Yahoo Tuning Groups Ultimate Backup tuning On realism and continuity

[Paul wrote (Aug 22) :]

<< It is, at this point, a dyadid discordance measure, which certainly
conforms to Pierre Lamothe's partial ordering for simple ratios, but is a
realistic, continuous function that is well-defined for all intervals,
simple ratios or otherwise. >>

I understand well the meaning of this remark. I won't comment at this level
but only by way of digression on association of terms : realistic and
continous. I want to express that it's slightly discordant in my
(philosophical) ear.

Continuity is a mind fiction. Nothing in known universe is continous, but
it remains true that a limited validity domain of reality may correspond to
our continuous fiction. Sure, in the order of Avogadro's number, validity
domain is very large, but at human informational scale we have to be
seriously questioning to avoid naïve representation.

More, there is no solid reason to think that space or time are continuous
substratum. In my opinion, apparent continuity of consciouness and lived
duration are also fiction. It's not non-existent. It's secreted by mind.
All that seems very far of music but I think that musical phenomenon is
bound with time perception and continuity secretion.

Pierre Lamothe

🔗Joseph Pehrson <pehrson@pubmedia.com>

🔗Pierre Lamothe <plamothe@aei.ca>

In 12950 message Joseph Pehrson wrote :

<< Paul... Is the harmonic entropy model bound up inextricably with the
notion of "continuity." I notice the graphs are continuous lines.
And, if so, what is Pierre talking about?? >>

Although question is addressed to Paul, I take liberty to precise what I'm
talking about.

I would like to emphasize that Paul's dissonance curves HAVE NOT TO BE
DISCONTINUOUS. It's the main quality of the model having a corresponding
reasonable dissonance value for all possible intervals. What I say is that
continuous curve is a relation between two representations : interval space
and dissonance space. As continuous, it's in mind.

My digression was at general level and wanted only to contain
interpretation. I will remain nearer of sound here.

It's easy to forget probability context of continuous curves and to
conceive perception as pure continuous transduction of precise interval to
precise dissonance sensation. Reality is always more complex than all our
models and appears with tausend forms of discontinuity. Here are few examples.

Seen of space, oceans appear like near perfect sphere, but seen from boat
in tempest evidence is well distinct.

Possility to add oil in olive barrel implies a discontinuity kind. Since 45
Mhz sampling is about limit of perceptibility, theorical possibility exists
to interpolate tons of imperceptible data at higher frequencies.

Limited number of Corti cells don't permit continuous process and we can
say by principle that all type of perception have grain.

Neurons are not continuous transductor with a N-dimensional function but
are fired by complex association (changing in time) of data flux.
Information is always distributed on group of neurons and has sense by mean
of collective response.

However, it's not really this resulting fine grain that worry me but
discontinuity implied at higher (semiotic) level of
sensibility/intelligibility articulation. We can distinct maybe 1800 pitch
levels, but few tens of tones are used in music. I think that this
restriction is not well understood. Restriction on tones is only a reflect
of deeper restriction since acceptable values for one tone form a
continuous space.

Pure sensitive approach with dissonance minima has only limited validity
domain that has to be contained. We have to take account also of other
parts of reality for musical perception understanding. Musical listening is
not a passive process but an active one that implies not only sensation but
pattern recognition, memorized categories, focusing attention and
retroactive action of brain on cochlea.

Retroaction (like phasing or counterphasing of outer hair cells) implies
that mind don't work from pure sensitive images contained in brain. Brain
actively participate to buid pertinent sensations helping intentional
presence at musical work.

All that are glimpses. My approach of tonal intelligibility by acoustical
parametric invariance gives access to an other part of reality which can't
be bypass, in my opinion.

At end, I'm also curious of several other parts of reality : impedance
model in cochear fluids and estimation of delays giving pressure difference
acting on basilar membrane, neuronal coincidence detectors as revealed in
visual cortex, chaotic analyse, etc.

I cut here. For now I want to begin re-working on my website.

