INFLATION on coherence

A day, Zenon said to Einsteinus : I can't attain any goal in discussion,
for to terminate an argument I have to go beyond the half of the argument
and new questions always arise before halfway, and that ad libitum ...

In message 14371 Paul wrote :

<< I would like to see if I can be the Einstein to your
Lorentz (not comparing myself to Einstein in anyway). >>

And just before :

<< unless I'm missing large portions of your theories,
they seem to be in need of underlying _musical_ principles >>.

It's why Hendrik Antoon (*) doing now in musical transformations would had
prefered to write at Johann Sebastian rather than Albert.

(*) Lorentz

------

My dear Albert,

It seems that something was wrong with your metempsychosis. Would you have
forgotten the difference between vague principle allowing plethora
explanations a posteriori without formal derivation and a true formal
principle like your fantastic one permitting to derive easily my henceforth
famous transformations?

Is'nt Feynmann who talked about soon known ultimate equation of physics,
the problem being not to express a principle but to establish a true formal
derivation?

Is'nt true that you answer now at a simple question like

<< Perhaps have you a definition for musical structure
not covered by these explanations. If it is the case,
could you explicit your definition? >>

by something like that

<< Musical structure
-- how music is constructed from the scale.
Melody, harmony, tonality as we know them
-- how do they arise?
How do their development influence the further
development of scales? >>

(What seems well appropriate in context)

but feeling perhaps uncomfortable with the consistency you refer now,
rather than define, like that

<< "musical structure" issues in _Tuning, Tonality,
and Twenty-Two Tone Temperament_ >>

and a long list of writings permitting to your reader to reconstitute
quickly the definition?

I would hesitate to ask you "What is a musical scale?". I'm afraid you
invite me to read the complete Congress Library.

Would you permit me, my dear Albert, to give the first definition of my
mathematical theories. It is the definition (a bit bourbakian) of the
minimal algebraic structure on a set with a partial internal binary
composition law called LARGE GROUPOID STRUCTURE.

-------------------------------------------------------
Let S be a set and G be a non-empty subset of S x S x S.
G "is" a LARGE GROUPOID STRUCTURE on S if G has property
(x,y,z) = (x,y,z')
-------------------------------------------------------

Do you ignore Albert, that starting with that I use only axioms in building
gammier theory, and that I use only two principles to justify these axioms.
The first one being the "algebraic coherence" and the second being the
"simplicity" of abelian group obtained by factorization class. (Such
principles being justified in human sciences like structural anthropology
and considerations about invariance in acoustical channel).

If I obtain with that, without musical considerations, results that could
be pertinents in music, it seems that it could be put to credit of the
process rather than to debit. Otherwise it seems you would have lost,
Albert, your first vision of the science.

I would like to be simply victim of a bad impression after what I could
recognize anew my Albert.

Your Andrik Antoon

Pierre, I would prefer a thousandfold if you tried to answer the
specific questions I ask about your theory rather than focus on a
wistful analogy I made (in the spirit of friendship and cooperation
and anticipation of the good things that may come _after_ the process
of educating one another is complete). Once again, if I contributed
in any way to a less-than-cooperative tone, I apologize.
>
> Would you permit me, my dear Albert, to give the first definition
of my
> mathematical theories. It is the definition (a bit bourbakian) of
the
> minimal algebraic structure on a set with a partial internal binary
> composition law called LARGE GROUPOID STRUCTURE.
>
> -------------------------------------------------------
> Let S be a set and G be a non-empty subset of S x S x S.
> G "is" a LARGE GROUPOID STRUCTURE on S if G has property
> (x,y,z) = (x,y,z')
> -------------------------------------------------------
>
> Do you ignore Albert, that starting with that I use only axioms in
building
> gammier theory, and that I use only two principles to justify these
axioms.
> The first one being the "algebraic coherence" and the second being
the
> "simplicity" of abelian group obtained by factorization class. (Such
> principles being justified in human sciences like structural
anthropology
> and considerations about invariance in acoustical channel).

Please educate me, with website links if you like! I'm open to
reading more than what is on this list!

> If I obtain with that, without musical considerations, results that
could
> be pertinents in music, it seems that it could be put to credit of
the
> process rather than to debit. Otherwise it seems you would have
lost,
> Albert, your first vision of the science.

Let's get off this track for now until I better understand your
theory. OK?

--- In tuning@egroups.com, "Paul Erlich" <PERLICH@A...> wrote:

http://www.egroups.com/message/tuning/14395

> Pierre, I would prefer a thousandfold if you tried to answer the
> specific questions I ask about your theory rather than focus on a
> wistful analogy I made (in the spirit of friendship and cooperation
> and anticipation of the good things that may come _after_ the
process
> of educating one another is complete). Once again, if I contributed
> in any way to a less-than-cooperative tone, I apologize.

