Re: replies to Ray Tomes by Paul Erlich

Paul H. Erlich [TD204.15]

>The current experimental and theoretical understanding of particle masses is
>embedded in the conceptual framework of Quantum Field Theory. In this
>theory, there is not only an uncertainty relation governing the positions
>and momenta of the particles, but also the very number of particles existing
>at a given point in time. I have not formally studied QFT, but I know that
>some of its predictions, such as the magnetic moment of the electron, are
>the most accurate (one part in 10^18) in all of science. You will have to
>come to terms with all its successes if you wish to propose a competing view
>of the universe. OK, that's enough particle physics for now.

I agree most strongly with the last sentence :-)
The values that agree so well are not exactly derived, they are
gradually honed in on by making many fine changes to the theory and as
such it cannot be said to be a single theory derivable from a single
axiom. In fact particle physics has dozens of axioms and fundamental
constants, a sure sign that it is not as fundamental as other branches
of physics.

The variations that you refer to as due to uncertainty are simply due to
the short lives of particles and every particle type has an exact
average value. It is these average values which are quoted by
physicists and which I am comparing as being nearly harmonically
related. I repeat that the similarities are just as great as the
similarities of the masses of isotopes.

>>If so, I suggest that this depends very strongly on the algorithm used
>>in the process. I dealt with some considerations in this regard a
>>couple of weeks ago and it is clear that slightly different algorithms
>>can jump to different notes under the same circumstances and introduce
>>ratios such as 80/81 etc.

>OK, but these jumps are quite foreign to any accepted performance practices,
>and many musical situations (such as the chord d-f-g-a-c in C major) could
>not be remedied by such jumps anyway -- the 80/81 must vanish.

The most obvious treatment of the chord d-f-g-a-c in C major is
20:24:27:30:36 which has the slightly ugly 20:27 which is what I assume
you refer to. In this case I think that it is the correct ratios and
see no reason why this must be tempered to get rid of the 80/81.

Conceivable something like 12:14:16:18:21 could be played and resolve
this problem, but if the piece in C then C is much more likely to want a
36 ratio than a 21 and this alternative simply makes a 63/64 wobble
instead of an 80/81 one.

>... What do you mean by "slight adjustements"? And how
>do you propose to physically account for the "undertones"? In steady-state
>oscillations, resonant cavities can do nothing more than selectively amplify
>frequencies already present. The question is how they get there in the first
>place.

The "slight adjustments" refers to the singers statements that he
produces the undertones by making only slight adjustments from the
position where there was only the fundamental. I am uncertain of the
physics but feel strongly that his description is much more consistent
with undertones than with hidden fundamentals and overtones.

A possible physics is that in a non-linear situation a subharmonic can
be driven by getting a kick by every second oscillation of the
fundamental. The subharmonic would require some tuning somewhere that
is approximately at half (or third or quarter) of the fundamental but it
need not be exact.

>I would argue that virtually every Western composer since the advent of the
>5-limit has been dealing not with the flat playing field you describe above,
>but a cylindrical one where the lattice bends back on itself so that
>commatic distinctions vanish.

You are probably right. I am glad that you wrote "western" because in
Indian music these difference notes are quite clearly found. IMO this
cylindrical thinking is wrong and results from giving the notes names
that are too limited. As I said elsewhere you would never play Db
instead of D so why should you play D- instead of D? The answer is only
because most people didn't realise that D- is a different note to D.

With regard to notation, if there is a convention on D and D+ etc
already in existence then I didn't mean to create confusion. I can see
good arguments for either of the notations given. The one that you gave
has a simpler layout whereas the one that I gave has all plain notes in
the key of C. The main thing is to be clear what we mean.

>Finding the correct place for "breaks" could
>certainly be handled as you describe, but would have nothing to do with
>anything that went on in the mind of the composer or in the actions of the
>finest performers of his/her music.

What goes on in the mind of the composer is not all conscious and
probably not describable in words at all. However it would be very
interesting to do some frequency analysis of the actual notes sung by
top performers in some of these cases so that we can see what actually
happens. Is there any information on this?