Pierre Lamothe

🔗Monz <MONZ@JUNO.COM>

--- In tuning@egroups.com, Pierre Lamothe <plamothe@a...> wrote:
> http://www.egroups.com/message/tuning/12967
>
> ... Neurons are not continuous transductor with a N-dimensional
> function but are fired by complex association (changing in time)
> of data flux. Information is always distributed on group of
> neurons and has sense by mean of collective response.
>
> However, it's not really this resulting fine grain that worry me
> but discontinuity implied at higher (semiotic) level of
> sensibility/intelligibility articulation. We can distinct maybe
> 1800 pitch levels, but few tens of tones are used in music.
> I think that this restriction is not well understood. Restriction
> on tones is only a reflect of deeper restriction since acceptable
> values for one tone form a continuous space.

Pierre, what you call a 'restriction' here is very closely allied
to my 'finity' concept:
http://www.ixpres.com/interval/dict/finity.htm

(and all related links)

I do believe, contrary to many other acoustic researchers and
tuning theorists, that there is some sort of 'prime-factorization'
calculator built into our ear/brain system, which is analyzing
time-sensitive data collected from groups of firing neurons.

I see recognition of the prime series as the ultimate reduction
of the various mathematics involved, even if the prime-factoring
is only an approximation of what the ear is actually hearing.

It seems to me to be at the same time both the simplest and the
most sophisticated means of recognizing pattern-relationship
in musical harmony.

> Pure sensitive approach with dissonance minima has only limited
> validity domain that has to be contained. We have to take account
> also of other parts of reality for musical perception
> understanding. Musical listening is not a passive process but
> an active one that implies not only sensation but pattern
> recognition, memorized categories, focusing attention and
> retroactive action of brain on cochlea.

Paul Erlich, Margo Schulter, myself, and others have emphasized
here again and again that an understanding of *musical* intonation
is highly dependent on both stylistic context and temporal
perception.

I'm very interested in your work, and wish I had the time to
devote to a really serious study of it.

-monz
http://www.ixpres.com/interval/monzo/homepage.html

🔗Jacky Ligon <jacky_ekstasis@yahoo.com>

🔗Pierre Lamothe <plamothe@aei.ca>

Monz,

I'll read soon on your finity concept.

You wrote :

<< I do believe, contrary to many other acoustic researchers and
tuning theorists, that there is some sort of 'prime-factorization'
calculator built into our ear/brain system, which is analyzing
time-sensitive data collected from groups of firing neurons. >>

Without having in head a clear concept for mechanism, I believe also that
there exist ways by which neuronal convergence is facilitated towards hard
relations contained in mathematical structures like Euclide/Stern-Brocot
trees and perhaps others not yet revealed under Riemann's Zeta function
related to prime numbers. Discovery of coincidence detector neurons in
cat's visual cortex for recollection of partial analysis to attribute at
same object seems to indicate that time-sensitive data process is current.

Besides, prime-factorization is essential on macrotonal viewpoint on wich I
want to focus in few days.

You wrote :

<< Paul Erlich, Margo Schulter, myself, and others have emphasized
here again and again that an understanding of *musical* intonation
is highly dependent on both stylistic context and temporal perception. >>

I'm very glad to read that. Not only I'm new on List but I have difficulty,
with my poor English, to perceive such clear conclusions among large amount
of text. I read only samples and I'm forced to presume, by time constraint,
for decision to read thoroughly or none. No doubt archives may contain
precious information for me, but I didn't find yet courage to scan them.

Pierre

🔗Monz <MONZ@JUNO.COM>

--- In tuning@egroups.com, "Jacky Ligon" <jacky_ekstasis@y...> wrote:
> http://www.egroups.com/message/tuning/12971
>
> --- In tuning@egroups.com, " Monz" <MONZ@J...> wrote:
> >
> > I see recognition of the prime series as the ultimate reduction
> > of the various mathematics involved, even if the prime-factoring
> > is only an approximation of what the ear is actually hearing.
>
> Monz,
>
> Hi! This is something I'd hoped you'd speak about. So in your
> theory, the prime series is more important than the odd limits
> of the overtone series for recognition of distinct interval
> classes,

Yes.

> where the 9, 15, 21, 25 etc... series would tend to be
> perceived as the numbers by which they would reduce to - prime
> limit-wise? Meaning "9" would still have a "3-ness" about it,
> and "15" - a 3 and 5 quality.

Yes.

