same tempered value : 22/21& 21/20,
16/15 & 15/14, 28/15 & 15/8, 40/21 & 21/11.

If any of my images (present or future) corresponds to the work of someone else, possibly Erv
Wilson here, I would like to be informed, so I could refer to him. I derive all from gammier theory.
However, I don't have interest to say all I derive is new. The worth of the theory stands as much
on its capacity to connect things already known as to its capacity to open new ways.

I would know better Erv Wilson if I had more patience. Each times I clicked on the Anaphoria
Island, I stressed for waiting and renounced by lack of patience. So, I know him only by some
remarks on this List and a past Rappoport's paper in MusicWorks. I just try to click anew on
Anaphoria Island and see there exist patents on keyboards. I take time to download one and
take a look, but keyboards are not my business. I want to use that only as background to show
structures.

Paul wote:
can i encourage you to publish in xenharmonikon?
Certainly. The thing is now possible. I had health problems all winter along and having to take
cortisone for a week I take advantage of a spectacular energy boost to change my mind and
decide of my actual graphical project.

Until date I tried to use sophisticated philosophical and mathematical approach to communicate
about tonal structures. I was like a chef giving recipes rather than dishes. The gammiers are so
simple things that it needs only good images to speak by itself.

Having found first the schocking formula justifying all the project, I prepare now templates for
many secondary objects like lattices, matrices, generators, treillis, keyboards, bar codes, etc.
all that tools permitting to compare and explore in-depht, for instance, the MIRACLE zone...

I probably will ask advice at ulterior phase of the project.

Pierre

🔗graham@microtonal.co.uk

In-Reply-To: <002e01c1d4ad$539ccbe0$512addd8@pierrela>
> Paul:
> these are beautiful images -- clearly indebted to erv wilson
> (yes?),=20
> but perhaps unknown to him.

This is an image that was attached to Pierre's original message.

Pierre:
> Indebted? Surely not directly but indirectly, maybe, I don't know. I
> was in=
> spired by the Dave
> Keenan's image Miracle45Keyboard.gif to use hexagonal shape rather than
> cir=
> cle, the first time,
> in the representation of the gammier ib1215, which differs, as you
> probably=
> know, very few from
> Studloco scale. I saw it would be easy to rotate and skew the hexagones
> so =
> intervals would be
> linearly projected as required by a pure mathematical approach.

That's
<http://www.uq.net.au/~zzdkeena/Music/Miracle/Miracle45Keyboard.gif>. You
can find George Secor's original article in Xenharmonikon 3 or at
anaphoria.com. A couple of Erv Wilson's papers are also in that issue of
Xenharmonikon. I have a summary of generalized keyboards at
<http://x31eq.com/notakey.htm>. For details on Xenharmonikon,
see <http://www.tiac.net/users/xen/xh/>.

> I would know better Erv Wilson if I had more patience. Each times I
> clicked=
> on the Anaphoria
> Island, I stressed for waiting and renounced by lack of patience. So, I
> kno=
> w him only by some
> remarks on this List and a past Rappoport's paper in MusicWorks. I just
> try=
> to click anew on
> Anaphoria Island and see there exist patents on keyboards. I take time
> to d=
> ownload one and
> take a look, but keyboards are not my business. I want to use that only
> as =
> background to show
> structures.=20

The diagram you gave is of a generalized keyboard mapping, whether you
know it or not. The articles in Xenharmonikon 3 explain these, along with
the those from Xenharmonikon 1 and 2 at
<http://www.anaphoria.com/wilson.html>. The patents are more specialist.

