Don't answer that. Your favorite numbers are now 1, 1.6, 2.5, 4, 6.3, 10, 16, 25, 40, 63, 100, ... because those are a Renard series of preferred numbers.
If you want to pick some numbers that are spaced about evenly on a log scale but don't have a lot of decimal places, Mr. Renard tells you which ones to pick. Or if you just need to pick a number at all, you might as well pick a Renard number.
ISO took this idea and made it a standard, as ISO 3.
The Wikipedia article is pretty thorough and starts out with two good examples:
- If some design constraints were assumed so that two screws in a gadget should be placed between 32 mm and 55 mm apart, the resulting length would be 40 mm, because 4 is in the R5 series of preferred numbers.
- If a set of nails with lengths between roughly 15 and 300 mm should be produced, then the application of the R5 series would lead to a product repertoire of 16 mm, 25 mm, 40 mm, 63 mm, 100 mm, 160 mm, and 250 mm long nails.
And then the third example on Wikipedia veers off into fantasyland:
- "If traditional English wine cask sizes had been metricated..." okay I'm gonna stop you there, because they weren't. You want a metric puncheon of wine to be 400 liters, but there is no such thing as a metric puncheon. Look I'm all for theorycrafting standards, I started a silly cohost page that verges on that sometimes, but maybe not on Wikipedia?
ISO vs IEC, fight!
I thought I'd seen this idea first when I took an electrical engineering class and learned about resistors only being available in specific values like 100 ohms, 150 ohms, 220 ohms... because a 200 ohm resistor would be within the margin of error of a 220 ohm resistor anyway.
Whoops, that's not the same series. That's the E series of preferred numbers, standardized by the IEC (International Electrotechnical Commission) before the ISO even existed.
I like to imagine this as a bitter rivalry between ISO and IEC:
- ISO: I'm thinking of a number between 60 and 70
- IEC: It's 62
- ISO: Shut the fuck up. It's 63
...but they're probably on pretty okay terms, and anyway they're doing slightly different things. ISO picks a series of 20 numbers (or 5, 10, or 40) where IEC picks 24 (or 6, 12, or 48).
I used this once
I've actually used the Renard series in software before, a couple of companies ago. If I remember the constraints:
- We were sub-licensing an API that got streams of topics from Twitter, back when there was value in that.
- When there were a lot of tweets in a topic, you could sub-sample: you could ask the API to give you back only, like, 2% of the tweets at random.
- But we didn't want to pay for a lot of streams. Each stream could combine multiple topics but had to have a single sampling rate.
So I made 11 streams that sampled at 1%, 1.6%, 2.5%, 4%, 6.3%, 10%, 16%, 25%, 40%, 63%, and 100%, and moved topics between them when necessary.
Ah, the standards of the night. What music they make!
I posted this earlier. The Renard series is not supposed to be a way of tuning a musical instrument. But it could be!
If you use the R40 series as numbers of hertz to tune to, you get a scale with 12 tones to the octave, just like the real chromatic scale! Except with some weird tuning choices that you wouldn't want. It turns out this works for the same reason we sometimes call 1024 bytes a "kilobyte".