> This is something that I can relate to, because when you look
> at the overtone series, you can see that the prime limits each
> create a unique set of pitches, where the others have redundant
> intervals that will reduce. Am I following your meaning?

Yes.

Your input provides one person's empirical evidence that I'm right.
:)

I've been embroiled in debates about the odd- vs. prime-
dichotomy here in the past, mostly with Paul Erlich, and Paul's
firm-as-concrete logic (backed up with agreement from Dave
Keenan's experiments [*]) has convinced me that I should agree
with him that odd-limit is the important consideration when
scrutinizing *intervals*, that is, dyads.

But for any more complex simultaneities (triads, tetrads, etc.),
or indeed for melodic (i.e., scalar) and certainly for systemic
considerations, prime-limit is where it's at.

Paul and others agree with this to some extent too. In fact,
I think we both agree that the prime-ness doesn't really come
out until three or more pitches are sounded collectively.

Bare dyads/intervals only seem to give a sense of 'prime-ness'
up to about the 11-limit or so, and then only for the 'basic'
harmonic intervals (3/2, 5/4, 7/4, 11/8), not for more complex
intervals like 6/5, 11/7, etc.

So even in the case of dyads, perception of prime-ness seems
to be bound together with perception of 'tonalness', which
I certainly think is true about tri- and higher-ads.

As you observe, the composite (= non-prime) ratios give recurring
interval sizes as one travels up the harmonic series, but the
primes always give distinct _gestalts_. I think this is the
most important observation about primes in harmonic theory.

Ivor Darreg made frequent reference to the individual 'moods'
of various ETs. I haven't done much research into this area yet,
but my contention is that these 'moods' are directly related to
the 'affect' we perceive thru the prime-factor reduction process.

I like to use prime-factoring for my lattice formula because
it gives me a way to look at *all* the rational tunings that
have been theorized, and to see at a glance what they have
in common or in difference.

Odd-factoring only complicates the matter, because composite
ratios occupy a redundant distinct odd-factor point in ratio-space
at the same time that they fit into their proper prime-factor
point; for example, 9/8 would be the first point along the 9-axis,
but it would also be the second point along the 3-axis.

I reiterate that I agree that odd-limit is preferable when
considering intervals, as in Paul's 'diadic harmonic entropy'
graphs. The prime-limit theory applies only when studying
pitch-aggregates larger than dyads, and there IMO it is more
important than odd-limit.

Another point to be made is that of naming or characterizing
these prime affects. We've discussed it a little here, but
most of us end up agreeing that the clearest way to talk about
it is simply to refer to '3-ness', 5-ness', '7-ness', etc.
I notice that you've opted for this approach too.

Many of us here also agree with what you said above, that
9/8 exhibits compond '3-ness', and that 15/8 exhibits a
mixture of '3-ness' and '5-ness', and so on. We've debated
where the limits of this perceptual ability lie, but with
no stronger conclusion than those similar to what I posted
about a week ago, 'somewhere between 11 and 23'.

As I said in the post you quoted, I believe that somehow my
prime-factor lattice formula is tied into how we perceive harmony
and 'tonalness'.

I wish I could say more about it, but thousands of mathematicians
have been studying the magic of the prime series for a long time,
and there are still very few conclusive statements that can be
drawn about it. Perhaps the very mysteriousness of how the
prime series works is ultimately why (if I'm right) we use it as
the ultimate numerical reductionary process... sort of like a
numerical 'God' concept.

Take a look at my 'Favorite Links' page: the 'Prime Pages' site
gives lots of info.

----
[*] This was during the discussion of complexity which occurred
here around April - June 1999. Check the archives. On my
computer the old Onelist posts don't come up in a search, so
I have to just go into the approximate date and hunt around.
Most of the relevant posts were by Paul Erlich (under his own
name and the alias of Brett Barbaro), Paul Hahn, Dave Keenan,
Carl Lumma, Manuel Op de Coul, and Daniel Wolf.

-monz
http://www.ixpres.com/interval/monzo/homepage.html

🔗Paul H. Erlich <PERLICH@ACADIAN-ASSET.COM>

Monz wrote,

>I reiterate that I agree that odd-limit is preferable when
>considering intervals, as in Paul's 'diadic harmonic entropy'
>graphs. The prime-limit theory applies only when studying
>pitch-aggregates larger than dyads, and there IMO it is more
>important than odd-limit.

