I was completely wrong!

[Doug Kerr]

In several threads here over the past couple of weeks, I have been fairly emphatic that there could be sequences of numbers that would obey both of these "rules" for a substantial number of values:

• If we go from one value to one 3 values further in the list, the value would change by exactly 2.

• If we go from one value to one 10 values further in the list, the value would change by exactly 10.

Fellow member Ted Cousins has challenged the validity of this.

Upon further study of this matter I realize that this is not so.

It turns out that in one table of values I constructed by a certain algorithm, those rules were not both scrupulously followed, but I had been too careless in my examination of the result to note that.

My apologies to those who might have been misled by this, and especially to Ted.

Best regards,

Doug

 

[Doug Kerr]

Here is an example of a sequence that can exist, the sequence of "preferred values" for reporting the ISO speed of a digital camera:

We note that in fact here every two values separated by 10 steps have a ratio of 10 in value.

But while most pairs of values separated by 3 steps have a value ratio of 2, not all such pairs do. Notable"bumps" in that ideal pattern are:

• 64-80-100-125 (125 is of course not exactly 2 times 64.)

• 640-800-1000-1250 (1250 is of course not exactly 2 times 640.)

Best regards,

Doug

 

[Ted Cousins]

Here is an example of a sequence that can exist, the sequence of "preferred values" for reporting the ISO speed of a digital camera:
View attachment 14446
We note that in fact here every two values separated by 10 steps have a ratio of 10 in value.

But while most pairs of values separated by 3 steps have a value ratio of 2, not all such pairs do. Notable"bumps" in that ideal pattern are:

• 64-80-100-125 (125 is of course not exactly 2 times 64.)

• 640-800-1000-1250 (1250 is of course not exactly 2 times 640.)

Best regards,

Doug

Looks familiar - I posted this a while ago:

https://kronometric.org/phot/exp/ISO%20speed%20latitude.gif

any sequence with "bumps" in it is not a geometric progression. Thanks, I.S.O.

best,

Ted.

 

[Ted Cousins]

Looks familiar - I posted this a while ago:

https://kronometric.org/phot/exp/ISO%20speed%20latitude.gif

The mapping ranges above:

Let's look at how the standard derives the exact range of 90 to 111 for ISO 100:

• Ideal Center (\(S_{\text{exact}}\)): 100.00
• Theoretical Lower Bound: \(\frac{100}{1.12246} = 89.090\)
• Theoretical Upper Bound: 100 × 1.12246 = 112.246

To ensure continuity across the index table without gaps, the standard maps the integer ranges as follows:

• The Floor: The lower boundary is rounded up to the nearest integer: 89.090 → 90.
• The Ceiling: The upper boundary defines where the next range starts. Since the next range (ISO 125) theoretically starts at 125.99 / 1.12246 = 112.246, its integer floor is rounded up to 112. Therefore, the ISO 100 range ends exactly one integer prior at 111.

I've just read that the ISO "rounding" is based upon a Renard series

Renard series - Wikipedia

en.wikipedia.org

The least rounded values in the R10 series look highly familiar 100, 125, 160, 200 ... ho ho

Nowhere near as simple as I thought, Doug!

best,

Ted.

 

[Doug Kerr]

Hi, Ted,

Thanks for that follow-up.

******

Now that I have realized that my "unicorn" cannot exist, I return to an actual list in use, the list of "reportable" ISO speed values for a digital camera given in ISO 12232.

This table shows that list along with an analysis of the inter-value ratios of interest. Note that I have taken the liberty of changing the value "12" to "12.5" (which it would presumably have been but for rounding to integers). This avoids the appearance of a number of "unseemly" ratios.

The column "Ratio - 3" shows, for each value, its ratio to the value three steps earlier. The column "Ratio - 10" shows, for each value, its ratio to the value 10 steps earlier. (Some values were too early to have one or both of these ratios.)

We see that the whole list obeys one of the "unicorn" rules: every value is 10 times the value 10 steps earlier. (All ratios are shown with all their significant figures)

For most of the list, it also obeys the other "unicorn" rule: every value is 2 times the value 3 steps earlier.

But we see that there are two of the 3-step intervals that don't do the latter: the interval from 64 to 125, and the interval from 640 to 1250. (For these intervals, the fist value is highlighted in yellow, and the second in pink.)

We can imagine that the developers of this list had in mind a "unicorn" progression, but of course could not do that completely. They seemingly took advantage of the need to put a couple of "bumps" in their list of values to keep the values in the list "tidy".

Best regards,

Doug

 

[Doug Kerr]

Now, for the sake of completeness, I show the ratio analysis for the "assigned" values of the 34 clicks in the speed scale of the Sekonic L-398 exposure meter (these probably apply to the L-398M and L-398A as well).

The scheme of ratio analysis is the same as I used earlier.

The values shown in bold are the only ones actually "labeled" on the scale.

Again I have taken the liberty of "unrounding" values 1 and 4 for the same reason as before.

I have highlighted all values that do not fit the "unicorn rues" (and the irregular ratio involved) in pink.