I am interested to know what you think they do?

>And again, there are cases where by your
>reckoning D and D- would have to occur at the same time, in a single
>sonority, so even "breaks" would not solve the problem.

I agree that two of these can occur in a single chord. I gave before an
example something like the ratios 4:7:12:18:42:63 where the lowest and
highest notes have the same name but are not the same note. The most
common cases of differences are 80/81, 63/64 (as above) and 35/36.

I see no problem in having such combinations if they are really required
by the music. It is certainly the case that music is so rich that there
are competing forces and ambiguities. Of course there are multiple ways
of resolving the tensions that are so created. Equitempered is one way.
Just Intonation with drift is another. JI with breaks at the weakest
points is another. Having a piece shift by half an octave is another,
though I certainly don't like the sound of it as a norm, and it doesn't
resolve all the problems anyway as you say.

My first preference is for breaks at the weakest points and my second
choice is the gradual drift (but I regard this as an easy way out and a
bit of a cop out). My opinion might well change when I became
acquainted with the actual top performance characteristics. What is not
clear to me Paul is what you are actually advocating?

-- Ray Tomes -- http://www.kcbbs.gen.nz/users/rtomes/rt-home.htm --
Cycles email list -- http://www.kcbbs.gen.nz/users/af/cyc.htm
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I wrote,

>>... What do you mean by "slight adjustements"? And how
>>do you propose to physically account for the "undertones"? In steady-state
>>oscillations, resonant cavities can do nothing more than selectively amplify
>>frequencies already present. The question is how they get there in the first
>>place.

Ray Tomes wrote,

>The "slight adjustments" refers to the singers statements that he
>produces the undertones by making only slight adjustments from the
>position where there was only the fundamental.

Yes! If you study chaos theory, you will see that at the bifurcation
points, a _sudden_ and _large_ shift in the oscillatory behavior
results from a very small change in the variable parameterizing the
nonlinearity of the system. So the "slight adjustments" are evidence
for, rather than against, my description of the phenomenon.

>I am uncertain of the
>physics but feel strongly that his description is much more consistent
>with undertones than with hidden fundamentals and overtones.

See above, and you still haven't given any kind of physical picture of
where your "undertones" could come from.

>A possible physics is that in a non-linear situation a subharmonic can
>be driven by getting a kick by every second oscillation of the
>fundamental.

Your thinking is not entirely on the wrong track but I think you'd
benefit greatly (and be delighted in the process) if you took the time to
study one of the references I posted or some other text on nonlinear
dynamical systems.

>The subharmonic would require some tuning somewhere that
>is approximately at half (or third or quarter) of the fundamental but it
>need not be exact.

What kind of process are you referring to as "tuning" here?

>>I would argue that virtually every Western composer since the advent of the
>>5-limit has been dealing not with the flat playing field you describe above,
>>but a cylindrical one where the lattice bends back on itself so that
>>commatic distinctions vanish.

>You are probably right. I am glad that you wrote "western" because in
>Indian music these difference notes are quite clearly found. IMO this
>cylindrical thinking is wrong

It is absurd to label the methods behind great work of art, let alone an
entire artistic tradition, "wrong". The quality of the work of art itself is
the only sensible criterion by which to judge the methods used to create it.
Unless you think you can write better music than Bach, Mozart, Chopin etc.,
calling cylindrical thinking "wrong" is wrong!

>With regard to notation, if there is a convention on D and D+ etc
>already in existence then I didn't mean to create confusion. I can see
>good arguments for either of the notations given. The one that you gave
>has a simpler layout whereas the one that I gave has all plain notes in
>the key of C.

I would disagree because the key of C has to have a good d-minor triad.
So at the very least the key of C has one commatic alteration in your/
Johnston's notation, while in the Helmholtz-Ellis/Wolf notation, there
would be four notes with a commatic alteration.

>What is notclear to me Paul is what you are actually advocating?