Did you see by response on Saturday to this contention? I have more up my
sleeve, too. Why don't you elaborate on your views here with some examples?

Monz wrote,

>Many of us here also agree with what you said above, that
>9/8 exhibits compond '3-ness', and that 15/8 exhibits a
>mixture of '3-ness' and '5-ness', and so on. We've debated
>where the limits of this perceptual ability lie, but with
>no stronger conclusion than those similar to what I posted
>about a week ago, 'somewhere between 11 and 23'.

Monz, by this logic 13/11 and 143/128 have the same "ness." What meaning
could that possibly have?

>As I said in the post you quoted, I believe that somehow my
>prime-factor lattice formula is tied into how we perceive harmony
>and 'tonalness'.

If 2 is considered an independent factor, then yes, this is true, but really
only reflects a characteristic of _mathematics_ than _how we hear_.
Similarly, if 2 is considered largely dispensible, the best modification of
the prime-factor lattice is an odd-factor one that is triangular -- again
for reasons of mathematics. The only thing that is "programmed" into us is
the integers and maybe octave-equivalence -- all the "magic" of primes is
already built into the integers, and affects us only to the extent that it
is. I can't argue with Joe that this is a large extent -- that's why the
definition of "limit" I wrote in the Dictionary has two parts -- "prime" and
"odd" -- but I can't see any justification for systems that treat primes
differently, whether it is to favor higher primes, or to weight against them
(the Euler, Barlow, and Wilson complexity measures do the latter.

🔗Monz <MONZ@JUNO.COM>

--- In tuning@egroups.com, Pierre Lamothe <plamothe@a...> wrote:
>
> ... Not only I'm new on List but I have difficulty, with my
> poor English, to perceive such clear conclusions among large
> amount of text. I read only samples and I'm forced to presume,
> by time constraint, for decision to read thoroughly or none.
> No doubt archives may contain precious information for me, but
> I didn't find yet courage to scan them.

Hello Pierre. Since you are mentioning the language barrier,
I thought these links might help.

Last year I translated a paper by Patrice Bailhache, about
the music-theories of the mathematician Euler:

http://www.ixpres.com/interval/monzo/euler/euler-en.htm

Since your native language is French, you'll benefit more
from the original:

http://bailhache.humana.univ-nantes.fr/thmusique/euler.html

But please do also read the notes I added to my translation.
Euler's theories have some relevance to my own work.

Except for the ancient Greek distinction between odd and even
numbers, which isolates 2 from the other prime-factors, Euler
seems to have been the first person to note the importance of
prime factors in musical harmony.

Also, I've made a translation into French of my paper
describing my own lattice formula:

http://www.ixpres.com/interval/monzo/lattices/lat-fren.htm

The translation is not great, but it should help you
if you also read the English version.

-monz
http://www.ixpres.com/interval/monzo/homepage.html

🔗Monz <MONZ@JUNO.COM>

--- In tuning@egroups.com, "Paul H. Erlich" <PERLICH@A...> wrote:
> http://www.egroups.com/message/tuning/12984
>
> Monz wrote,
>
> > I reiterate that I agree that odd-limit is preferable when
> > considering intervals, as in Paul's 'diadic harmonic entropy'
> > graphs. The prime-limit theory applies only when studying
> > pitch-aggregates larger than dyads, and there IMO it is more
> > important than odd-limit.
>
> Did you see by response on Saturday to this contention?

Hmmm... I'd appreciate the link, that would make it easier.

> I have more up my sleeve, too. Why don't you elaborate on your
> views here with some examples?

Jeez, I'm involved in so many other projects now that I wouldn't
even know where to begin this one. Besides, I'm more interested
at this point in seeing what else is 'up your sleeve' than in
defending my own statements on this particular topic.

I'm trying hard to maintain an open viewpoint about the whole
business of prime vs. odd, affects, etc. etc.

I do believe that harmonic entropy is a very important new
addition to psychoacoustic theory, and only hope that some of
what I say helps propel the work into giving us a few answers.

> Monz, by this logic 13/11 and 143/128 have the same "ness."
> What meaning could that possibly have?