Graham

🔗Pierre Lamothe <plamothe@aei.ca>

🔗paulerlich <paul@stretch-music.com>

--- In tuning@y..., "Pierre Lamothe" <plamothe@a...> wrote:

> I attach here a light version of two images published about 7
months ago. I would also appreciate any
> comment about the link between the gammier ib1215, the studloco
set, the decatonic system, etc.

the earliest published suggestion of this pattern may have been in
1975, on page 3 of this:

http://www.anaphoria.com/secor.PDF

and of course dave keenan rediscovered this arrangement more recently.

my comment is that you appear to be giving 0 a priviledged position
here, while a generalized keyboard (and the periodicity block theory)
should really allow all modes and all transpositions of a scale to be
played (or thought about) with equal facility. of course, there's
nothing wrong with your generalized keyboard design here per se --
but let's say we were to give this to joseph pehrson right now . . .
he uses blackjack and thinks of G as a tonic (0), so the section of
the keyboard he'd be interested in would be

..................23....30....37....44....51....58....65.....0....7..

..0....7....14....21....28....35....42....49....56....63....70....5..

.70....5....12....19.................................................

the omission of note 70 (G<) in your diagrams would probably be
confusing to him and to me, while perhaps you share some common
ground with george secor (as indicated by the first diagram on page 3
of his paper) which, now that he's here, you could perhaps profitably
discuss with him . . .

. . . well, i tried.

🔗Alf B. Gjerstad <alfbg@online.no>

Hello to Pierre Lamonthe!
I have not followed the group, but this message interests me really!
I cant open your pictures today (something wrong..), but I'm an fine artist and musican working with harmonies, and would like to see your pictures. If you have more visual stuff, please send them to me!
Regards ABG.

----- Original Message -----
From: Pierre Lamothe
To: Tuning
Sent: Monday, March 25, 2002 7:41 PM
Subject: [tuning] Visual perceptive illusions

Making many tests for my graphical project, I observed, in one of them, not less than four perceptive
illusions in a same image, presented here in pdf and swf formats.

This image showing harmonics and subs in MIRACLE zone of a keyboard had goal to test gradient
treatment in Acrobat Reader and Shockwave. The Flash vectorial image is remarkably light (7k).

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🔗graham@microtonal.co.uk

In-Reply-To: <001d01c1d583$3db83900$1e2addd8@pierrela>
Pierre Lamothe wrote:

> Wonderful. I knew it was vectorial but not already known as generalized
> key=
> board. As I said, I prefer
> to be the nearest possible of what Erv Wilson and others have already
> made.=
> It gives more credit to
> the gammier approach.

Do you have links to your other diagrams?

Possibly we could define a "generalized keyboard" as being like a lattice
but showing cells instead of connected points. In that case, your
gammier diagrams may simply belong to the same category as lattices and
generalized keyboards and only this one happens to be a generalized
keyboard we've already seen.

> On Fri Sep 7, 2001, I post on the Tuning-math (# 1000) on the thread
> About =
> hypothesis and theorem,
> some images leaving apparently all the members indifferent. Why nobody
> rema=
> rked, at this moment,
> that the keyboard image was similar to the Wilson mapping? Was that
> only be=
> cause I didn't use there
> hexagonal shape?

I probably didn't notice you had attached the images. I didn't realise
until Paul commented on pictures I hadn't seen that you could send
attachments to these groups. To save all subscribers downloading them, it
would be better to put them on a website. You can have space on mine if
you don't have your own. Also, you keep posting messages and then
disappearing before we can start a discussion.

It's a Secor rather than a Wilson mapping, as we now know. The hexagons
make it look more like one of Wilson's diagrams, although I don't think
even they are his innovation. The idea of generalized keyboards goes back
to Bosanquet, but that's only for fifth-generated scales.

> I attach here a light version of two images published about 7 months
> ago. I=
> would also appreciate any
> comment about the link between the gammier ib1215, the studloco set,
> the de=
> catonic system, etc.

That's certainly a miracle/decimal layout, and studloco is a miracle
scale. Note I use "decimal" for the 10 note miracle scale and "decatonic"
for Paul Erlich's 10 notes from 22-equal scales.

> Incidently, at the gammier theory viewpoint, the 5-line staff of the
> Graham=
> 's decimal notation is a great
> idea, at less for my graphical project, and I intend to use that
> greatly.