We see that the "bumps" here are slightly different than in the ISO 12232 list shown earlier.

Best regards,

Doug

 

[Ted Cousins]

I've just read that the ISO "rounding" is based upon a Renard series

Renard series - Wikipedia

en.wikipedia.org

The least rounded values in the R10 series look highly familiar 100, 125, 160, 200

And this looks familiar too:

Each of the Renard sequences can be reduced to a subset by taking every nth value in a series, which is designated by adding the number n after a slash. For example, "R10″/3 (1…1000)" designates a series consisting of every third value in the R″10 series from 1 to 1000, that is, 1, 2, 4, 8, 15, 30, 60, 120, 250, 500, 1000.

[looks just like shutter speeds on our Sekonics]

 

[Doug Kerr]

Hi, Ted,

Thnaks for that. Very interesting and relevant. I was not aware of that.

I became aware of the different preferred value system used, for example, for resistor values, many years ago. It has today been well codified, and the value sequences are identified by "E" numbers. Resistors with a 20% tolerance, which I would mostly use in electronics projects( I could, and still mostly can, read the color codes for these "at sight"), follow what is today called the "E6" series. The "6" means that it has 6 values per decade, such as:

10, 15, 22, 33, 47, 68 (and then 100, 150, 220, 330, 470, 680, etc.

The system is based on a logarithmic theoretical concept, but with rounding done according to various rules. In the E6 series, the theoretical values progress, as we might expects, in the ratio of 6th root of 10. The theoretical value for the "15" step is about 14.678

Thanks again for the scoop on the Renard system.

Best regards,

Doug

 

[Doug Kerr]

i see that the preferred values for f-numbers at intervals of 1 stop, 1/2 stop, and 1/3 stop are all the same as or (for some early ones) rounded from subsets of the Renard R40 list.

Neat-O!

Best regards,

Doug

 

[Doug Kerr]

Hi, Ted,

Interesting that the theoretical Renard lists are all based on a span of 10 in the value. But every 6th value in the theoretical R40 list rounds nicely to our standard f-number list, ahead by exactly 1 stop for each 12 steps.

Best regards,

Doug

 

[Ted Cousins]

i see that the preferred values for f-numbers at intervals of 1 stop, 1/2 stop, and 1/3 stop are all the same as or (for some early ones) rounded from subsets of the Renard R40 list.

Neat-O!

Best regards,

Doug

As to f/numbers, I imagine that it is likely that matches would be found in the Renard R40 list, bearing in mind that it is based on the 40th root of 10, is it not?

I rather like the most-rounded R''20 list on the right of the Wiki table where every value seems to be a good match to photographic values with no gaps ...

... BUT, Google AI insists that the photographic f/number single-stop sequence is firmly based on the square root of two and not any sequence involving roots of ten. However, it is often said that AI can be wrong:- although in this case, I tend to agree.

best,

Ted.

 

[Doug Kerr]

I am hampered in this by not having yet found the official ISO lists of preferred shouter speed and aperture values. I am working for the moment from the list of available settings for the Canon EOS 3 camera, taken from the manual for same.
******
I think there is little justification for saying that the list of preferred values for aperture is derived from a Renard series. But one can make a case that they are drawn from the Renard R40 series (40 steps per decade), the values rounded in various ways.

We do see the "shadow of 10" in that two assigned values in the 1/3-stop series are f/1 and f/10 (those being 20 steps apart, that spanning a Renard R40 series "decade").

I have an Excel spreadsheet that lays this out. I would be glad to send it via email.

Best regards,

Doug

 

[Doug Kerr]

I do note that in the Canon 1/2 stop and 1/3 stop aperture value series, if we start with f/1, then every 2 stops the assigned value exactly doubles. But is we start on a "between full stops" value, the assigned values do not exactly double in an interval of one stop. This is of course an artifact of the "rounding" chosen here.

Best regards,

Doug

 

[Ted Cousins]

I think there is little justification for saying that the list of preferred values for aperture is derived from a Renard series.

Hi, Doug,

Here is a LibreOffice Renard spreadsheet downloaded from AI showing R5, R10, R20 rounded per ISO and the deviation caused thereby, then uploaded to my website:

https://kronometric.org/phot/temp/renard_series_values(1).ods

ISO rounding for preferred numbers

• Preferred Numbers: For standardized product sizing or nominal values rather than test data, ISO uses the Renard Series (geometric progression steps like R5, R10, R20) defined in standards like ISO 3 and ISO 497.

In the R20 sequence, do notice the every-third values 1, 1.4, 2.8, 4, 5.6, 8 which look rather familiar ...

Little justification ?

best,

Ted

 

[Ted Cousins]

I don't know what "Official ISO Standard Value" means. Is this from some IOS standard codifying the Renard sequences? Or is this a list of "preferred" aperture f-numbers from some IOS photographic standard?

ISO rounding for preferred numbers

• Preferred Numbers: For standardized product sizing or nominal values rather than test data, ISO uses the Renard Series (geometric progression steps like R5, R10, R20) defined in standards like ISO 3 and ISO 497.