I'm beginning to lose confidence that Phillipe Lamothe's theories can
withstand close intellectual scrutiny -- language barrier or no
language barrier. Sorry, Phillipe, for this perception... I hope it
is a MIS-perception!
___________ ____ __ _
Joseph Pehrson

I wrote,

>> Pierre, I would prefer a thousandfold if you tried to answer the
>> specific questions I ask about your theory rather than focus on a
>> wistful analogy I made (in the spirit of friendship and cooperation
>> and anticipation of the good things that may come _after_ the
process
>> of educating one another is complete). Once again, if I contributed
>> in any way to a less-than-cooperative tone, I apologize.

Joseph Pehrson wrote,

>I'm beginning to lose confidence that Phillipe Lamothe's theories can
>withstand close intellectual scrutiny -- language barrier or no
>language barrier. Sorry, Phillipe, for this perception... I hope it
>is a MIS-perception!

I don't know who Phillipe is, but his brother Pierre's theories, I feel,
_can_ withstand close intellectual scrutiny -- if he is willing to help us
understand them.

--- In tuning@egroups.com, "Paul H. Erlich" <PERLICH@A...> wrote:

http://www.egroups.com/message/tuning/14478

> I don't know who Phillipe is, but his brother Pierre's theories, I
feel,can_ withstand close intellectual scrutiny -- if he is willing
to help us understand them.

Well, this is good, and, of course, I was talking about Phillipe,
*not* Pierre. I certainly wouldn't want to cast aspersions about
Pierre's theories! (whew!)

Joseph Pehrson wrote,

> I'm beginning to lose confidence that Phillipe Lamothe's theories
can withstand close intellectual scrutiny -- language barrier or no
language barrier.

Hmm, what makes you think that? I think there're many things going
on... one being someone talking in something like their own tuning
language; in other words "outsider" language for those who are used to
this list and the lingo and ideas that frequent it... another being
that Pierre seems to be interpreting Paul's inquiries as a bit of an
annoyance, though I think is just a clash of presentation styles more
than anything; Paul wanting to understand what exactly Pierre is
posting, and Pierre (perhaps) taking this as a bit of an "attack" on
his ideas...

I really don't understand why you'd post something like this unless
you were sure of such a thing... maybe a poke to get him to post more?
I dunno... it seems to me like it would do just the opposite through!

--Dan Stearns

--- In tuning@egroups.com, "D.Stearns" <STEARNS@C...> wrote:

http://www.egroups.com/message/tuning/14480

> I really don't understand why you'd post something like this unless
> you were sure of such a thing... maybe a poke to get him to post
more?
> I dunno... it seems to me like it would do just the opposite
through!
>
>
> --Dan Stearns

As usual, Dan, you are right about "list etiquette." I was just
getting a little frustrated with all this "Einstein" business..

Apologies to all.

Joseph

Joseph wrote,

>As usual, Dan, you are right about "list etiquette." I was just
>getting a little frustrated with all this "Einstein" business..

Well, I have to take the blame for bringing up Einstein in the first place,
but let me try to clafiry what I was getting at with an analogy.

In the periodicity block formalism, one starts with the prime vector
coordinates of a set of "unison vectors" -- small intervals. For example,
the syntonic comma of 21.5 cents comes from tuning four fifths up and a
major third down, so its prime vector coordinates are (4, -1). The
diaschisma of 19.6 cents comes from tuning four fifths down and two major
thirds down, so its prime vector coordinates are (-4,-2). Now one writes
these vectors in a matrix:

(-4 -2)
( )
( 4 -1)

Then one calculates the determinant of this matrix. The determinant of the
matrix

( a b)
( )
( c d)

is written

| a b|
| |
| c d|

and equals a*d - b*c.

So

|-4 -2|
| | = (-4)*(-1) - 4*(-2) = 4 - (-8) = 12.
| 4 -1|

So somehow the syntonic comma and the diaschima give a 12-tone scale. You
can try this for many sets of commas, including ones involving the primes 7
and 11 (for which you need 3-by-3 and 4-by-4 matrices, and somehow the
determinant always gives you the number of notes in some system that has
been used or proposed somewhere in the world at some time.

This may seem like magic, or more likely, luck, to a skeptical observer. But
it isn't -- and the explanation is provided in the _Gentle Introduction_.
The determinant counts the number of equivalence classes on the just lattice
that exist when the commas are considered to generate an equivalence
relation. Hence, the determinant counts the number of categorically distinct
pitches one can find by starting at a given pitch in the just lattice and
adding more and more pitches, through consonances with one another,
discarding any new pitch if it is a comma away from a starting pitch.

What I'm seeing in Pierre's work is a mysterious mathematical formalism,
which I haven't seen presented in its entirety, but I must assume is quite
simple and beautiful. What I'm not seeing an inkling of is the "explanation"
-- the demonstration that reduces the mathematical abstraction to a
straightforward set of rules grounded in acoustics, psychology, or a
combination of the two.

I'll be very happy if Pierre proceeds without providing any such
"explanation". What seemed to infuriate him was the idea that I might come
up with such an "explanation" for him. I hope Pierre will forgive me for any
arrogance and/or misinterpretation that this suggestion may have implied,
and proceed as if it had never been brought up.

Pierre?