Yes, it's the obvious way of notating music for a keyboard laid out like
in these diagrams. You can always find such a notation for any
generalized keyboard. But I don't know how close your gammiers are to
generalized keyboards without seeing more examples.

I did find this link
<http://www.ixpres.com/interval/dict/lamothe/gammier.htm> from which it
appears your "chordoid" or "harmoid" is like Partch's "lambdoma" or
"tonality diamond". You can find out more of these from Wilson as well.

Graham

🔗Carl Lumma <carl@lumma.org>

🔗dkeenanuqnetau <d.keenan@uq.net.au>

🔗genewardsmith <genewardsmith@juno.com>

🔗graham@microtonal.co.uk

🔗Pierre Lamothe <plamothe@aei.ca>

Thanks Paul and Graham for engaging a new dialog.

I'm not yet in full shape and I want to avoid long discussions but it's ok for short and sweet.

A note for Alf B. Gjerstad: we could communicate privately to talk about formats and contents.

--------------------------------------------------------------------------------

Paul:
my comment is that you appear to be giving 0 a priviledged position
here, while a generalized keyboard (and the periodicity block theory)
should really allow all modes and all transpositions of a scale to be
played (or thought about) with equal facility.
Apparently I have an opposite viewpoint but I would say it's rather complementary. Keyboards and
temperament problematics in general use the tonal space: a set of absolute pitches in which tonic
and scales are transposed. The gammiers use simply the modal space. Unison is priviledged in the
modal space, in sense it's a monovalent degree, but it's not a limitation to choose any key as tonic,
so there's not a physical hole around the tonic on the keyboard, but a virtual modal hole around the
unison.

Besides, there are solid arguments to limit the amount of intervals used in music, but it appears to
me circonstantial that pitch spaces itself be limited. Technology progress could change that: tonic
changes, tonal translations, fifth cycles, modal transformations, tempered derives, all that were more
or less coupled in the past, so tonal and modal spaces in representation.

For the moment, it seems simple to limit the tonic at 72 fixed tempered values, so transpositions be
tempered, but nothing might prevent to use at need, on an adapted instrument, just values defined
relatively to the momentary tonic (even if few could hear the difference between just and tempered).

Paul:
of course, there's
nothing wrong with your generalized keyboard design here per se --
but let's say we were to give this to joseph pehrson right now . . .
he uses blackjack and thinks of G as a tonic (0), so the section of
the keyboard he'd be interested in would be

..................23....30....37....44....51....58....65.....0....7..

..0....7....14....21....28....35....42....49....56....63....70....5..

.70....5....12....19.................................................

the omission of note 70 (G<) in your diagrams would probably be
confusing to him and to me,
Well, I had no intention, at this moment to propose a keyboard design, but only to show in one of my
sketch, where I was testing gradient with pdf and swf, a minimum of 4 perceptive illusions in that image.
Since it was question abundantly of perceptive phenomena about the "third", I wanted only to say that
perceptive illusions are frequent, for vision. (Has someone seen these visual effects?)

If I had to propose a practical keyboard design, maybe I would try to avoid confusing users.

Paul:
while perhaps you share some common
ground with george secor (as indicated by the first diagram on page 3
of his paper) which, now that he's here, you could perhaps profitably
discuss with him . . .
Effectively. I will show later how I used similar extended 72-matrices to represent, for instance, any
fifth cycle and particularly the Safi al-Din set. I can't now, for I want to keep the punch of this kind
of representation, using also the Graham's staff.

I tried also to design modified I and T or other accidentals but I wait a minimal consensus before
to try anew.

Paul:
. . . well, i tried.
I appreciate.

