Darkroom arithmetic for f-stop working.

[fidget]

I'm making an attempt to work in "f-stops" rather than simply seconds.

This has already simplified my workflow, apart from my test strips which suffer from a failure in arithmetic as I wrestle with elementary arithmetic on the fly......

It goes like this, start at say, 8s, add 1/2 stop (half of 8) = 12s, add 1/2 stop (half of 12) = 18, add 1/2 stop (half of 18) = 27s, add 1/2 stop (half of 27) = 40s.

So, in half stops, it progresses 8,12,18,27,40.
But wait! That can't be right,
it must at least go 8,x,16,y,32.

What has happened here. I seem to have two half stops adding up to one and one eighth
Not such a disaster for my test strips, but had me puzzled for a while.....

I guess that I shouldn't be compounding the initial half stop in my sums....

Now, where's that pension forecast, better to make sure that they DO compound my dwindling funds......

Dave..

[Shadowplay]

It depends on what you're looking to make your exposure relevant to.

If you are basing it all off of 8s, then you need to keep your half-stops relevant to 8s, so 8,12,16,20,24,28,32.

If you're basing it off of your latest exposure and want to add a half stop, then you had it right. But this would (one would think) require you to evaluate each individual print after making it, rather than "bracketing" and just making a bunch of prints at once. So, 8s - evaluate and add a half stop to this exposure = 12s. 12s - evaluate and add a half stop to this exposure = 18s. 18s - evaluate and add a half stop to this exposure = 27s. So on and so forth. Provided I understand the question, I suppose .

Comprende mi amigo?

eta a bit of clarity

[fidget]

Yes, you have it right (but your sequence is off). A start of 8s is just an example. In terms of incremental changes to a given exposure, it must be valid.
In doing this for test exposures, it simply gives and exposure time in seconds that happened to yield the best strip. So I guess that what the increments were doesn't matter. More a little amusement that I didn't see why my "counting" didn't follow plan.

The prints were fine, BTW, and the test strips are pretty good too...

[Rob Hale]

Hi fidget

Surely thirds and half for 8 secs would be :-

10.08

11.31

12.70

16.00

I think you are looking at a log 2 calculation.

Best Regards

Rob

[vdonovan]

I've started working in stops too and it definitely is worth the trouble.

Regarding stop math, I have a degree in physics so you'd think I could do the math in my head, but I cheat. I printed out the stop timing table from darkroomagic.com. I just look on there to get the number of seconds for each increment. After a while they stick in your head.

[pau3]

If you want half stops, you should multiply each time by 1.4 (roughly, square root
of 2). If you start by 8, you will get: 8, 11, 16, 22, 32, 45 (I'm rounding off). You can
think that each time is 40% longer than the previous one. If you want fouth stops,
you should increase your time 20% (roughly speaking): 8, 9.5, 11, 13.5, 16, 19, 22,...

Best,
Pau

[titrisol]

That is why I love the Kodak Exposure Aid pie
It comes in 1/2 stops as follows:
2-3-4-6-8-12-16-24-32-48-60 s

[Justin Low]

Originally Posted by pau3

If you want half stops, you should multiply each time by 1.4 (roughly, square root
of 2). If you start by 8, you will get: 8, 11, 16, 22, 32, 45 (I'm rounding off).

I use this scale too, and my mnemonic is the aperture scale on my lenses. 2, 2.8, 4, 5.6, 8...

However, I once tried to figure it out: on a lens, 2 to 2.8 is one stop, and 4 to 8 is two stops, yet on paper, 2 to 2.8 is half a stop, and 4 to 8 is only one stop...

[Chris101]

This used to be de rigueur but now even has a name: reciprocity. Well, I guess that was always the name, due to the reciprocal/square root relationship between the opening diameter of the lens, and the shutter speed.

[oftheherd]

Maybe I misunderstand what the OP was after, but I think some are confusing the names of f/stops with what they are supposed to do. Each incremental stop lets in twice or half as much light as the next/previous one. So, as I think everyone knows, f/2.8 lets in twice as much light as f/2, and 1/2 as much light as f/4. Don't forget that the number is a fraction related to the maximum lens diameter. So f/stops are actually 1/1.4, 1/2, 1/2.8, 1/4, etc.

Shutter speeds do the same. 1/125 lets in twice as much light as 1/250.

The refresher being over, you were correct that 1/2 more than 8 seconds is 8 plus 8/2 which is 12. Just as 1/2 more than 1/125 would be 1/125 plus 1/62.5 or 1/187.5 which a stepless shutter would give you, but you could not acheive on a camera with increments that double or halve exposures mechanically. You were in effect becoming the shutter by changing the number of seconds

The way we acheive aperture values aside, the values are to give us 1/2 more or less light. Shutter speeds do the same. That gives us reciprocity, where a change in shutter speed to let in half as much light, and the f/stop to let in twice as much light gives us the same amount of light. That is what you were seeking by going from 8 sec to 12 sec.

Reciprocity failure is a characteristic of film at very high or low speeds, when reciprocity doesn't give us the effect we seek. The film doesn't react correctly to acheive reciprocity and we have to compensate.

[Rob Hale]

Hi Dave,
I had this carefully explained to me using all log functions, you may prefer something with less logs in it.
Here is a slightly fuller explanation which can be used with calculator which has the log function, using this you can chart out test strips etc. or make a spread sheet.

Log 2 = .30103
Divided by 1/2s, 1/3s, 1/4s, 1/6s, which ever you need.
Anti log ( usually a function change key and 10x ).
Multiply by “start time”
So for 8 seconds “start time” for plus f 2/3s.
Log 2 = .30103
.30103 / 3 * 2 = .200686
anti log = 1.5874
multiplied by start time of 8 secs = 12.699 secs.

So if you wanted to make up a set of strip test times based on start time of 8 secs.for say a Patterson 5 strip test print easel, in 1/3 f stops.
Strip 1 would be 8 secs exposure
Strip 2 = ((((.30103 / 3 ) anti log ) * 8) – 8) = 2.08 ( or 2.1 ) secs exposure ( now has a total exposure of 8 secs plus 2.1 ).
Strip 3 = ((((.30103 / 3 * 2) anti log ) * 8) – 8) = 4.699 ( or 4.7 ) secs exposure ( now has a total exposure of 8 secs plus 2.1 plus 4.7 ).
Strip 4 = ((((.30103 ) anti log ) * 8) – 8) = 8 exposure (now has a total exposure of 14.8 secs )
Strip 5 = ((((.30103 ) + (.30103 / 3 ) anti log ) * 8) – 8) = 12.1 secs exposure ( exposure of 26.95 secs or 30 secs )
You can of course rearrange these to suit your self.

If you have sorted out the log 2 calc ignore this lot !

Best Regards Rob

[fidget]

Hi all, and thanks for the explanations.
Please don't misunderstand my original post, it was meant to show how easily I am confused, a sort of amusing story.
I have no problem in producing my test strips, I simply recognised that the way I was calculating (which I believe to be correct for what I was trying to achieve) didn't line up with the standard doubling of the time to double the exposure.

This anomaly is simply due to my working in half stop intervals and being mildly surprised to find that they did not agree with the same arithmetic applied to whole stops.

Thanks for the technical detail, some of which appears to be a sort of hybrid based on aperture ratios, which of course has no bearing on time. I guess that we all have our own way of calculating our time increments for test strips.



Dave....