Right, Paul - these are exactly the ratios you asked me about
long ago when we debated the 'Hendrix Chord'. I was careful
to qualify my statement (which you quoted) with the subsequent
paragraph (which you didn't quote) that these perceptions only
seem to be valid in corroboration with the perception of
'tonalness', in other words, when there is a numerary nexus
common to all of the ratios being considered.

I can answer your question above with something you'll agree
with: there is no same 'ness' perceivable between 13/11 and
143/128. It only happens with low-integer ratios and with
a numerary nexus.

> > [me, monz]
> >
> > As I said in the post you quoted, I believe that somehow my
> > prime-factor lattice formula is tied into how we perceive harmony
> > and 'tonalness'.
>
> [Paul]
>
> ...I can't argue with Joe that this is a large extent -- that's
> why the definition of "limit" I wrote in the Dictionary has two
> parts -- "prime" and "odd" -- but I can't see any justification
> for systems that treat primes differently, whether it is to favor
> higher primes, or to weight against them (the Euler, Barlow, and
> Wilson complexity measures do the latter.

But what about the redundancy I mentioned, where composite ratios
occupy the points indicated by both their prime-limits and odd-
limits? Isn't that something superfluous, that would be better
eliminated from the lattice? (especially in my case, where I
analyze all sorts of historical tuning systems)

-monz
http://www.ixpres.com/interval/monzo/homepage.html

🔗Paul H. Erlich <PERLICH@ACADIAN-ASSET.COM>

Monz wrote,

>I was careful
>to qualify my statement (which you quoted) with the subsequent
>paragraph (which you didn't quote) that these perceptions only
>seem to be valid in corroboration with the perception of
>'tonalness', in other words, when there is a numerary nexus
>common to all of the ratios being considered.

Well then you're not really talking about ratios, but about positions on the
integer series; or, if you're using octave-equivalence, the odd series. As I
mentioned before, primality is relevant to these in a mathematical sense and
has no more or less applicability to them in this musical context.

>> ...I can't argue with Joe that this is a large extent -- that's
>> why the definition of "limit" I wrote in the Dictionary has two
>> parts -- "prime" and "odd" -- but I can't see any justification
>> for systems that treat primes differently, whether it is to favor
>> higher primes, or to weight against them (the Euler, Barlow, and
>> Wilson complexity measures do the latter.

>But what about the redundancy I mentioned, where composite ratios
>occupy the points indicated by both their prime-limits and odd-
>limits? Isn't that something superfluous, that would be better
>eliminated from the lattice? (especially in my case, where I
>analyze all sorts of historical tuning systems)

As you can see from my definition (perhaps you should look at it again), I
believe that when you are looking at tuning systems, prime-limit is clearly
much more relevant, for precisely the reason you mention.

🔗Joseph Pehrson <pehrson@pubmedia.com>

--- In tuning@egroups.com, Pierre Lamothe <plamothe@a...> wrote:

http://www.egroups.com/message/tuning/12967

>
> However, it's not really this resulting fine grain that worry me but
> discontinuity implied at higher (semiotic) level of
> sensibility/intelligibility articulation. We can distinct maybe
1800 pitch levels, but few tens of tones are used in music. I think
that this restriction is not well understood. Restriction on tones is
only a reflect of deeper restriction since acceptable values for one
tone form a continuous space.

Thank you very much, Pierre, for your response. J'entende! This is
an interesting point of view, and I will be interested in what Paul
Erlich responds to this, if he hasn't already... But, I'm not
certain that he has ever *insisted* on the presence of "continuity"
anyway...

>
> Pure sensitive approach with dissonance minima has only limited
validity domain that has to be contained. We have to take account
also of other parts of reality for musical perception understanding.
Musical listening is not a passive process but an active one that
implies not only sensation but pattern recognition,

D'accord!

> At end, I'm also curious of several other parts of reality :
impedance model in cochear fluids and estimation of delays giving
pressure difference acting on basilar membrane, neuronal coincidence
detectors as revealed in visual cortex, chaotic analyse, etc.
>

Alright! Sounds fascinating. Please continue. Don't forget to use
your new method of "summary" here with more detailed French web
pages... It will force a few of us to get our our French
dictionaries ... quelle dommage!

_____________ ____ __
Joseph Pehrson