--------------------------------------------------------------------------------

Graham:
Possibly we could define a "generalized keyboard" as being like a lattice
but showing cells instead of connected points. In that case, your
gammier diagrams may simply belong to the same category as lattices and
generalized keyboards and only this one happens to be a generalized
keyboard we've already seen.
"Generalized keyboard" has more affinity with tempered approach than gammier approach. It's only
for particular gammier, like ib1215, where the shrutal treillis gives a compact lattice in tonal-modal
representation, that it becomes interessant to consider that as a possible "generalized keyboard".

It suffices then to made an affine transformation: rotation to horizontalize the octave and skew for a
perfect linear projection on x-axis.

The first page of the pdf attached shows the tonal-modal representation of the shrutal treillis of the
t-gammier which is the 72-tET image of the gammier ib1215. We can see immediately both virtual
"generalized keyboard" and "secor" generator.

I precise that any gammier has a shrutal treillis. The tonal shruti is the minimal step of the gammier
while the modal shrutis are the unison vectors basis. So in Indian system, the tonal shruti is 256/243
while the modal shrutis are 81/80 and 25/24.

In the 72-tET image of ib1215, the image of the steps < 22/21 21/20 16/15 15/14 12/11 10/9 > is
[5 5 7 7 9 11] so the tonal shruti is 5 and the unison vectors [0 2 0 2 2], so a unique modal shruti 2,
and thus the shrutal treillis is a regular lattice. More, it's almost perfectly compact.

These qualities, compacity and quasi-unicity of modal shruti, are not a logic result of the gammier
axiomatic, and tempered approach on the List has better tools to explain that MIRACLE.

However, the gammier theory may enlighten the scale interpretation within the MIRACLE zone. The
goal of my graphical project is to exhibit at less all proper substructures of ib1215 and some improper
like japanese, for instance, and ib1215 itself, which has an improprer 11/10 (degree 2) lesser than the
step 10/9.

Graham:
To save all subscribers downloading them, it
would be better to put them on a website. You can have space on mine if
you don't have your own.
I have mine but I consider these attached files as temporary. I want eventually write a new website and
I find I have already too much links to keep active. This times yet I attached a pdf but I will try to find a
solution. Maybe a section tuning post on my website.

Graham:
Also, you keep posting messages and then
disappearing before we can start a discussion.
I have difficulty with that, effectively. I take much time to write even in French, so in English it's terrible.
I'm afraid of past too long discussions. I became stressed and even aggressive with Gene. So I apologize
for that. I want both remain open for discussion but stop before lost energies.

Graham:
Do you have links to your other diagrams?
I did't write on my website since august 2000 but only add material for the tuning Lists. I suggest to wait
my new material. I add to the mentionned shrutal treillis, in the pdf attached, some diagrams among the
testing sketchs I made these days.

Pierre

🔗genewardsmith <genewardsmith@juno.com>

🔗dkeenanuqnetau <d.keenan@uq.net.au>

--- In tuning@y..., "genewardsmith" <genewardsmith@j...> wrote:
> --- In tuning@y..., "dkeenanuqnetau" <d.keenan@u...> wrote:
>
> > The principle is: There is a one-to-one correspondence between a
> > generalised keyboard layout and a linear temperament. The keyboard
has
> > all the temperament's chains of generators as parallel straight
lines,
> > arranged so that octaves (or more generally, intervals of
equivalence)
> > are horizontal, and pitch strictly increases from left to right.
>
> Why not simply use two generators of the linear temperament of a
size you find congenial? For instance you could use a major and minor
semitone.
>

It's to do with the _boundaries_ of the keyboard layout.

What you suggest will of course give the same lattice geometry, but
will make it much harder to specify the boundaries. Typically a layout
is for a particular MOS (or "well formed" scale) of a temperament.
This has a specific number of notes per interval-of-equivalence (IoE),
usually an octave, but has an unspecified number of IoEs.

This is most simply specified by insisting that one of the generators
must be an integer division of the IoE, which we call the period, and
then we can simply give the length of the (open) chains of the other
generator.

Does this make sense, or am I missing something? Can you give me the
cents for the pair of generators you would suggest for meantone?