The film speed scale of the Sekonic L-398 family of exposure meters

[Doug Kerr]

[This has been edited to correct an error in the "purple boxes" portion of the table.]

The following table shows the assignment of film speed values to the "clicks" of the film scale dial, based on data in the manual for the L-398. I presume it also applies to the L-398A, whose manual does not have that information.

There are 34 "clicks" in the scale range, only every third one labeled on the dial.

The table is set up to reveal the interplay of the two schemes of values followed by this scale:

• If we move up by 3 steps, the speed value changes by a factor of 2.

• If we move up by 10 steps, the speed value changes by a factor of 10.

The columns at the right (with the colored boxes) show the recurrence of these to patterns. There are three patterns of the first type and 10 patterns of the second type (I only show the first 3 and the last one to save space.

Note that some early step values do not exactly follow the patterns, owing to rounding, and the last step does not quite fit either (that may be just an expedient to save space in the labeling).

Best regards,

Doug

 

[Doug Kerr]

I hasten to note that these niceties of the meter's sensitivity ("speed") dial are of no real consequence to our work, and are only of intellectual interest.

The "discrepancies" discussed here are minuscule, and are probably dwarfed by the actual error error of a given meter's calibration situation.

But it's what I do these days.

Best regards,

Doug

 

[Ted Cousins]

The following table shows the assignment of film speed values to the "clicks" of the film scale dial, based on data in the manual for the L-398. I presume it also applies to the L-398A, whose manual does not have that information.

View attachment 14435

There are 34 "clicks" in the scale range, only every third one labeled on the dial.

The table is set up to reveal the interplay of the two schemes of values followed by this scale:

• If we move up by 3 steps, the speed value changes by a factor of 2.

• If we move up by 10 steps, the speed value changes by a factor of 10.

Doug,

From a mathematical point of view, I must object. I don't agree that the click ratio can conveniently change between two different values** depending on the range or position of clicks, e.g. going from ISO 50 to ten clicks "up" gets you 504 rounded, not the implied exact 500.

** cube root of two
** tenth root of ten

best,

Ted.

Since my view is only mathematical, perhaps I stay out this thread ...

 

[Ted Cousins]

From a mathematical point of view, I must object. I don't agree that the click ratio can conveniently change between two different values depending on the range or position of clicks.

Trick question: On the L-398 (not A), what is the click ratio for the DIN scale? does it change depending on the number of clicks or is it always the cube root of two for each click?

 

[Doug Kerr]

Doug,

From a mathematical point of view, I must object. I don't agree that the click ratio can conveniently change between two different values** depending on the range or position of clicks, e.g. going from ISO 50 to ten clicks "up" gets you 504 rounded, not exactly 500.

** cube root of two
** tenth root of ten

It is only the ratio of the assigned values of the clicks (not all labeled) that follow those two different interval systems (interleaved).

I have shown in another recent post the construction of a list of numbers that clearly obey those two different interval systems. Do you find any fallacy or impossibility in that?

On the meter there are two different assigned value interval schemes, coexisting interleaved (which they can do for a series of not more than 30 values).

From the standpoint of the working of the slide rule, two adjacent clicks are always separated in their "effective" value by the 3rd root of two. But they are the bearers of labels that follow two different interval schemes (interleaved).

Of course this means that for many clicks, the assigned value departs from the effective value (albeit by only a small factor)

Best regards,

Doug

 

[Doug Kerr]

Hi, Ted,

Trick question: On the L-398 (not A), what is the click ratio for the DIN scale? does it change depending on the number of clicks or is it always the cube root of two for each click?

Almost certainly, as to the "effective" values (by which the slide rule works), the clicks on that scale are intended to be at an interval of the 3rd root of 2,, It also appears that the DIN assigned values (only every 3rd one labeled) are associated with successive such clicks. (I have to dig my L-398 out of storage to look at that to be sure.)

