Digital BW, The Print

Roy,

Once again I salute your logic and agree. I think one of the nice things you
learn when you first use a view camera is that there are no clicks or
detents for the f-stops. On my Nikor and Copal shutters I can set the
aperture anywhere I want between the limits of fully open to it's minimum or
anywhere in-between. The variable of aperture size is scale-less until we
chose to impose one for the sake of convenience.

The variable, be it volume or density or aperture size, is not controlled by
the scale we hold up to it.

"Discernible difference" is completely unrelated to the number of tones,
volumes, etc. available.

Martin


----- Original Message -----
From: "royvharrington" <roy@...>
To: <DigitalBlackandWhiteThePrint@yahoogroups.com>
Sent: Wednesday, April 10, 2002 6:22 PM
Subject: [Digital BW] Ongoing Saga - a brief interlude


>
> Austin et al,
>
> I don't know if you are listening to me any more but I'll try.
> Here's a light hearted attempt.  Maybe it'll be amusing enough
> to bother reading and ease the tension.
>
> Briefly, I'd like to get really simple -- let's get away from
> DyR and talk about elementary school rulers.  Dumb question:
> How many inches in a 12 inch ruler?  12.   How do you know?
> (12 inches/1 inch) = 12 steps.  How many quarter inches in the
> same ruler?  48 = (12 / (1/4)).  How many inches in a 36 inch
> yard stick?  36.   blah blah blah.  This so obvious that its
> painful. --- please no more examples!
>
> This is approximately what you've been feeling in some of the
> posts.  Close maybe?
>
> Austin:  this is so obvious why are we talking about it.
> Roy:  I know, I know, but... I have a different ruler ...
> Austin:  no, no,  who cares if its metric or time or anything
>      just take the last number (12) by the first number (1)
>      and you'll know how many units.  it always works.
> Roy:  Well it works a lot of the time, but what about ...
> Austin: come on, really, this is idiotic.
> Roy:  Well I've a couple of rulers that're different. Can
>       I tell you about them?
> Austin: (you'll have to supply this one!)
>
> Roy: This ruler I have goes from 1 to 16.
> Austin: Great (16/1) = 16. It must have 16 steps.
>
> Roy: Well I only see 8 even marks on it, but maybe they just
>      missed every other one.
>
> Austin: Yep.
>
> Roy: Hey, I have another that also goes from 1 to 16,
>     but it only has 4 steps.
>
> Austin:  Jees, Why don't you just go buy some decent rulers.
>     Or at least add the marks they left out and just
>     relabel them with all the numbers.  it'll be good as new.
>     its so simple: 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16
>
> Roy:  Well, I sure like these rulers, I've used them for
>     years and they've always worked perfectly.  Maybe
>     I'll start with cleaning them up and polishing.
>
> Austin: Great. Go for it.
>
> Roy: Hey, guess what that first ruler actually goes all
>      the way to 32 now.  Cool, clear  from 1 to 32.
>
> Austin: Well that sounds a lot longer. How the heck did
>      you miss the whole other half of the ruler?
>
> Roy: I didn't miss half!  It's just a little longer than
>      I thought.  In fact there's only 2 more marks on it.
>      So its 10 marks long not the 8 marks I thought it was.
>
> Austin:  This is getting nuttier and nuttier.  How are you
>      ever going to get all 32 marks you need on that
>      dumb ruler.  Buy a new one.
>
> Roy:  Well I'm going to clean some more and see if there's
>       any more stuff written under all this gunk.
>
> Austin:  You're wasting your time.
>
> Roy:  Well its really starting to look good now.  In fact
>       it turns out that there really are numbers on all
>       the marks.  But, they sure don't look like we
>       expected.  Here's what's written on the marks:
>
>       1, 1.4, 2, 2.8, 4, 5.6, 8, 11, 16, 22, 32.
>       Boy, it sure is good I didn't put those other
>       numbers on it.  It would have confused things royally.
>
>       My other ruler goes: 1, 2, 4, 8, 16
>       Its a lot shorter, they didn't bother with the
>       intermediate numbers.
>
> ----------------------------
>
> Well obviously the rulers are on my lens,  The first one
> is the aperture ring and the second one is the shutter
> speed.  I wanted to illustate how different an exponential
> series is from a linear series.  Linear is so natural to
> our thinking many of its properties just seem universal.
> Any kid can answer the questions in my first paragraph
> without any deep thought.  Exponential series on the
> other hand are very non-intuitive.
>
> Quick Question: How many stops are between f5.6 and f64?
> Ask experienced photographers who've known the series for years.
> How many know the answer instantly?
> How many can calculate stops = 2*log2(f1/f2) in their head?
> How many are reduced to kindergarten counting on fingers?
> See my point.  It is not intuitive.
>
> Going back to my two "rulers", we know that the aperture
> scale is a series of equivalent intervals.  They don't
> really "look" equivalent but they sure work that way.
> Similarly, the intervals of the shutter speed series are
> all equivalent. In going from 1 to 16 there are 8 intervals
> on the aperture scale but only 4 intervals on the shutter
> scale.  Are the intervals bigger on the shutters?  No,
> as photographers we all know that intervals on both scales are
> also equivalent to each other.  I.e. every interval = one stop.
>
> Notice that the end points of 1 and 16 tell us nothing
> about how many steps there are.  For the same overall
> ratio of (16/1) we come up with two different numbers of
> steps even when we've used the same "photographic" sense
> of one step = one stop.  Actually could also have tick
> marks on the lens for fractional stops, giving more
> possible "number of steps" values.
>
>
> Mathematically, within an exponential series a ratio
> of any two elements only gives you a relative measure
> of "how far apart they are" not any sense of "how much
> stuff (how many elements) are between them".
>
> The identical analogy in a linear series would be subtracting
> two elements.  Using the ruler, I can say 5 - 3 = 2 inch
> interval tells me nothing about how many tick marks there
> are in the 2 inches.
>
> ------------------------------------------
>
> The DynRange formula is always based on a ratio of two
> measured values.  The formula doesn't "care" which kind
> of underlying scale is used for the two values.
> But the meaning of the underlying scale effects the
> meaning of the ratio which finally effects the meaning
> of DynRange.
>
> You've stated quite a few times that the "meaning" of
> DynRange is number of steps. I entirely agree if the
> underlying scale means something as a linear scale.
> But I think the meaning of DynRange loses that connotation
> when applied to a scale whose meaning is only as an
> exponential scale.
>
> Kind of dense wordage so here's an example.
> I consider the fstop scale exponential; but is that really
> builtin?  After all its based on a measuring the aperture
> size in mm and the focal length in mm.  What if it wasn't?
> How about a lens that had: f1,f2,f3,f4,f5,f6,f7...f16.
> It wouldn't be very useful because photographically
> the intervals would all be different sizes.  So if
> you were to apply DynRange the "meaning" of the
> results would have no notion of "number of steps".
>
> --------------------------------------
>
> So going way back.  I think the DynRange formula for
> sound is fairly well documented and agreed on.  Its based
> on the ratio of power levels delivered to sounds waves and
> to our ears.  The power scale must be exponential to
> give an evenly spaced perception of sound.  Therefore
> the DynRange of that sound has no notion of number of
> sounds levels.  In a much earlier post I showed my analogies
> from sound to light and all the same scaling existed
> in light as well as sound.  So I keep coming to the
> conclusion that number of gray tones in a print can't
> be a property measured by DynRange.
>
>
> Roy
>
>
>
>
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