As I have stated before, I think most common-practice music sounds of
the Renaissance, Baroque, and early Classical eras sounds best in
something close to meantone temperament. The theorists of the time were
certainly in agreement with this viewpoint. In discussion with John
deLaubenfels I agreed that adaptively retuning the chords from meantone
most of the way toward JI (except for inherently tempered chords like
d-f-g-a-c) is ideal when the luxury of adaptive tuning is available,
but I showed that keeping the roots in meantone was preferable (in terms
of minimizing retune motion associated with commatic shifts) to his
proposal of using a centered shift relative to 12-tET so that the
simultaneities (again, excepting chords such as d-f-g-a-c) are as in JI.

However, much music of the late Classical and Romantic periods are founded
on 12-tET logic. Cycles of major thirds, diminished seventh chords as
modulational pivots, and other uses of enharmonic equivalence would make
something like deLaubenfels's proposal the closest you could get to putting
such music in JI. There the thinking is not cylindrical but toroidal.

Paul Erlich [TD208.11]

>Yes! If you study chaos theory, you will see that at the bifurcation
>points, a _sudden_ and _large_ shift in the oscillatory behavior
>results from a very small change in the variable parameterizing the
>nonlinearity of the system. So the "slight adjustments" are evidence
>for, rather than against, my description of the phenomenon.

But chaos bifurcation always introduces a higher frequency not a lower
one.

>See above, and you still haven't given any kind of physical picture of
>where your "undertones" could come from.

This is pure guesswork. It could be any resonances in the body and not
confined to sound resonances or cavities. It only requires an
approximate tuning and a non-linearity for the mechanism of each cycle
of the original frequency to be able to give a small kick to the
subharmonic (on each 2nd or 3rd cycle) to keep it synchronised.
For example it might be that as well as the resonance in cavities there
might be nerve paths that control muscles that are being affected.

>What kind of process are you referring to as "tuning" here?

I mean having a resonance of about the right frequency.

R Tomes
>>IMO this cylindrical thinking is wrong

>It is absurd to label the methods behind great work of art, let alone an
>entire artistic tradition, "wrong".

OK, call it excessively limiting then.

>The quality of the work of art itself is
>the only sensible criterion by which to judge the methods used to create it.
>Unless you think you can write better music than Bach, Mozart, Chopin etc.,
>calling cylindrical thinking "wrong" is wrong!

I certainly cannot. However I do not accept that the above gentleman
where limited to cylindrical thinking. They clearly demonstrated that
they understood the meanings of D and D- and D+ even if they did not use
that notation.

>As I have stated before, I think most common-practice music sounds of
>the Renaissance, Baroque, and early Classical eras sounds best in
>something close to meantone temperament. The theorists of the time were
>certainly in agreement with this viewpoint. In discussion with John
>deLaubenfels I agreed that adaptively retuning the chords from meantone
>most of the way toward JI (except for inherently tempered chords like
>d-f-g-a-c) is ideal when the luxury of adaptive tuning is available,
>but I showed that keeping the roots in meantone was preferable (in terms
>of minimizing retune motion associated with commatic shifts) to his
>proposal of using a centered shift relative to 12-tET so that the
>simultaneities (again, excepting chords such as d-f-g-a-c) are as in JI.

OK, thanks for that description. Our differences are not as great as
might at first have appeared. However I would still favour as near to
JI as possible. Perhaps we are just disagreeing about what is possible.

Would you agree that some classical music has chords that are not far
apart (in time) that use D and D- for example? Would you further agree
that there are cases where these should be played as JI D and D-?

>... There the thinking is not cylindrical but toroidal.

If one goes far enough down the 12-tet path then such things are
possible. I am looking at a different path and thought that you were
also, so in that case we just accept that someone else is using a
different framework.