The sensitivity ("film speed") ratio between the sensitivity represented by consecutive DIN values (all integers) is by definition exactly the 10th root of 10.

But on the meter scale, a distance of 3 steps in the DIN labels is between clicks with a effective value ratio intended to be of 1:2.

Thus there is this a small progressive error in the relationship between the DIN labels and the effective values of the associated clicks. For an interval of 30 clicks, that error would be 1024/1000. [(2^10)/10^3)]

Best regards,

Doug

 

[Doug Kerr]

Hi Ted,

For convenience, here is the table that shows the development of a series of numbers that obeys both:

• Values separated by 3 positions have a ratio of exactly 2

• Values separated by 10 positions have a ratio of exactly 10

View attachment 14435

Do you find any fallacy in this?

Best regards,

Doug

 

[Doug Kerr]

Hi, Ted,

In pondering this matter, we must keep distinct two quite separate things:

(a) The "effective values" of the ticks on the scale., These are the values that theoretically are associated with the clicks (given the way that slide rules work).

(b) The values assigned by Sekonic to the clicks (only every third one being actually labeled on the scale).

The values in (a) are ideally uniformly separated by intervals of the 3rd root of 2.

The values in (b) have these two properties:

(c) The values assigned to clicks 3 clicks apart have a ratio of 1:2.

(d) The values assigned to clicks 10 clicks apart have a ratio of 1:10.

Strange as it might at first seem, I have demonstrated earlier that properties (c) and (d) can both be satisfied for a list of values not over 30 values long.

If we don't keep separate in our thoughts (a) and (b), certainly paradoxes seem to appear.

Best regards,

Doug

 

[Ted Cousins]

Hi Ted,

For convenience, here is the table that shows the development of a series of numbers that obeys both:

• Values separated by 3 positions have a ratio of exactly 2

• Values separated by 10 positions have a ratio of exactly 10

View attachment 14435

Do you find any fallacy in this?

Best regards,

Doug

Not now, Doug. I've just read in a credible reference that the DIN scale is indeed based on the 10th root of 10 just as you said, and consequently a change of three degrees does not exactly double or halve a sensitivity but is of course good enough for government work ...

... thank you for your patience,

Ted.

 

[Doug Kerr]

Hi, ted,

Not now, Doug. I've just read in a credible reference that the DIN scale is indeed based on the 10th root of 10 just as you said, and consequently a change of three degrees does not exactly double or halve a sensitivity but is of course good enough for government work ...

Indeed.

... thank you for your patience,

And thank you for yours.

Best regards,

Doug

 

[Doug Kerr]

Hi, Ted,

This table summarizes the various values involved with the film speed scale on the Sekonic L-398 exposure meter:

The column "Effective value - Value" is what we will assume is the intended effective value of each click (the value that affects its role in the working of the slide rule), based on the presumption that the value "100" (sown in bold) is in fact correct.

We presume that these effective values are intended to be uniformly separated by the ratio of the 3rd root of 2 (as shown in the "Ratio" column for those values).

The column "Assigned value - Value" gives the value "assigned" to each of the 34 clicks by Sekonic (as shown in the manual for the L-398). Only the ones shown in bold are actually "labeled" on the scale.

We see that the ratio between adjacent values in this list varies, in many cases being 1.25, in some cases 1.28, in a couple of cases 1.2, and in same cases 1.333_. The ratios for a few of the lower values are different from what we might expect because of the rounding that visit there.

We note that as to these assigned values follow the "3-2" and "10-10" guidelines discussed earlier. The few at the bottom and the topmost one depart. There is also a "bump" between 100 and 125, between 1000 and 1200 (the latter of which which, to follow the guidelines precisely, would have to be 1250 or 1280), and between 10000 and 12000. Keep in mind that these "preferred values" we chosen to be 'handy" values, which in some cases overrode the "3-2" and "10-10" guidelines.

At the far right we see how the assigned values differ from the "effective" values. For the most part, the "discrepancy" is not over 1%.

Best regards,

Doug