uoficowboy
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However, this formula only seems to work for E48 and E96 and 191/192 E192 values. Specifically - 10^(185/192) = 9.19479. So rounding to two decimal points gives you 9.19. But In every E192 table I see I see this listed as 920. What's the deal here?
I don't know the original source, but the Wikipedia explanation (in the German article) that it's an intentional rounding to achieve a more uniform series sounds very plausible.Honestly I do not know but I guess it is a genetic error that has propagated for so long that little can be done now. Only thing we can safely do is to speculate!
I don't know the original source, but the Wikipedia explanation (in the German article) that it's an intentional rounding to achieve a more uniform series sounds very plausible.
Sure it does, the E192 series is 9.09, 9.20, 9.31, better than individually rounded 9.09. 9.19, 9.31
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The empirical rounding rule applied in this case is that the increment shouldn't vary more than 1 digit between adjacent steps.
Might be, believe it or not. I see no harm in turning to this or the other explanation.These values were calculated in the 1940s without modern electronic calculators--a rounding error was made in one of them.
Each series "E-n" is considered as the logarithmically equidistant distribution of "n" values within the whole scale from 1 to 10. Perhaps a more convenient approach would be to plot a continuous curve with the expected value, and see if that specific value of the E-series standard is closer to which other neighbor value of the expected curve - on a log scale - to make a visual check to see if the rounding makes sense on that scale.
Believe it or not.
The applied rounding is obviously implementing a local (differential) rather than global (integral) uniformity rule. Although the chosen value has a larger distance to expected value 9.1948, it lays nearer to the geometrical center of preceding 9.09 and succeeding 9.31.
What's your answer to the question I asked you: Then what is the empirical rounding rule in the E48 series? The increment in that series is sometimes 1, sometimes 2 and one time it's 3. What rule is that?
A possible rule: Rounded geometric series + the inclement has to be monotonous. 9.19 would be the only violation.
Might be, believe it or not. I see no harm in turning to this or the other explanation.
No open questions, I think.
A possible explanation, (it is not accurate in mathematics) is that you take the first value (1 in this case), multiply by the geometrical progression factor (10^(1/192)=1.012064831) to get the next number, round it off and repeat. AND this will be simpler in your excel!!
Perhaps you will get better agreement.
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I always thought that the 1-2-5 sequence we see on many instruments is THE E3 SERIES.
(and I am still learning)
When calculating the E192 series just test for the value 9.19 and replace it with 9.20--problem solved
I can't see any general rule on that at all, as mentioned above, the decision to round based only on an assumption does not explain whether there is a mathematical reason or not. Until an overall analysis is done on the correct (logarithmic) scale, we will be in an endless debate.
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