-- Ray Tomes -- http://www.kcbbs.gen.nz/users/rtomes/rt-home.htm --
Cycles email list -- http://www.kcbbs.gen.nz/users/af/cyc.htm
Alexandria eGroup list -- http://www.kcbbs.gen.nz/users/af/alex.htm
Boundaries of Science http://www.kcbbs.gen.nz/users/af/scienceb.htm

> >Yes! If you study chaos theory, you will see that at the bifurcation
> >points, a _sudden_ and _large_ shift in the oscillatory behavior
> >results from a very small change in the variable parameterizing the
> >nonlinearity of the system. So the "slight adjustments" are evidence
> >for, rather than against, my description of the phenomenon.
>
> But chaos bifurcation always introduces a higher frequency not a lower
> one.

Quite the contrary! Bifurcation introduces a frequency half the original one.

> >See above, and you still haven't given any kind of physical picture of
> >where your "undertones" could come from.
>
> This is pure guesswork. It could be any resonances in the body and not
> confined to sound resonances or cavities. It only requires an
> approximate tuning and a non-linearity for the mechanism of each cycle
> of the original frequency to be able to give a small kick to the
> subharmonic (on each 2nd or 3rd cycle) to keep it synchronised.

That's quite what I've been saying, and what chaos theory explains.

> For example it might be that as well as the resonance in cavities there
> might be nerve paths that control muscles that are being affected.
>
> >What kind of process are you referring to as "tuning" here?
>
> I mean having a resonance of about the right frequency.

OK, well I don't think that's necessary (or even possible in the case of the super low notes), but it couldn't hurt.

> R Tomes
> >>IMO this cylindrical thinking is wrong
>
> >It is absurd to label the methods behind great work of art, let alone an
> >entire artistic tradition, "wrong".
>
> OK, call it excessively limiting then.

As Gary Morrison likes to point out, limits are the greatest aid to artistic cohesiveness.

> >The quality of the work of art itself is
> >the only sensible criterion by which to judge the methods used to create it.
> >Unless you think you can write better music than Bach, Mozart, Chopin etc.,
> >calling cylindrical thinking "wrong" is wrong!
>
> I certainly cannot. However I do not accept that the above gentleman
> where limited to cylindrical thinking. They clearly demonstrated that
> they understood the meanings of D and D- and D+ even if they did not use
> that notation.

Their music clearly demonstrates that they wished to represent these meanings with a single pitch.

> >As I have stated before, I think most common-practice music sounds of
> >the Renaissance, Baroque, and early Classical eras sounds best in
> >something close to meantone temperament. The theorists of the time were
> >certainly in agreement with this viewpoint. In discussion with John
> >deLaubenfels I agreed that adaptively retuning the chords from meantone
> >most of the way toward JI (except for inherently tempered chords like
> >d-f-g-a-c) is ideal when the luxury of adaptive tuning is available,
> >but I showed that keeping the roots in meantone was preferable (in terms
> >of minimizing retune motion associated with commatic shifts) to his
> >proposal of using a centered shift relative to 12-tET so that the
> >simultaneities (again, excepting chords such as d-f-g-a-c) are as in JI.
>
> OK, thanks for that description. Our differences are not as great as
> might at first have appeared. However I would still favour as near to
> JI as possible. Perhaps we are just disagreeing about what is possible.

John deLaubenfels and I only advocate JI in simultaneities (vertical JI), not in horizontal motion.

> Would you agree that some classical music has chords that are not far
> apart (in time) that use D and D- for example? Would you further agree
> that there are cases where these should be played as JI D and D-?

In the adaptive retuning schemes that John deLaubenfels and I discussed, there are many possible tunings of the note D, which tend to differ by considerably less than a syntonic comma.

> >... There the thinking is not cylindrical but toroidal.
>
> If one goes far enough down the 12-tet path then such things are
> possible. I am looking at a different path and thought that you were
> also, so in that case we just accept that someone else is using a
> different framework.

Yes -- but we can still argue over what frameworks are most appropriate for existing works of music. As for me, the path suggested by my paper would be toroidal thinking embedded in 4-d space (since you need an extra dimension for the ratios of 7).