Precisely anything can never be achieved by any means whatever

While I was looking up that tuning list thread starting with
/tuning/topicId_29654.html#29654
I noticed something I don't think I ever responded to.

Me:
I think JIS is a better term than RI [for intervals like 64:81]
because it allows that these intervals may have a tolerance too, and
don't have to be precisely rational (which can only be achieved by
extraordinary digital means in any case).

Gene:
Precisely anything can never be achieved by any means whatever.

Translation by Bob Wendell:
Nothing can be achieved with total precision no matter what means are
chosen in the attempt.

I suppose I agree with this. But what about those electronic musical
instruments, such as George Secor's Scalatron, where the frequencies
are all obtained by digital frequency division (counting of pulse
edges) from a single master oscillator. Do we not then have strictly
rational relationships between all the notes, so long as the
instrument is functioning correctly?

I suppose we have to consider the possibilty that thermal or other
noise will eventually cause a miscount somewhere, but I expect one
could be built so that, had it been put into operation soon after the
big bang, we would expect no such error to have occurred by now.

So, even if they are not precisely rational, they are so many orders
of magnitude closer to it, that they need to be distinguished from
other instruments that do not guarantee phase-locking even when
functioning correctly.

--- In tuning-math@yahoogroups.com, "Dave Keenan" <d.keenan@b...>
wrote:
>
> I suppose we have to consider the possibilty that thermal or other
> noise will eventually cause a miscount somewhere, but I expect one
> could be built so that, had it been put into operation soon after
the
> big bang, we would expect no such error to have occurred by now.
>
> So, even if they are not precisely rational, they are so many orders
> of magnitude closer to it, that they need to be distinguished from
> other instruments that do not guarantee phase-locking even when
> functioning correctly.

Hmm, I did not follow that thread, but: do we need to refer to the big
bang? The limitation of human hearing should be enough to make the
qestion whether "precisely rational" or not meaningless, isn't it?

Hans Straub

--- In tuning-math@yahoogroups.com, "hstraub64" <straub@d...> wrote:
> Hmm, I did not follow that thread, but: do we need to refer to the big
> bang? The limitation of human hearing should be enough to make the
> qestion whether "precisely rational" or not meaningless, isn't it?
>
> Hans Straub

I have no doubt that it's psychoacoustically or perceptually
meaningless. And indeed one can go further and show that it's
immeasurable unless over infinite time. This was more a question of
philosophy, in particular epistememology, and as such I suppose it is
off topic. But the question is "Can we know that two frequencies are
in a precise ratio N:M by knowing that the mechanism that produces
them does it by counting every Nth pulse in one case and every Mth in
the other, of a single master frequency source?"

--- In tuning-math@yahoogroups.com, "hstraub64" <straub@d...> wrote:
> --- In tuning-math@yahoogroups.com, "Dave Keenan" <d.keenan@b...>
> wrote:
> >
> > I suppose we have to consider the possibilty that thermal or other
> > noise will eventually cause a miscount somewhere, but I expect one
> > could be built so that, had it been put into operation soon after
> the
> > big bang, we would expect no such error to have occurred by now.

> Hmm, I did not follow that thread, but: do we need to refer to the
big
> bang? The limitation of human hearing should be enough to make the
> qestion whether "precisely rational" or not meaningless, isn't it?

Certainly if human hearing is the point it will. However even if you
are counting events, there is no way to make the events you count
precisely of the same duration--for quantum uncertainty reasons at
least, if no other.

> I have no doubt that it's psychoacoustically or perceptually
> meaningless. And indeed one can go further and show that it's
> immeasurable unless over infinite time. This was more a
question of
> philosophy, in particular epistememology, and as such I
suppose it is
> off topic. But the question is "Can we know that two
frequencies are
> in a precise ratio N:M by knowing that the mechanism that
produces
> them does it by counting every Nth pulse in one case and every
Mth in
> the other, of a single master frequency source?"

We don't need infinite time to show that we can't measure the
true values. The true value of anything measured can never be
known, which is why metrology deals heavily with statistical error
calculation.

Aaron

--- In tuning-math@yahoogroups.com, "pitchcolor" <pitchcolor@a...> wrote:
> We don't need infinite time to show that we can't measure the
> true values. The true value of anything measured can never be
> known, which is why metrology deals heavily with statistical error
> calculation.

OK. Skip the infinite-time thing. But what about the ratio thing?
Surely _counting_ can be considered precise, assuming the counting
mechanism is not faulty, since it only needs whole numbers.

--- In tuning-math@yahoogroups.com, "Dave Keenan" <d.keenan@b...>
wrote:

> OK. Skip the infinite-time thing. But what about the ratio thing?
> Surely _counting_ can be considered precise, assuming the counting
> mechanism is not faulty, since it only needs whole numbers.

But what you are counting is not absolutely precise, so it doesn't
matter.