Observe how I.S.O. likes to render information as abstrusely as possible:

https://cdn.standards.iteh.ai/samples/4548/eea948d9047b4a82b62a7ed459f7eaa4/ISO-497-1973.pdf

Scroll down to see the Renard stuff ...

The table for Renard values is a jewel but it does show intermediate values for different degrees of rounding ...

 

[Doug Kerr]

Hi, Ted,

Hi, Doug,

Here is a LibreOffice Renard spreadsheet downloaded from AI showing R5, R10, R20 rounded per ISO and the deviation caused thereby, then uploaded to my website:

https://kronometric.org/phot/temp/renard_series_values(1).ods

Thanks. Very useful.

I don't know what "Official ISO Standard Value" means. Is this from some IOS standard codifying the Renard sequences? Or is this a list of "preferred" aperture f-numbers from some IOS photographic standard?

In the R20 sequence, do notice the every-third values 1, 1.4, 2.8, 4, 5.6, 8 which look rather familiar ...

May not be a coincidence. Those might in fact be the list of ISO photographic aperture values, not part of any standard codifying the Renard series for various uses.

Little justification ?

You are probably right.

Best regards,

Doug

 

[Ted Cousins]

Those might in fact be the list of ISO photographic aperture values, not part of any standard codifying the Renard series for various uses.

As shown earlier, ISO 497-1973 codifies the Renard series in a table.

https://cdn.standards.iteh.ai/samples/4548/eea948d9047b4a82b62a7ed459f7eaa4/ISO-497-1973.pdf

ISO-517 codifies f/numbers without stating a basis:

https://cdn.standards.iteh.ai/samples/50089/796cb13d68a648b386176d3fe20c1323/ISO-517-2008.pdf

The standard series of f-number marking shall be as follows:
0,5 – 0,7 – 1 (or 1,0) – 1,4 – 2 – 2,8 – 4 – 5,6 – 8 – 11 – 16 – 22 – 32 – 45 – 64 – 90 – 128

ISO 3 shows Renard series without mentioning the name "Renard"

https://cdn.standards.iteh.ai/samples/3564/b371a39798db4f9fbd40f09ca0b7d71d/SIST-ISO-3-1995.pdf

best,

Ted.

 

[Doug Kerr]

Hi, Ted,

Aha! Preferred values seemingly based on the Renard series are in ISO 3. I do not have all of it, but I do have the table of preferred values.

The "R20" list in that table is in fact (in part):

1.00, 1.12, 1.25, 1.40, 1.60, 1.80, 2.00. 2.24, 2.50, 2.80, etc.

For comparison, here is a parallel list of values from the Canon EOS 3 list for 1/3 stop increments:

1.0, 1.1, 1.2, 1.4, 1.6, 1.8, 2.0, 2.2, 2.5, 2.8, etc.

So indeed that appears to be the Renard series further rounded, seemingly, as you mentioned earlier, following the "most rounded" form of the R20 sequence shown in the Wikipedia article.

(I can't tell if that is presented in part of ISO 3 I don't have).

All interesting,

Best regards,

Doug

 

[Doug Kerr]

Hi, Ted,

It is interesting that for shutter speed and sensitivity, values at an interval of 1/2 stop cannot all be directly derived from values in the Renard R20 series. They must come from every 3rd value in the Renard R40 series.

Values of time and sensitivity at an interval of 1/2 stop can come from the R20 series (every value) (or every other value in the R40 series).

Values of aperture, time, and sensitivity at 1/3 stop intervals can be based on the Renard R20 series.

The difference of course is that with respect to aperture, the photographic exposure is (inversely proportional to the square of the f-number.

Are we having fun yet?

Best regards,

Doug

 

[Ted Cousins]

Hi, Ted,

It is interesting that for shutter speed and sensitivity, values at an interval of 1/2 stop cannot all be directly derived from values in the Renard R20 series. They must come from every 3rd value in the Renard R40 series.

Yes, I did notice that.

Are we having fun yet?

I looked up your E6 resistor preferred values:

Example: The E6 Series

The E6 series divides each decade into 6 logarithmic steps (N = 6) and is typically used for components with a ± 20% tolerance.The math steps: \(10^{\frac{0}{6}} = 1.00\), \(10^{\frac{1}{6}} = 1.47\), \(10^{\frac{2}{6}} = 2.15\), \(10^{\frac{3}{6}} = 3.16\), \(10^{\frac{4}{6}} = 4.64\), \(10^{\frac{5}{6}} = 6.81\).

Rounded standard values:1.0, 1.5, 2.2, 3.3, 4.7, and 6.8.

https://www.electronics-tutorials.ws/resources/standard-resistor-values.html

I assume that you can decode the math ... too much trouble to turn it into UniCode!

Notice the use of roots of ten and number of steps designated as N

best,

Ted.

 

[Ted Cousins]

I assume that you can decode the math ... too much trouble to turn it into UniCode!

On-line app for that:

unicodeit.net

 

[Doug Kerr]

Hi, Ted,

On-line app for that:

unicodeit.net

Thanks.

Best regards,

Doug